From crose Tue Sep 9 09:59:34 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02118; Tue, 9 Sep 97 09:59:33 EDT Date: Tue, 9 Sep 97 09:59:33 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709091359.AA02118@MOGLI.rutgers.edu> To: 330_501 Subject: problem set 1 Cc: crose@MOGLI.rutgers.edu Status: RO You should be able to do problem set 1 after today's class. If you'd like the TA to look at it the due date is 9/16/97. No late submissions allowed. Cheers, Chris Rose From efy@ccrl.nj.nec.com Tue Sep 9 10:22:25 1997 Return-Path: Received: from overdrive.ccrl.nj.nec.com by MOGLI.rutgers.edu (4.1/25-eef) id AA02229; Tue, 9 Sep 97 10:22:23 EDT Received: by overdrive.ccrl.nj.nec.com (4.1/YDL1.9-920708.13) id AB17290(overdrive.ccrl.nj.nec.com); Tue, 9 Sep 97 09:30:56 EDT From: efy@ccrl.nj.nec.com (Eldar F. Yuzbashev) Received: by sovok (4.1/CNC-Client) id AA04099; Tue, 9 Sep 97 09:30:54 EDT Date: Tue, 9 Sep 97 09:30:54 EDT Message-Id: <9709091330.AA04099@sovok> To: crose@MOGLI.rutgers.edu Subject: Re: problem set 1 Reply-To: eldar@ece.rutgers.edu Status: RO > From crose@MOGLI.rutgers.edu Tue Sep 9 09:01:14 1997 > Date: Tue, 9 Sep 97 09:59:33 EDT > From: Christopher Rose > To: 330_501@MOGLI.rutgers.edu > Subject: problem set 1 > Cc: crose@MOGLI.rutgers.edu > The clock on your computer may not be set correctly. Compare the times in the 1st and 2nd lines of the headers above. -- Eldar Yuzbashev From brajesh@caip.rutgers.edu Tue Sep 9 18:08:52 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA02704; Tue, 9 Sep 97 18:08:52 EDT Received: from caipfs.rutgers.edu (root@caipfs.rutgers.edu [128.6.19.100]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id RAA15240 for ; Tue, 9 Sep 1997 17:13:23 -0400 Received: from gorkon.rutgers.edu (gorkon.rutgers.edu [128.6.155.16]) by caipfs.rutgers.edu (8.8.5/8.8.5) with ESMTP id RAA20945 for ; Tue, 9 Sep 1997 17:17:28 -0400 (EDT) Received: (brajesh@localhost) by gorkon.rutgers.edu (8.7.6/8.6.9) id RAA13516 for crose@ece; Tue, 9 Sep 1997 17:17:27 -0400 (EDT) From: "Rajesh Balchandran" Message-Id: <9709091717.ZM13514@gorkon.rutgers.edu> Date: Tue, 9 Sep 1997 17:17:27 -0400 X-Mailer: Z-Mail (3.2.0 06sep94) To: crose@ece.rutgers.edu Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Dear Prof. Rose, I was having some confusion about causality of a system and a causal signal. I have seen many books say that 'a signal is causal if it is zero for all t < 0'. Is this a definition or is it in way related to the causality of a system - which says that an output y(t) does not depend on any input applied after t. Please clarify. Thanks, Rajesh -- From crose Tue Sep 9 20:52:02 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02798; Tue, 9 Sep 97 20:52:01 EDT Date: Tue, 9 Sep 97 20:52:01 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709100052.AA02798@MOGLI.rutgers.edu> To: brajesh@caip.rutgers.edu Subject: Hi Cc: crose@MOGLI.rutgers.edu Status: RO A causal system cannot "react" before an input is applied. So for a linear system, it's impulse response has to lie to the right of the origin (non-negative time values). A causal signal is a signal which is nonzero only for non-negative values of it's argument. Cheers, Chris Rose From crose Tue Sep 9 21:26:37 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02834; Tue, 9 Sep 97 21:26:36 EDT Date: Tue, 9 Sep 97 21:26:36 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709100126.AA02834@MOGLI.rutgers.edu> To: 330_501 Subject: froebenius Status: RO HEY FOLKS!!!! Sorry I had to rush today, but we need to get this stuff out of the way so we can actually play with some systems. At this rate, I figure the exam will cover not too much more than chapter 1 and maybe some of chapter 2. NEWS FLASHES! 1) YUP, ELDAR IS RIGHT! Eldar claimed that the K_2 bounding value for a linear matrix mapping (y = Ax+f) is the froebenius norm and I was unsure. Well, Eldar is right! K_2, the bound for the rho_2 norm for a linear mapping (matrix A) is exactly the Froebenius norm. It's in your book and I forgot. You can also find it in some linear systems books but not all (for example, see Brad Dickinson's nice little book on Systems) I've used froebenius theory (peron-froebenius) for various things, but I've never used the f-norm directly in my work, at least that I can remember now :) In any case, you can file that factoid away for a rainy day. Also, you should cross file it with POSITIVE MATRIX THEORY which is where froebenius theory pops up a lot (see Karlin/Taylor A first course in stochastic processes... very useful for discrete time markov models which are usually built on non-negative matrices) 2) AND the MORE IMPORTANT NEWS ABOUT BOUNDEDNESS and CONTINUITY: I think it may have looked like we proved the wrong thing in haste!!!!! Bounded -> continuous but continuous DOES NOT IMPLY BOUNDED. Our proof went as follows. a) assume bounded b) show that when bounded, IF x_n -> x* THEN A(x_n) -> A(x*) which means that A() is a continuous mapping. This is what we showed. we did NOT SHOW bounded -> continuous (because it's NOT TRUE!!!!) Think about A(x) = x^2 on [0, inf) and the |x-y| norm. |N-(N+epsilon)| = epsilon > 0, but | N^2 - (N+epsilon)^| = 2*epsilon*N + epsilon^2 which is UNBOUNDED IN N. So for any fixed value of K we can always find an N such that |A(N)-A(N+espilon)| > K*epsilon and violates boundedness! 3) Iliya, as for having to prove that all we can find all cauchy sequences... I'm now not at all sure what you meant. Why exactly did you think we needed to prove that one could find all the sequences which converge to x*????? Cheers ALL, Chris Rose From crose Tue Sep 9 23:23:37 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02957; Tue, 9 Sep 97 23:23:36 EDT Date: Tue, 9 Sep 97 23:23:36 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709100323.AA02957@MOGLI.rutgers.edu> To: matei@caip.rutgers.edu Subject: Re: froebenius Cc: crose@MOGLI.rutgers.edu Status: RO BOGDAN! Why did you not correct me!?!?!?!?!? I'm sorry to have munged your name! I'll remember next time. Yup, svd is more stable, though I've no ideas about the vagaries of the video coding business. Have used it a number of times (numerically as opposed to algorithm development). As for rho_inf, you're right on the money. As you take p-> inf the largest difference dominates (for a finite element vector at least) and then you just take its p_th root! So yes, Minkowski with p->in is the rho_inf norm! Good homework or quiz problem :) Cheers, Chris Rose From ilija@research.att.com Wed Sep 10 09:58:13 1997 Return-Path: Received: from ns.research.att.com by MOGLI.rutgers.edu (4.1/25-eef) id AA03312; Wed, 10 Sep 97 09:58:12 EDT Received: from research.att.com ([135.205.32.20]) by ns; Wed Sep 10 09:05:03 EDT 1997 Received: from hermes.research.att.com ([135.207.16.38]) by research; Wed Sep 10 09:02:36 EDT 1997 Received: from carp.research.att.com (carp [135.207.16.86]) by hermes.research.att.com (8.8.5/8.8.5) with ESMTP id JAA21517; Wed, 10 Sep 1997 09:02:34 -0400 (EDT) Received: from carp (localhost.research.att.com [127.0.0.1]) by carp.research.att.com (8.8.5/8.8.4) with SMTP id JAA19353; Wed, 10 Sep 1997 09:02:35 -0400 (EDT) Sender: ilija@research.att.com Message-Id: <34169A6B.6956@research.att.com> Date: Wed, 10 Sep 1997 09:02:35 -0400 From: Ilija Zeljkovic Organization: AT&T X-Mailer: Mozilla 3.0 (X11; I; IRIX 6.3 IP32) Mime-Version: 1.0 To: Christopher Rose Cc: 330_501@MOGLI.rutgers.edu Subject: Re: froebenius References: <9709100126.AA02834@MOGLI.rutgers.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Christopher Rose wrote: > > HEY FOLKS!!!! > > Sorry I had to rush today, but we need to get this stuff out of the > way so we can actually play with some systems. At this rate, I figure > the exam will cover not too much more than chapter 1 and maybe some of > chapter 2. > > NEWS FLASHES! > > 1) YUP, ELDAR IS RIGHT! Eldar claimed that the K_2 bounding value for > a linear matrix mapping (y = Ax+f) is the froebenius norm and I was > unsure. Well, Eldar is right! K_2, the bound for the rho_2 norm for > a linear mapping (matrix A) is exactly the Froebenius norm. It's in > your book and I forgot. You can also find it in some linear systems > books but not all (for example, see Brad Dickinson's nice little book > on Systems) > > I've used froebenius theory (peron-froebenius) for various things, but > I've never used the f-norm directly in my work, at least that I can > remember now :) > > In any case, you can file that factoid away for a rainy day. Also, > you should cross file it with POSITIVE MATRIX THEORY which is where > froebenius theory pops up a lot (see Karlin/Taylor A first course in > stochastic processes... very useful for discrete time markov models > which are usually built on non-negative matrices) > 3) Iliya, as for having to prove that all we can find all cauchy > sequences... I'm now not at all sure what you meant. Why exactly did > you think we needed to prove that one could find all the sequences > which converge to x*????? > > Cheers ALL, > > Chris Rose A: My question was much simpler and based on: 1) We proved that if {x_n} -> x^*, n->oo , then {x_n} is a Chauchy sequence. 2) In Bounding proof we assumed that for any x^* there is {x_n} -> x^* ;it is Cauchy, from 1) My Q was: Do we have to prove that for any x^* it exist (at least one) Cauchy sequence that converges to it (x^*)? Maybe it is trivial? Ilija Zeljkovic From crose Wed Sep 10 12:30:31 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA03455; Wed, 10 Sep 97 12:30:30 EDT Date: Wed, 10 Sep 97 12:30:30 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709101630.AA03455@MOGLI.rutgers.edu> To: crose@MOGLI.rutgers.edu, ilija@research.att.com Subject: Re: froebenius Cc: 330_501@MOGLI.rutgers.edu Status: RO Hi Ilija, There is at least one always ---> just the limit point repeated over and over. But the bounding proof was a little different. We assume the mapping is bounded and want to know whether it's continuous too. The condition for continuity is the sequence convergence stuff implying convergence of the mapping. So the short answer is no, we don't have to find Cauchy sequences around each point. We assume they are given and that we only want to determine whether the mapping in continuous (which is what you assume when checking for continuity) Hope that helps... let's keep the email lines open. I enjoy this sort of colloquy immensely (and student onlookers oftern enjoy it too :) Cheers, Chris Rose From crose Thu Sep 11 21:17:16 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02680; Thu, 11 Sep 97 21:17:15 EDT Date: Thu, 11 Sep 97 21:17:15 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709120117.AA02680@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: mailing list Status: RO Hi Folks, This is the latest test of the mailing list! 1) 501 FOLK: Good class (for me... had fun). I"m going to have to do less proving and more lecturing... but I know I won't :) In any case, read up through the linear algebra stuff on matrix norms and onward to functions of matrices I'd like to get through chapter 1 by (AT THE LATEST) the end of next week. It's tough going, but it's useful as a thinking organizer 2) 543 FOLK: At Zhou Lin's suggestion I'm going to go over the TDM switch example (framining and "diagonal" discovery) again next class just ot make sure it stuck. Start reading chapter 3. I think we'll fly through it since most of the proofs are reasonably easy. Cheers, Chris Rose From chriskly@er4.rutgers.edu Mon Sep 15 15:35:22 1997 Return-Path: Received: from er4.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA07069; Mon, 15 Sep 97 15:35:21 EDT Received: (from chriskly@localhost) by er4.rutgers.edu (8.8.5/8.8.5) id OAA26594; Mon, 15 Sep 1997 14:42:56 -0400 (EDT) Date: Mon, 15 Sep 97 14:42:56 EDT From: Christine Kleiwerda To: Joseph Papa Cc: "'330_543@mogli.rutgers.edu'" <330_543@MOGLI.rutgers.edu> Subject: Re: Commuting partner In-Reply-To: Your message of Mon, 15 Sep 1997 11:47:52 -0400 Message-Id: Status: RO > Hey class, > > I was wondering if there is anyone that lives/works in Monmouth county = > taking this course. I live in Middletown, and it would be nice to have = > a commuter(s) to carpool. > > Please send me email or give me a call if you're interested. > > Joe > j.papa@ieee.org > 732 495-1740 > Hi! I work in Middletown, so if you ever want a ride TO class, I'd lovet eh company. Unfortunately, fortunately, I live in New Brunswick, so getting you home could be a bit of a problem. (You might get stuck on busch and end up sleeping in Hill Ctr...) Anyhow, if you can come up with a ride home, i wouldnt mind driving you to class (every class or once in a while) Christine From crose Tue Sep 16 16:18:32 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA08594; Tue, 16 Sep 97 16:18:31 EDT Date: Tue, 16 Sep 97 16:18:31 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709162018.AA08594@MOGLI.rutgers.edu> To: minfan@paul.rutgers.edu Subject: Re: Office hour for the TA Cc: 330_501, 330_543 Status: RO ************* Could you please tell me what is the office hour for the TA? I have lots of questions which I can figure out my self. Thanks. ********************* Hi, Have you tried posting your questions to the mailing list yet? That's the first thing to do. Also, to which course do you refer (501 or 543). Cheers, Chris Rose From crose Tue Sep 16 16:27:17 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA08635; Tue, 16 Sep 97 16:27:16 EDT Date: Tue, 16 Sep 97 16:27:16 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709162027.AA08635@MOGLI.rutgers.edu> To: 330_501 Subject: problem set 2 Cc: crose@MOGLI.rutgers.edu Status: RO Hi Folks, You'll want to start on problem set 2 soon. The test will cover all of chapter 1 and a bit of chapter 2. Let's set the due date for the problem set as a week from today (9/23). Reminder: test on tueday 9/30 in class (and period afterward as well). NO CLASS Thursday 9/25. Cheers, Chris Rose From crose Thu Sep 18 02:26:58 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA11135; Thu, 18 Sep 97 02:26:58 EDT Date: Thu, 18 Sep 97 02:26:58 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709180626.AA11135@MOGLI.rutgers.edu> To: 330_501 Subject: archive of email Status: RO Hey Folks, There is an archive of all email snt by the class on this address (330_543) linked to the web page. It's in text form (just a copy of my save file for class correspondence). Cheers Chris Rose From crose Thu Sep 18 02:28:27 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA11140; Thu, 18 Sep 97 02:28:26 EDT Date: Thu, 18 Sep 97 02:28:26 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709180628.AA11140@MOGLI.rutgers.edu> To: 330_501 Subject: whoops! Status: RO That should have read 330_501 (not 330_543). Same basic message to both classes and I forgot to change the email number. YOu're also welcome to check out the email archive on 330_543 if you'd like :) From crose Sat Sep 20 19:49:17 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AB02276; Sat, 20 Sep 97 19:48:39 EDT Date: Sat, 20 Sep 97 19:48:39 EDT From: Mail Delivery Subsystem Full-Name: Mail Delivery Subsystem Message-Id: <9709202348.AB02276@MOGLI.rutgers.edu> Subject: Returned mail: User unknown To: crose Status: RO ----- Transcript of session follows ----- 550 /usr/crose/system/501: line 2: utgers.edu... User unknown 550 crose@mogli.r... Host unknown 550 log... User unknown ----- Unsent message follows ----- Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02274; Sat, 20 Sep 97 19:48:39 EDT Date: Sat, 20 Sep 97 19:48:39 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709202348.AA02274@MOGLI.rutgers.edu> To: 330_501 >From cripop@ece.rutgers.edu Sat Sep 20 17:49:33 1997 Return-Path: Received: from zen.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA02185; Sat, 20 Sep 97 17:49:32 EDT Received: from chess.rutgers.edu (chess.rutgers.edu [128.6.46.113]) by zen.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id QAA02602 for ; Sat, 20 Sep 1997 16:52:18 -0400 From: Dimitrie Popescu Message-Id: <199709202052.QAA02602@zen.rutgers.edu> Subject: mailing list error To: crose@ece.rutgers.edu Date: Sat, 20 Sep 1997 16:46:48 -0400 (EDT) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 2992 Status: R Dear dr. Rose, I have tried to send the following message to the 330_501 mailing list (330_501@mogli.rutgers.edu) but it has been returned twice with the same error message "User unknown". Did I do something wrong? Also, maybe you can post the following message to the mailing list. Otilia Popescu PS. I receive messages from 330_501@mogli.rutgers.edu, but I haven't been able to send any messages. >From Postmaster Fri Sep 19 12:43:15 1997 Received: from localhost (localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with internal id MAA10603; Fri, 19 Sep 1997 12:43:15 -0400 Date: Fri, 19 Sep 1997 12:43:15 -0400 From: Mail Delivery Subsystem Subject: Returned mail: User unknown Message-Id: <199709191643.MAA10603@ece.rutgers.edu> To: cripop MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="MAA10603.874687395/ece.rutgers.edu" Status: RO This is a MIME-encapsulated message --MAA10603.874687395/ece.rutgers.edu The original message was received at Fri, 19 Sep 1997 12:43:13 -0400 from cripop@localhost ----- The following addresses had delivery problems ----- 330_501@mogli.rutgers.edu (unrecoverable error) ----- Transcript of session follows ----- ... while talking to mogli.rutgers.edu.: >>> RCPT To:<330_501@mogli.rutgers.edu> <<< 550 /usr/crose/system/501: line 2: utgers.edu... User unknown 550 330_501@mogli.rutgers.edu... User unknown ----- Original message follows ----- --MAA10603.874687395/ece.rutgers.edu Content-Type: message/rfc822 Return-Path: cripop Received: (from cripop@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) id MAA10602 for 330_501@mogli.rutgers.edu; Fri, 19 Sep 1997 12:43:13 -0400 Date: Fri, 19 Sep 1997 12:43:13 -0400 From: Dimitrie Popescu Message-Id: <199709191643.MAA10602@ece.rutgers.edu> To: 330_501@mogli.rutgers.edu Subject: Cayley-Hamilton Theorem Content-Length: 1048 This is a proof of the Cayley-Hamilton Theorem in the general case. No assumption is made about matrix A; just that is a square matrix of dimension nxn. Let us denote the characteristic polynomial of A: Phi(s)=det(sI-A)=s^n+a_1s^(n-1)+...+a_n Let us also take the inverse of sI-A: (sI-A)^(-1)=(sI-A)*/det(sI-A)=B(s)/Phi(s) where (sI-A)*=B(s) is the adjoint matrix of sI-A. Rewrite the above relation as: Phi(s)I_n=(sI-A)B(s) because the highest power of s in Phi(s) is n, then the highest power of s in B(s) will be n-1. B(s) can be written as: B(s)=B_0s^(n-1)+B_1s(n-2)+...+B_(n-1) After performing the multiplication and identifying coefficients we get: s^n: I=B_0 s^(n-1): a_1I=B_1-AB_0 s^(n-2): a_2I=B_2-AB_1 ........ s^1: a_(n-1)I=B_(n-1)-AB_(n-2) s^0: a_nI= -AB_(n-1) These relations are equivalent with: B_0=I B_1=A+a_1I B_2=A^2+Aa_1+a_2I ......... B_(n-1)=A^(n-1)+A^(n-2)a_1+...+a_(n-1)I 0 =A^n+A^(n-1)a_1+...+Aa_(n-1)+a_nI The last relation is in fact Phi(A)=0 and the proof is completed. Otilia Popescu --MAA10603.874687395/ece.rutgers.edu-- From cripop@ece.rutgers.edu Sat Sep 20 17:49:33 1997 Return-Path: Received: from zen.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA02185; Sat, 20 Sep 97 17:49:32 EDT Received: from chess.rutgers.edu (chess.rutgers.edu [128.6.46.113]) by zen.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id QAA02602 for ; Sat, 20 Sep 1997 16:52:18 -0400 From: Dimitrie Popescu Message-Id: <199709202052.QAA02602@zen.rutgers.edu> Subject: mailing list error To: crose@ece.rutgers.edu Date: Sat, 20 Sep 1997 16:46:48 -0400 (EDT) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 2992 Status: RO Dear dr. Rose, I have tried to send the following message to the 330_501 mailing list (330_501@mogli.rutgers.edu) but it has been returned twice with the same error message "User unknown". Did I do something wrong? Also, maybe you can post the following message to the mailing list. Otilia Popescu PS. I receive messages from 330_501@mogli.rutgers.edu, but I haven't been able to send any messages. >From Postmaster Fri Sep 19 12:43:15 1997 Received: from localhost (localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with internal id MAA10603; Fri, 19 Sep 1997 12:43:15 -0400 Date: Fri, 19 Sep 1997 12:43:15 -0400 From: Mail Delivery Subsystem Subject: Returned mail: User unknown Message-Id: <199709191643.MAA10603@ece.rutgers.edu> To: cripop MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="MAA10603.874687395/ece.rutgers.edu" Status: RO This is a MIME-encapsulated message --MAA10603.874687395/ece.rutgers.edu The original message was received at Fri, 19 Sep 1997 12:43:13 -0400 from cripop@localhost ----- The following addresses had delivery problems ----- 330_501@mogli.rutgers.edu (unrecoverable error) ----- Transcript of session follows ----- ... while talking to mogli.rutgers.edu.: >>> RCPT To:<330_501@mogli.rutgers.edu> <<< 550 /usr/crose/system/501: line 2: utgers.edu... User unknown 550 330_501@mogli.rutgers.edu... User unknown ----- Original message follows ----- --MAA10603.874687395/ece.rutgers.edu Content-Type: message/rfc822 Return-Path: cripop Received: (from cripop@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) id MAA10602 for 330_501@mogli.rutgers.edu; Fri, 19 Sep 1997 12:43:13 -0400 Date: Fri, 19 Sep 1997 12:43:13 -0400 From: Dimitrie Popescu Message-Id: <199709191643.MAA10602@ece.rutgers.edu> To: 330_501@mogli.rutgers.edu Subject: Cayley-Hamilton Theorem Content-Length: 1048 This is a proof of the Cayley-Hamilton Theorem in the general case. No assumption is made about matrix A; just that is a square matrix of dimension nxn. Let us denote the characteristic polynomial of A: Phi(s)=det(sI-A)=s^n+a_1s^(n-1)+...+a_n Let us also take the inverse of sI-A: (sI-A)^(-1)=(sI-A)*/det(sI-A)=B(s)/Phi(s) where (sI-A)*=B(s) is the adjoint matrix of sI-A. Rewrite the above relation as: Phi(s)I_n=(sI-A)B(s) because the highest power of s in Phi(s) is n, then the highest power of s in B(s) will be n-1. B(s) can be written as: B(s)=B_0s^(n-1)+B_1s(n-2)+...+B_(n-1) After performing the multiplication and identifying coefficients we get: s^n: I=B_0 s^(n-1): a_1I=B_1-AB_0 s^(n-2): a_2I=B_2-AB_1 ........ s^1: a_(n-1)I=B_(n-1)-AB_(n-2) s^0: a_nI= -AB_(n-1) These relations are equivalent with: B_0=I B_1=A+a_1I B_2=A^2+Aa_1+a_2I ......... B_(n-1)=A^(n-1)+A^(n-2)a_1+...+a_(n-1)I 0 =A^n+A^(n-1)a_1+...+Aa_(n-1)+a_nI The last relation is in fact Phi(A)=0 and the proof is completed. Otilia Popescu --MAA10603.874687395/ece.rutgers.edu-- From crose Sat Sep 20 20:07:29 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02430; Sat, 20 Sep 97 20:06:57 EDT Date: Sat, 20 Sep 97 20:06:57 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709210006.AA02430@MOGLI.rutgers.edu> To: 330_501 Subject: problem with mailing list Cc: crose@MOGLI.rutgers.edu Status: RO Hi Folks, We had a problem with the mailing list. if you've posed anything in the past few days (from about thursday night onward, please repost (that means YOU Otilia :) Cheers, Chris Rose From crose Sat Sep 20 20:30:31 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA02444; Sat, 20 Sep 97 20:30:30 EDT Date: Sat, 20 Sep 97 20:30:30 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709210030.AA02444@MOGLI.rutgers.edu> To: cripop@ece.rutgers.edu, crose@ece.rutgers.edu Subject: Re: mailing list error Cc: crose@MOGLI.rutgers.edu Status: RO Otilia, Thanks for the proof. To be complete, you need to specify that when you take the inverse of (sI-A) that you make sure s is not an eigenvalue of A so that inverse exists. You can also try a Jordan form version for fun. Same result.. This is mostly review for anyone who's had linear alg but not so for others who've not. So I'm trying to keep it simple (hence the simple diagonal proof for diagonalizeable matrices) Cheers, Chris Rose From cripop@ece.rutgers.edu Sat Sep 20 21:06:41 1997 Return-Path: Received: from zen.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA02488; Sat, 20 Sep 97 21:04:18 EDT Received: from chess.rutgers.edu (chess.rutgers.edu [128.6.46.113]) by zen.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id UAA02702 for <330_501@mogli.rutgers.edu>; Sat, 20 Sep 1997 20:07:03 -0400 From: Dimitrie Popescu Message-Id: <199709210007.UAA02702@zen.rutgers.edu> Subject: Cayley-Hamilton Theorem To: 330_501@mogli.rutgers.edu Date: Sat, 20 Sep 1997 20:01:32 -0400 (EDT) Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 1049 Status: RO this is a proof of the Cayley-Hamilton Theorem in the general case. No assumption is made about matrix A; just that is a square matrix of dimension nxn. Let us denote the characteristic polynomial of A: Phi(s)=det(sI-A)=s^n+a_1s^(n-1)+...+a_n Let us also take the inverse of sI-A: (sI-A)^(-1)=(sI-A)*/det(sI-A)=B(s)/Phi(s) where (sI-A)*=B(s) is the adjoint matrix of sI-A. Rewrite the above relation as: Phi(s)I_n=(sI-A)B(s) because the highest power of s in Phi(s) is n, then the highest power of s in B(s) will be n-1. B(s) can be written as: B(s)=B_0s^(n-1)+B_1s(n-2)+...+B_(n-1) After performing the multiplication and identifying coefficients we get: s^n: I=B_0 s^(n-1): a_1I=B_1-AB_0 s^(n-2): a_2I=B_2-AB_1 ........ s^1: a_(n-1)I=B_(n-1)-AB_(n-2) s^0: a_nI= -AB_(n-1) These relations are equivalent with: B_0=I B_1=A+a_1I B_2=A^2+Aa_1+a_2I ......... B_(n-1)=A^(n-1)+A^(n-2)a_1+...+a_(n-1)I 0 =A^n+A^(n-1)a_1+...+Aa_(n-1)+a_nI The last relation is in fact Phi(A)=0 and the proof is completed. Otilia Popescu From crose Sun Sep 21 11:14:48 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA03104; Sun, 21 Sep 97 11:14:21 EDT Date: Sun, 21 Sep 97 11:14:21 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709211514.AA03104@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: ece machine Cc: crose@MOGLI.rutgers.edu Status: RO Hi Folks, The ECE machine seems to be fried. Hopefully it will be fixed by monday. In the mean time, even I cannot get access to the web page (both front AND back doors). I'll make copies of the PS solutions and distribute them in class. I'll also look into moving the web page to a more reliable machine. For some reason ece is flaky. Cheers, sort of, Chris ROse From crose Tue Sep 23 12:50:22 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA05676; Tue, 23 Sep 97 12:42:27 EDT Date: Tue, 23 Sep 97 12:42:27 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709231642.AA05676@MOGLI.rutgers.edu> To: 330_501@MOGLI.rutgers.edu, matei@caip.rutgers.edu Subject: Re: Mideterm Status: RO Hi Folks, Will respond fully when I get in, my internet link from home stinks. Bottom line, there are lots of problems with that midterm (two of the things I asked to prove are untrue!). However, the poblem is interesting . I'll checkinto the issue of the actual problem statement not being on line. There should be dispclaimers saying that the last two parts are wrong (in the statement). The solutions seek to rectify the rror and explore the problem in more detail. this typong blind is driving me crazy. i'll say more when I come in.. Cheers From postmaster@cbgw2.lucent.com Tue Sep 23 14:29:09 1997 X-UIDL: 5f305fc3136f54f5fe31a7e82b4dc77b Return-Path: Received: from cbgw2.lucent.com by MOGLI.rutgers.edu (4.1/25-eef) id AA05960; Tue, 23 Sep 97 14:29:04 EDT Message-Id: <9709231829.AA05960@MOGLI.rutgers.edu> From: postmaster@cbgw2.lucent.com Date: Tue, 23 Sep 97 13:14 EDT To: crose@MOGLI.rutgers.edu Status: RO Mail to `lucent.com!tonyhinds', 'lucent.com!kheyward' from 'MOGLI.rutgers.edu!crose' (MOGLI.rutgers.edu!crose) failed. The mailer `exec route.toig 'MOGLI.rutgers.edu!crose'' returned error status f00. The error message was: uux failed ( -15 ) The message began: Received: by cbgw2.lucent.com; Tue Sep 23 13:06 EDT 1997 Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA05676; Tue, 23 Sep 97 12:42:27 EDT Date: Tue, 23 Sep 97 12:42:27 EDT From: Christopher Rose Message-Id: <9709231642.AA05676@MOGLI.rutgers.edu> To: 330_501@MOGLI.rutgers.edu, matei@caip.rutgers.edu Subject: Re: Mideterm Hi Folks, Will respond fully when I get in, my internet link from home stinks. Bottom line, there are lots of problems with that midterm (two of the things I asked to prove are untrue!). However, the poblem is interesting . I'll checkinto the issue of the actual problem statement not being on line. There should be dispclaimers saying that the last two parts are wrong (in the statement). The solutions seek to rectify the rror and explore the problem in more detail. this typong blind is driving me crazy. i'll say more when I come in.. Cheers From matei@caip.rutgers.edu Tue Sep 23 11:05:49 1997 Return-Path: Received: from caipfs.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA05455; Tue, 23 Sep 97 11:03:16 EDT Received: from matisse.rutgers.edu (matisse.rutgers.edu [128.6.43.23]) by caipfs.rutgers.edu (8.8.5/8.8.5) with ESMTP id KAA00216 for <330_501@MOGLI.rutgers.edu>; Tue, 23 Sep 1997 10:09:33 -0400 (EDT) Received: (matei@localhost) by matisse.rutgers.edu (8.7.6/8.6.9) id KAA12868 for 330_501@MOGLI.rutgers.edu; Tue, 23 Sep 1997 10:09:33 -0400 (EDT) From: "Bogdan Matei" Message-Id: <9709231009.ZM12866@matisse.rutgers.edu> Date: Tue, 23 Sep 1997 10:09:31 -0400 X-Mailer: Z-Mail (3.2.0 06sep94) To: 330_501@MOGLI.rutgers.edu Subject: Mideterm Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Dear Dr. Rose, I have downloaded the midterm examination problems for 95 and 96. The problem is that the file for the 96 is the same for 95. The files with the solutions are OK. Maybe is a name problem in the hot link on the page. So for 96 midterm only the solutions are provided! Second question arises from the conceptual difference between stability and contraction. Obviously stability is obtained when |eval] < 1, while contraction, at least the norm 2 is obtained when max|eval(A^H*A)| < 1. As a matter of fact a have demonstrated that a stability is equal to a contraction if the matrix is real and symmetric. In this case the evals of A^H*A are the same with the evals of A raised to the second power. BUT in most of the cases the matrix formed with the evectors is not unitary so the above argument doesn't hold. The question is what is the difference between the fixed point of a mapping when the system is stable and the fixed point obtained when we have a contraction. This appears more clearly in the problem 1 from the 95 midterm where the alpha and beta found at (b) are not the same as the ones found at (c). In my opinion stability implies convergence, without implying contraction, so the contraction is a stronger assumption about a system. Other problem: you state that if you want a system to blow up if all the evals of a matrix should be greater (or equal) than 1 (solutions, problem 3 c), 95). Is it necessary that ALL be greater or suffices only one? Best regards, Bogdan -- --------------------------------------------------------| Bogdan MATEI | | OFFICE: | HOME : | CAIP | BPO 23805 PO Box 1119 | PO Box 1390 | Piscataway,NJ 08855-1119 | Piscataway, NJ 08855-1390 | (Tel) (908) 7430806 | (Tel) (908)4454268 |---------------------------| E-mail: matei@caip.rutgers.edu | Web page: http://www.caip.rutgers.edu/~matei | --------------------------------------------------------| From crose Tue Sep 23 21:41:16 1997 X-UIDL: 46b7603fd80e0a9df95631ccad769f4f Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA06608; Tue, 23 Sep 97 21:34:29 EDT Date: Tue, 23 Sep 97 21:34:29 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709240134.AA06608@MOGLI.rutgers.edu> To: 330_501 Subject: stuff Status: RO Hi Folks, I had fun tonight. Hope you did too. In any case, I've put the correct 1996 midterm on the web (which had problems with the statement anyway) and have deleted the overly problematic 1995 midterm which had a problem which was just too confusing for words. I've also made a duplicate of the web page on a winlab machine so that just in case ece goes down, you can still get at the stuff http:/winwww.rutgers.edu/pub/about/people/crose/winlab501.html is the URL. Not everything works (like the signup for instance), but the PS files are there and readable as well as the email archive (which will be updated with your mailings in my absence so keep an eye out for it). See you when I get back (10/2). I should have the exams graded about a week from then is not sooner. Cheers Chris Rose PS: Anybody know how to get from the airport in Budapest to local hotels? From SIZE=2535@att.com Tue Sep 23 22:30:30 1997 Return-Path: Received: from att.com (kcgw2.att.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA06714; Tue, 23 Sep 97 22:30:30 EDT Received: by kcgw2.att.com; Tue Sep 23 20:22 CDT 1997 Received: from localhost (localhost) by kcig2.att.att.com (AT&T/GW-1.0) with internal id UAA29669; Tue, 23 Sep 1997 20:26:57 -0500 (CDT) Date: Tue, 23 Sep 1997 20:26:57 -0500 (CDT) From: Mail Delivery Subsystem Message-Id: <199709240126.UAA29669@kcig2.att.att.com> To: crose@MOGLI.rutgers.edu Mime-Version: 1.0 Content-Type: multipart/report; report-type=delivery-status; boundary="UAA29669.875064417/kcig2.att.att.com" Subject: Returned mail: Service unavailable Auto-Submitted: auto-generated (failure) Status: RO This is a MIME-encapsulated message --UAA29669.875064417/kcig2.att.att.com The original message was received at Tue, 23 Sep 1997 20:26:55 -0500 (CDT) from nuucp@localhost ----- The following addresses had permanent fatal errors ----- ustad.att.com!rice ustad.att.com!jdodley ----- Transcript of session follows ----- ... while talking to ustad.ho.att.com.: >>> MAIL From: SIZE=2435 <<< 554 Cannot bind to domain ustaddomain: can't communicate with ypbind 554 ustad.att.com!rice,ustad.att.com!jdodley... Service unavailable --UAA29669.875064417/kcig2.att.att.com Content-Type: message/delivery-status Reporting-MTA: dns; kcig2.att.att.com Arrival-Date: Tue, 23 Sep 1997 20:26:55 -0500 (CDT) Final-Recipient: RFC822; rice@ustad.ho.att.com Action: failed Status: 5.0.0 Remote-MTA: DNS; ustad.ho.att.com Diagnostic-Code: SMTP; 554 Cannot bind to domain ustaddomain: can't communicate with ypbind Last-Attempt-Date: Tue, 23 Sep 1997 20:26:57 -0500 (CDT) Final-Recipient: RFC822; jdodley@ustad.ho.att.com Action: failed Status: 5.0.0 Remote-MTA: DNS; ustad.ho.att.com Diagnostic-Code: SMTP; 554 Cannot bind to domain ustaddomain: can't communicate with ypbind Last-Attempt-Date: Tue, 23 Sep 1997 20:26:57 -0500 (CDT) --UAA29669.875064417/kcig2.att.att.com Content-Type: message/rfc822 Return-Path: Received: (from nuucp@localhost) by kcig2.att.att.com (AT&T/GW-1.0) id UAA29667; Tue, 23 Sep 1997 20:26:55 -0500 (CDT) >Received: by kcgw2.att.com; Tue Sep 23 20:22 CDT 1997 Received: by kcgw2.att.com; Tue Sep 23 20:22 CDT 1997 Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA06701; Tue, 23 Sep 97 22:29:11 EDT Date: Tue, 23 Sep 97 22:29:11 EDT From: Christopher Rose Message-Id: <9709240229.AA06701@MOGLI.rutgers.edu> To: 330_501@MOGLI.rutgers.edu, matei@caip.rutgers.edu Subject: Re: Mideterm Content-Type: text Hi Bogdan, I've addressed your first issue (midterm95/96). You are completely correct in your second paragraph about A being real and symm so that the eigenvalues of A having magnitude < 1 means contraction. BUt as you also point out, it's JUST NOT TRUE IN GENERAL that eigenvalues mag < 1 implies contraction. What you proved would have made an interesting problem for an exam (but won't appear this time alas :) Now as for the other issue. Stability (assymptotic that is) implies convergence BUT DOES NOT IMPLY A CONTRACTION map exactly as you say. Now as for your third point. The issue is that you must have all eval mags > 1 because you could excite the system only along a mode for which the eval mags were < 1 (and avoid the modes where eval mags > 1). However, if one is a purist, then you only need one eval mag >1 to have the system unstable (meaning that for SOME intial condition, the system state (x) is unbounded). Hope taht helps... Cheers, Chris ROse PS: I was asked before class about exponentiation of the Jordan form. Remember that f(A) = taylor series of f(x) evaluated with A replaced for x? Well, with a Jordan form block this leads to f(J) = (first row) f(lamda) f'(lamda) f''(lamda)/2 ..... f^(n-1)(lambda)/(n-1)! (secnd row) 0 f(lamda) f'(lamda) ......... f^(n-2)(lambda)/(n-2)! etc (last row) 0 ..............................f(lambda) Now let's say we want to evaluate f(Jt). In this case you have to go back to the derivation (see page 34) and look at what happens when you ust At instead of A. What you see is that the final term (1.39) becomes (letting lambda = L) f(A) = sum_{el=0}^{v-1} (Nt)^el sum_k (k choose el) a_k (Lt)^(k-el) = sum_{el=0}^{v-1} (Nt)^el f^(el)(Lt)/el! So the derivatives are always with respect to the function argument. That is given f(x), we use f'(x) in the jordan expansion and substitute in lambda. The only thing to remember is that there is that (Nt)^el floating around which dumps a power of t on you as you move accross the columns. So e^(Jt) is e^Jt = (first row) f(lamda) tf'(lamda) ..... t^(n-1)f^(n-1)(lambda)/(n-1)! (secnd row) 0 f(lamda) .......t^(n-2)f^(n-2)(lambda)/(n-2)! etc (last row) 0 ..............................f(lambda) This would also have made a good quiz problem! --UAA29669.875064417/kcig2.att.att.com-- From crose Tue Sep 23 22:33:34 1997 X-UIDL: 78b8b55d1c53c76298da8ccd645fc09c Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA06701; Tue, 23 Sep 97 22:29:11 EDT Date: Tue, 23 Sep 97 22:29:11 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709240229.AA06701@MOGLI.rutgers.edu> To: 330_501@MOGLI.rutgers.edu, matei@caip.rutgers.edu Subject: Re: Mideterm Status: RO Hi Bogdan, I've addressed your first issue (midterm95/96). You are completely correct in your second paragraph about A being real and symm so that the eigenvalues of A having magnitude < 1 means contraction. BUt as you also point out, it's JUST NOT TRUE IN GENERAL that eigenvalues mag < 1 implies contraction. What you proved would have made an interesting problem for an exam (but won't appear this time alas :) Now as for the other issue. Stability (assymptotic that is) implies convergence BUT DOES NOT IMPLY A CONTRACTION map exactly as you say. Now as for your third point. The issue is that you must have all eval mags > 1 because you could excite the system only along a mode for which the eval mags were < 1 (and avoid the modes where eval mags > 1). However, if one is a purist, then you only need one eval mag >1 to have the system unstable (meaning that for SOME intial condition, the system state (x) is unbounded). Hope taht helps... Cheers, Chris ROse PS: I was asked before class about exponentiation of the Jordan form. Remember that f(A) = taylor series of f(x) evaluated with A replaced for x? Well, with a Jordan form block this leads to f(J) = (first row) f(lamda) f'(lamda) f''(lamda)/2 ..... f^(n-1)(lambda)/(n-1)! (secnd row) 0 f(lamda) f'(lamda) ......... f^(n-2)(lambda)/(n-2)! etc (last row) 0 ..............................f(lambda) Now let's say we want to evaluate f(Jt). In this case you have to go back to the derivation (see page 34) and look at what happens when you ust At instead of A. What you see is that the final term (1.39) becomes (letting lambda = L) f(A) = sum_{el=0}^{v-1} (Nt)^el sum_k (k choose el) a_k (Lt)^(k-el) = sum_{el=0}^{v-1} (Nt)^el f^(el)(Lt)/el! So the derivatives are always with respect to the function argument. That is given f(x), we use f'(x) in the jordan expansion and substitute in lambda. The only thing to remember is that there is that (Nt)^el floating around which dumps a power of t on you as you move accross the columns. So e^(Jt) is e^Jt = (first row) f(lamda) tf'(lamda) ..... t^(n-1)f^(n-1)(lambda)/(n-1)! (secnd row) 0 f(lamda) .......t^(n-2)f^(n-2)(lambda)/(n-2)! etc (last row) 0 ..............................f(lambda) This would also have made a good quiz problem! From crose Tue Sep 23 22:50:27 1997 X-UIDL: f5ce9d185a9515d6d0764f4d1f5b2189 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA06815; Tue, 23 Sep 97 22:43:19 EDT Date: Tue, 23 Sep 97 22:43:19 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709240243.AA06815@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: signup Status: RO Even the signup now works on winlab. So everything should be ok! Cheers, and good luck on the exams! Chris Rose From Stamosteve@aol.com Wed Sep 24 10:09:50 1997 Return-Path: Received: from emout28.mail.aol.com (emout28.mx.aol.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA00190; Wed, 24 Sep 97 10:04:16 EDT Received: (from root@localhost) by emout28.mail.aol.com (8.7.6/8.7.3/AOL-2.0.0) id AAA07032 for crose@mogli.rutgers.edu; Wed, 24 Sep 1997 00:50:49 -0400 (EDT) Date: Wed, 24 Sep 1997 00:50:49 -0400 (EDT) From: Stamosteve@aol.com Message-Id: <970923214225_123239510@emout16.mail.aol.com> To: crose@mogli.rutgers.edu Subject: Re: stuff Status: RO Professor Rose, Can you please put out the 1996 midterm as a GIF file? I am having trouble viewing the PS file THanks Steve Wahlgren From aonweller@maerskdata-usa.com Wed Sep 24 10:12:56 1997 Return-Path: Received: from msrvr.maerskdata-usa.com by MOGLI.rutgers.edu (4.1/25-eef) id AA00212; Wed, 24 Sep 97 10:12:53 EDT Received: from [10.1.25.41] ([207.242.160.66]) by msrvr.maerskdata-usa.com (Netscape Mail Server v2.02) with SMTP id AAA40; Wed, 24 Sep 1997 11:30:45 +0000 Message-Id: <3428F94C.605C@maerskdata-usa.com> Date: Wed, 24 Sep 1997 07:28:13 -0400 From: aonweller@maerskdata-usa.com (Allen Onweller) X-Mailer: Mozilla 3.01-C-MACOS8 (Macintosh; I; PPC) Mime-Version: 1.0 To: Christopher Rose Cc: 330_501@MOGLI.rutgers.edu, 330_543@MOGLI.rutgers.edu Subject: Problems with alternate 543 Web Site? References: <9709240243.AA06815@MOGLI.rutgers.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO I think that the correct URL is: http://winwww.rutgers.edu/pub/about/people/staff/crose/winlab543.html From crose Wed Sep 24 11:20:00 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA00365; Wed, 24 Sep 97 11:19:58 EDT Date: Wed, 24 Sep 97 11:19:58 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709241519.AA00365@MOGLI.rutgers.edu> To: Stamosteve@aol.com Subject: Re: stuff Cc: crose@MOGLI.rutgers.edu Status: RO Hi Steve, It does not exist as gif (drivers are broken). Take a peek at the links to ghostview PS viewers that you can load on your pc... Barring that, you can print the beasts out at RU (or at work?) Cheers, Chris Rose From crose Wed Sep 24 11:24:50 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA00375; Wed, 24 Sep 97 11:21:54 EDT Date: Wed, 24 Sep 97 11:21:54 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709241521.AA00375@MOGLI.rutgers.edu> To: aonweller@maerskdata-usa.com Subject: Re: Problems with alternate 543 Web Site? Cc: 330_501, 330_543 Status: RO What URL did I provide? Regardless, what you have looks right. You can also reach it by going to my home page http:/winwww.rutgers.edu/pub/about/people/staff/crose/crose.html and following the links at the bottom of the page Cheers, ALL From crose Wed Sep 24 11:33:42 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA00403; Wed, 24 Sep 97 11:31:28 EDT Date: Wed, 24 Sep 97 11:31:28 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9709241531.AA00403@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: ARRRRRRRGGGGGGGGGGHHHHHHH!!! Cc: crose@MOGLI.rutgers.edu Status: RO Hi Folks, I left out a protion of the path for the alternate site url It should have read: http:/winwww.rutgers.edu/pub/about/people/staff/crose/winlabXXX.html where XXX is either 501 or 543. Sorry bout that.... Allen Onweller bailed me out on that one. Thanks Also, for 501 students. GIF files for the old midterm and solutions don't exist! Sorry for the inconvenience. You can always print them out at RU. But a better idea is to follow the links provided to get some ghostview software which you can load on your PC to view postscript files. I've never tried it, but also there's adobe acrobat which I would think should be able to view Postscript somehow (same company which puts out adobe postscript, no?) Cheers ALL I leave today. Let's hope I can avoid a flight 800 sort of deal :) From mae@ece.rutgers.edu Thu Sep 25 22:50:08 1997 X-UIDL: f992d72cac18beea5d164cf79a05c9e6 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA02213; Thu, 25 Sep 97 22:43:48 EDT Received: from ece.rutgers.edu (localhost [127.0.0.1]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id VAA00335; Thu, 25 Sep 1997 21:45:34 -0400 Sender: mae@ece.rutgers.edu Message-Id: <342B13BE.4CD5@ece.rutgers.edu> Date: Thu, 25 Sep 1997 21:45:34 -0400 From: Hideki Mae X-Mailer: Mozilla 3.01Gold (X11; I; SunOS 5.5 sun4m) Mime-Version: 1.0 To: 330_501@mogli.rutgers.edu Cc: mae@ece.rutgers.edu Subject: linearization Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Suppose you are given the following system: x1dot = (x1+x2)^2 x2dot = exp(x1-x2) - 1 y = x1^2 + 2*x2 If it is non-linear (which it is) find a nontrivial (nonzero) equilibrium state and provide the linearized equation around this equilibrium. When I tried to find the equilibrium state I get the following (x1+x2)^2 = 0 and exp(x1-x2) -1 = 0 Solving for x1 and x2 I get 0 which is not what the problem asks for. What do I do in this case? From mae@ece.rutgers.edu Sat Sep 27 18:23:43 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA04274; Sat, 27 Sep 97 18:22:51 EDT Received: from ece.rutgers.edu (localhost [127.0.0.1]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id RAA09554; Sat, 27 Sep 1997 17:24:17 -0400 Sender: mae@ece.rutgers.edu Message-Id: <342D7981.4754@ece.rutgers.edu> Date: Sat, 27 Sep 1997 17:24:17 -0400 From: Hideki Mae X-Mailer: Mozilla 3.01Gold (X11; I; SunOS 5.5 sun4m) Mime-Version: 1.0 To: 330_501@mogli.rutgers.edu Cc: mae@ece.rutgers.edu Subject: how to answer Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Question: You are given a system xdot(t) = A*x(t) + B*u(t) with output eqn. y(t) = C*x(t) When can we guarantee that the system: a) is completely controllable b) is completely observable c) can be made to follow any arbitrary trajectory x(t) by appropriate choice of u(t). Did you want a simple answer like: a) When controllabiltiy matrix K = [B| A*B|...|A^n-1 * B] has full rank n. Or did you want something more? From jsucec@ece.rutgers.edu Sat Sep 27 20:20:03 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA04372; Sat, 27 Sep 97 20:17:29 EDT Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id TAA11421 for <330_501@MOGLI.rutgers.edu>; Sat, 27 Sep 1997 19:18:54 -0400 Date: Sat, 27 Sep 1997 19:18:54 -0400 (EDT) From: John Sucec To: 330_501@MOGLI.rutgers.edu Subject: Question on HW Set 1 Solutions Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO I have a question concerning the solution given for problem 3 of the 1st homework set (Ch.[1], prob. 4)... Maybe someone can help me. What is the metric (i.e., the "rho") used for closed ball 2 (B_2)? Is the rho for B_2 implied somehow by the definition of the space M=B_2((0,0)0.5)? Or was the omission a rho specification for B_2 an oversight in the problem solution? Or something else ??? Anyway, I know that it is important to specify a rho for closed ball 1 (B_1)... After all, this is what allowed us to contrive a closed ball that is a proper subset of B_2 even though its radius exceeds the radius of B_2. I just thought that it is equally important to specify the rho for B_2 for completeness. Thanks in advance to anyone who can clarify this for me. ...John From jdodley@ustad.ho.att.com Mon Sep 29 11:50:02 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA05919; Mon, 29 Sep 97 11:50:01 EDT Received: from att.com (cagw1.att.com [192.128.52.89]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id KAA05698 for ; Mon, 29 Sep 1997 10:51:07 -0400 Received: by cagw1.att.com; Mon Sep 29 10:50 EDT 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by caig1.att.att.com (AT&T/GW-1.0) with SMTP id KAA05372 for ; Mon, 29 Sep 1997 10:47:08 -0400 (EDT) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA11413; Mon, 29 Sep 97 10:59:09 EDT Received: from vega1.ho.att.com by nj-mailnet.ho.att.com with SMTP (Microsoft Exchange Internet Mail Service Version 5.0.1458.49) id TY1YJTAX; Mon, 29 Sep 1997 10:55:24 -0400 Message-Id: <342FC12D.505F@ustad.att.com> Date: Mon, 29 Sep 1997 10:54:37 -0400 From: JP Dodley Organization: AT&T X-Mailer: Mozilla 3.01 (Win95; I) Mime-Version: 1.0 To: crose@ece.rutgers.edu Subject: Mid Term 1 97 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Dear Dr. Rose, Is section 2.1.2 "Solution of linear diff eqns" included in the exam? Thanks. J.P. dodley From cwrice@att.com Tue Sep 30 12:41:14 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA07114; Tue, 30 Sep 97 12:41:13 EDT Received: from att.com (cagw1.att.com [192.128.52.89]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id LAA14170 for ; Tue, 30 Sep 1997 11:42:08 -0400 Received: by cagw1.att.com; Tue Sep 30 11:41 EDT 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by caig1.att.att.com (AT&T/GW-1.0) with SMTP id LAA28529 for ; Tue, 30 Sep 1997 11:38:10 -0400 (EDT) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA13183; Tue, 30 Sep 97 11:49:55 EDT Message-Id: <9709301549.AA13183@hoccson.ho.att.com> Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id ; Tue, 30 Sep 1997 11:46:12 -0400 From: "Rice, Chris" To: crose@ece.rutgers.edu Cc: "Dodley, JP" Subject: Questions and Observations Date: Tue, 30 Sep 1997 11:45:55 -0400 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: RO Class/Dr. Rose, Fall 1995 Midterm Question #1 b) How doe we know |A| is equal to max i SQRT (li), as opposed to another norm? Fall 1995 Midterm Question #1 c) Would not the correct interval for ab be: -3/4 < ab <1/4. I got this by using ab is real, since a and b are real; therefore, SQRT(ab) is either positive semidefinite (>=0) or purely imaginary if ab <0. Then use |l|<1 for each case. Fall 1995 Midterm Question #3 b) Would we not have to prove that this is a contraction, not merely a fixed point as in the answer sheet, since it says UNIQUE stationary (fixed) point? Fall 1996 Midterm Question #3 e) This would be correct is it just said sufficient, as opposed to necessary and sufficient, and this could be proven by using contraction definition and using ||A||2 {it is not on the answer sheet; so, I thought it was worth mentioning}. Thanks, Chris Rice From cwrice@att.com Tue Sep 30 15:02:56 1997 Return-Path: Received: from att.com (kcgw2.att.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA07224; Tue, 30 Sep 97 15:01:44 EDT Received: by kcgw2.att.com; Tue Sep 30 12:52 CDT 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by kcig2.att.att.com (AT&T/GW-1.0) with SMTP id MAA27418 for <330_501@mogli.rutgers.edu>; Tue, 30 Sep 1997 12:57:08 -0500 (CDT) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA16371; Tue, 30 Sep 97 14:10:26 EDT Message-Id: <9709301810.AA16371@hoccson.ho.att.com> Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id ; Tue, 30 Sep 1997 14:06:44 -0400 From: "Rice, Chris" To: 330_501@mogli.rutgers.edu Date: Tue, 30 Sep 1997 14:06:35 -0400 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: RO Class/Dr. Rose, Fall 1995 Midterm Question #1 b) How do we know |A| is equal to max i SQRT (li), as opposed to another norm? Fall 1995 Midterm Question #1 c) Would not the correct interval for ab be: -3/4 < ab <1/4. I got this by using ab is real, since a and b are real; therefore, SQRT(ab) is either positive semidefinite (>=0) or purely imaginary if ab <0. Then use |l|<1 for each case. Fall 1995 Midterm Question #3 b) Would we not have to prove that this is a contraction, not merely a fixed point as in the answer sheet, since it says UNIQUE stationary (fixed) point? Fall 1996 Midterm Question #3 e) This would be correct is it just said sufficient, as opposed to necessary and sufficient, and this could be proven by using contraction definition and using ||A||2 {it is not on the answer sheet; so, I thought it was worth mentioning}. Thanks, Chris Rice From jsucec@ece.rutgers.edu Fri Oct 3 14:28:05 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA10961; Fri, 3 Oct 97 14:25:44 EDT Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id NAA13390 for <330_501@MOGLI.rutgers.edu>; Fri, 3 Oct 1997 13:26:07 -0400 Date: Fri, 3 Oct 1997 13:26:06 -0400 (EDT) From: John Sucec Reply-To: John Sucec To: 330_501@MOGLI.rutgers.edu Subject: Good Existence/Uniqueness Reference Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO This E-Mail might interest anyone who feels that the treatment of the Existence and Uniqueness Theorem and Picard iteration in our class test [S&B] is either difficult to understand or inadequate... If you have an undergraduate reference on differential equations, you may want to brush the dust off of it and take at look at it's content on the Existence and Uniqueness Theorem and Picard iteration. I did this Wednesday night and found that it contained far more examples and detail than our class text. For instance, my old differential equations reference points out that the Existence and Uniqueness Theorem predicts only a conservative allowable range for t such that the IVP dy/dy=f(t,y), y(t_0)=y_0, has a unique solution. In reality the allowable range for t may be much greater than the range predicted by the E&U Theorem. I don't know how important this detail is for the purposes of 501, but it certainly is not aspect of E&U Theorem that is obvious from our text. Anyway, if you don't have your old differential equations book, there probably some good references in the library. I think my old text is a good reference for the E&U and Picard topics and it as follows: "Differential Equations and Their Applications" by Martin Braun, 3rd Edition, 1986, Springer-Verlag. I have no idea whether this reference is available in the library, but if it is available and you're like me and need a different reference for the topics discussed in section 2.1.1 of our text, I highly recommend it. ...John From crose Fri Oct 3 14:38:04 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA10988; Fri, 3 Oct 97 14:36:52 EDT Date: Fri, 3 Oct 97 14:36:52 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710031836.AA10988@MOGLI.rutgers.edu> To: 330_501@MOGLI.rutgers.edu, jsucec@ece.rutgers.edu Subject: Re: Good Existence/Uniqueness Reference Status: RO Thanks John! Flks should also look up the classic book by Simmons (Differential Equations with Applications and Historical Notes, McGraw-Hill publishers). Cheers From yuqing@er3.rutgers.edu Sun Oct 12 21:10:42 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA22644; Sun, 12 Oct 97 21:10:40 EDT Received: from er3.rutgers.edu (yuqing@er3.rutgers.edu [165.230.180.141]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id UAA13092 for ; Sun, 12 Oct 1997 20:09:21 -0400 Received: from localhost (yuqing@localhost) by er3.rutgers.edu (8.8.5/8.8.5) with SMTP id UAA15154 for ; Sun, 12 Oct 1997 20:13:51 -0400 (EDT) Date: Sun, 12 Oct 1997 20:13:51 -0400 (EDT) From: Yuqing Xie To: crose@ece.rutgers.edu Message-Id: Mime-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="-559023410-851401618-876701631=:13724" Status: RO This message is in MIME format. The first part should be readable text, while the remaining parts are likely unreadable without MIME-aware tools. Send mail to mime@docserver.cac.washington.edu for more info. ---559023410-851401618-876701631=:13724 Content-Type: TEXT/PLAIN; charset=US-ASCII Dr. Rose: I have a question on Example 2.5 of class 501 book. Attached is MS word file. Sorry for inconvenience to get my question. Because I can only use MS Word to type those Math. stuff. May be there are some other way. Thanks Becky(Yuqing) Xie From crose Sun Oct 12 23:11:02 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22780; Sun, 12 Oct 97 23:11:02 EDT Date: Sun, 12 Oct 97 23:11:02 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710130311.AA22780@MOGLI.rutgers.edu> To: yuqing@eden.rutgers.edu Subject: Hi Cc: crose@MOGLI.rutgers.edu Status: RO Unfortunately, my computer does not speak ms word. Try using latex-like symbolism and i'll be able to read it fine. If you don't know latex wait till class or just try any old symbols. Regardless, I'm sure I know what your question is. The answer is that you look and see that the differential equation in x_2 dot is only in terms of x_2 and t. Then you use variable separation to solve for x_2. >From this you can then use your result and solve for x_1. i.e.; say dq/dt = tq then we (effectively) do dq/q = t dt integrate both sides to obtain log q = t^2/2 + c where c is a constant So that q = A e^(t^2/2) were A = e^c. you do something similar for the equation in x_1. Cheers, Chris Rose From crose Sun Oct 12 23:17:24 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22794; Sun, 12 Oct 97 23:14:54 EDT Date: Sun, 12 Oct 97 23:14:54 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710130314.AA22794@MOGLI.rutgers.edu> To: 330_501 Status: RO >From crose Sun Oct 12 23:11:02 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22780; Sun, 12 Oct 97 23:11:02 EDT Date: Sun, 12 Oct 97 23:11:02 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710130311.AA22780@MOGLI.rutgers.edu> To: yuqing@eden.rutgers.edu Subject: Hi Cc: crose@MOGLI.rutgers.edu Status: R Unfortunately, my computer does not speak ms word. Try using latex-like symbolism and i'll be able to read it fine. If you don't know latex wait till class or just try any old symbols. Regardless, I'm sure I know what your question is. The answer is that you look and see that the differential equation in x_2 dot is only in terms of x_2 and t. Then you use variable separation to solve for x_2. >From this you can then use your result and solve for x_1. i.e.; say dq/dt = tq then we (effectively) do dq/q = t dt integrate both sides to obtain log q = t^2/2 + c where c is a constant So that q = A e^(t^2/2) were A = e^c. you do something similar for the equation in x_1. Cheers, Chris Rose From yuqing@er6.rutgers.edu Mon Oct 13 11:52:30 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA23860; Mon, 13 Oct 97 11:52:29 EDT Received: from er6.rutgers.edu (yuqing@er6.rutgers.edu [165.230.180.134]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id KAA24182 for ; Mon, 13 Oct 1997 10:51:04 -0400 Received: from localhost (yuqing@localhost) by er6.rutgers.edu (8.8.5/8.8.5) with SMTP id KAA28609 for ; Mon, 13 Oct 1997 10:55:32 -0400 (EDT) Date: Mon, 13 Oct 1997 10:55:31 -0400 (EDT) From: Yuqing Xie To: crose@ece.rutgers.edu Subject: Example 2.5 of class 501 book Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Dr. Rose: Sorry to bother you again. On the reference of the class mail I get the idea how could I type those mathematic symbol now. My question is: In the book of class 501, the Example 2.5. I just could not figure out From: (x dot)=[t t x(0)=[1 0 2t]x 1] How to get: Q(t,0)=[ e^((t^2)/2) -e^((t^2)/2)+e^(t^2) 0 e^(t^2) ] We have: x(t)=Q(t,t_0)x_0, then just integrate (x dot) to get x(t). But what I do with x in the x(t) form? Or is there another way to get Q(t,t_0) Thanks and best regards Becky (Yuqing) Xie From crose Mon Oct 13 11:55:52 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA23869; Mon, 13 Oct 97 11:55:51 EDT Date: Mon, 13 Oct 97 11:55:51 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710131555.AA23869@MOGLI.rutgers.edu> To: yuqing@eden.rutgers.edu Subject: Re: Example 2.5 of class 501 book Cc: crose@MOGLI.rutgers.edu Status: RO I think I answered the question before. Look at the scalar differenctial equation in x_2(t) (your vector equation has (x_1(t), x_2(t)) multiplied by your matrix Q. Cheers, Chris Rose PS: If this sounded testy I did not mean it. I'm in a hurry right now. From cwrice@att.com Tue Oct 14 09:54:00 1997 X-UIDL: 212df09b4195781dde5b67b987ac528f Return-Path: Received: from att.com (cagw2.att.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA25113; Tue, 14 Oct 97 09:47:50 EDT Received: by cagw2.att.com; Tue Oct 14 08:47 EDT 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by caig2.att.att.com (AT&T/GW-1.0) with SMTP id JAA12808 for <330_501@mogli.rutgers.edu>; Tue, 14 Oct 1997 09:02:12 -0400 (EDT) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA09950; Tue, 14 Oct 97 08:54:25 EDT Message-Id: <9710141254.AA09950@hoccson.ho.att.com> Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id <4WKX0SAX>; Tue, 14 Oct 1997 08:50:42 -0400 From: "Rice, Chris" To: 330_501@mogli.rutgers.edu Subject: Allowable region of s for Laplace Transform Date: Tue, 14 Oct 1997 08:50:28 -0400 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: RO In class, we derived the Laplace transform and came up with an allowable region for s as Re(s-a)>=0. I believe this region should be Re(s-a)>0 (no equals). As an example, the Laplace transofrm of e^(at) is 1/(s-a). Obviously, at Re(s-a) = 0, this transform is undefined. Chris Rice From yuqing@er7.rutgers.edu Tue Oct 14 10:37:32 1997 X-UIDL: 0786b7d0187ceebd14f3aacfcbcbc176 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA25146; Tue, 14 Oct 97 10:37:31 EDT Received: from er7.rutgers.edu (yuqing@er7.rutgers.edu [165.230.180.135]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id JAA03469 for ; Tue, 14 Oct 1997 09:35:56 -0400 Received: from localhost (yuqing@localhost) by er7.rutgers.edu (8.8.5/8.8.5) with SMTP id JAA10046 for ; Tue, 14 Oct 1997 09:40:25 -0400 (EDT) Date: Tue, 14 Oct 1997 09:40:24 -0400 (EDT) From: Yuqing Xie To: crose@ece.rutgers.edu Subject: Thanks Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Dr. Rose: I totally understand now. I should not send you the second mail.(I was not realized what you talking about in the first mail. See how stupid I was.) Sorry about that. Thank you very much. Becky (Yuqing) Xie From crose@ece.rutgers.edu Tue Oct 14 11:41:00 1997 X-UIDL: 2f12d8b1a13b703f736cf025ab9b50ad Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA25230; Tue, 14 Oct 97 11:40:59 EDT Received: from localhost.localdomain (root@ppp-10.ts-4.nyc.idt.net [169.132.97.82]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id KAA05470 for ; Tue, 14 Oct 1997 10:36:51 -0400 Received: from ece.rutgers.edu (localhost [127.0.0.1]) by localhost.localdomain (8.8.5/8.8.5) with ESMTP id KAA01469; Tue, 14 Oct 1997 10:30:13 -0400 Sender: crose@mogli.rutgers.edu Message-Id: <344381F5.8A99B815@ece.rutgers.edu> Date: Tue, 14 Oct 1997 10:30:13 -0400 From: Christopher Rose Organization: Rutgers.University X-Mailer: Mozilla 4.02b7 [en] (X11; I; Linux 2.0.30 i586) Mime-Version: 1.0 To: "Rice, Chris" Cc: 330_501@mogli.rutgers.edu Subject: Re: Allowable region of s for Laplace Transform References: <9710141254.AA09950@hoccson.ho.att.com> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Rice, Chris wrote: > > In class, we derived the Laplace transform and came up with an allowable > region for s as Re(s-a)>=0. I believe this region should be Re(s-a)>0 > (no equals). As an example, the Laplace transofrm of e^(at) is 1/(s-a). > Obviously, at Re(s-a) = 0, this transform is undefined. > > Chris Rice Yup, I agree with you! -- ********************************************************************** * Dr. Christopher Rose * * * Associate Professor of * \ / -----------> \ / * * Electrical & Computer Engineering * | | * * Rutgers University -- WINLAB * | | * * (732) 445-5250 * * * crose@ece.rutgers.edu ******************************** * http://winwww.rutgers.edu/pub/about/people/staff/crose/crose.html * ********************************************************************** From crose@ece.rutgers.edu Tue Oct 14 11:41:34 1997 X-UIDL: bb0a7c94f106ceeef299e37a7d0663ee Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA25249; Tue, 14 Oct 97 11:41:34 EDT Received: from localhost.localdomain (root@ppp-10.ts-4.nyc.idt.net [169.132.97.82]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id KAA05602 for ; Tue, 14 Oct 1997 10:39:58 -0400 Received: from ece.rutgers.edu (localhost [127.0.0.1]) by localhost.localdomain (8.8.5/8.8.5) with ESMTP id KAA01487; Tue, 14 Oct 1997 10:33:33 -0400 Sender: crose@mogli.rutgers.edu Message-Id: <344382BC.831FA8AA@ece.rutgers.edu> Date: Tue, 14 Oct 1997 10:33:32 -0400 From: Christopher Rose Organization: Rutgers.University X-Mailer: Mozilla 4.02b7 [en] (X11; I; Linux 2.0.30 i586) Mime-Version: 1.0 To: Yuqing Xie Subject: Re: Thanks References: Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Yuqing Xie wrote: > > Dr. Rose: > > I totally understand now. I should not send you the second mail.(I was not > realized what you talking about in the first mail. See how stupid I was.) > Sorry about that. > > Thank you very much. > > Becky (Yuqing) Xie Dear Becky, NO, please don't think that your question was stupid! It was a perfectly reasonable question. I was just in a big hurry when I sent you the last mail (so maybe it sounded clipped and annoyed). I'm glad you see the answer, but if you have any more questions PLEASE PLEASE PLEASE email the group/me again. Cheers, Chris Rose -- ********************************************************************** * Dr. Christopher Rose * * * Associate Professor of * \ / -----------> \ / * * Electrical & Computer Engineering * | | * * Rutgers University -- WINLAB * | | * * (732) 445-5250 * * * crose@ece.rutgers.edu ******************************** * http://winwww.rutgers.edu/pub/about/people/staff/crose/crose.html * ********************************************************************** From crose@ece.rutgers.edu Tue Oct 14 11:47:32 1997 X-UIDL: bd4a8833d7a715638b8159adee6d8087 Return-Path: Received: from localhost.localdomain (ppp-10.ts-4.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA25226; Tue, 14 Oct 97 11:37:31 EDT Received: from ece.rutgers.edu (localhost [127.0.0.1]) by localhost.localdomain (8.8.5/8.8.5) with ESMTP id KAA01469; Tue, 14 Oct 1997 10:30:13 -0400 Sender: crose@mogli.rutgers.edu Message-Id: <344381F5.8A99B815@ece.rutgers.edu> Date: Tue, 14 Oct 1997 10:30:13 -0400 From: Christopher Rose Organization: Rutgers.University X-Mailer: Mozilla 4.02b7 [en] (X11; I; Linux 2.0.30 i586) Mime-Version: 1.0 To: "Rice, Chris" Cc: 330_501@mogli.rutgers.edu Subject: Re: Allowable region of s for Laplace Transform References: <9710141254.AA09950@hoccson.ho.att.com> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Rice, Chris wrote: > > In class, we derived the Laplace transform and came up with an allowable > region for s as Re(s-a)>=0. I believe this region should be Re(s-a)>0 > (no equals). As an example, the Laplace transofrm of e^(at) is 1/(s-a). > Obviously, at Re(s-a) = 0, this transform is undefined. > > Chris Rice Yup, I agree with you! -- ********************************************************************** * Dr. Christopher Rose * * * Associate Professor of * \ / -----------> \ / * * Electrical & Computer Engineering * | | * * Rutgers University -- WINLAB * | | * * (732) 445-5250 * * * crose@ece.rutgers.edu ******************************** * http://winwww.rutgers.edu/pub/about/people/staff/crose/crose.html * ********************************************************************** From crose Wed Oct 15 12:15:41 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA26760; Wed, 15 Oct 97 12:11:40 EDT Date: Wed, 15 Oct 97 12:11:40 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710151611.AA26760@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: regrade policy Status: RO Hi Folks, Now that the solutions are out, you have a week to send me your complaints IN WRITING along with your exam. I'll regrade and that grade will be final. Don't hesitate to ask questions throug the regrade process. I'm not an ogre and will probably not dock yoy points on other sections unless I determine I was asleep when I graded them :) Cheers, Chris Rose From crose Thu Oct 16 22:06:28 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA28800; Thu, 16 Oct 97 22:05:39 EDT Date: Thu, 16 Oct 97 22:05:39 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710170205.AA28800@MOGLI.rutgers.edu> To: 330_501 Subject: potential energy Cc: crose@MOGLI.rutgers.edu Status: RO Hi Folks, I had a LOT of fun tonite! It's fun to mix it up and get a colloquy going. I hope it's not too disturbing to you when it feels like we're on shifting sands. Just rest assured that the confusion is sown with the best of intentions and I'll always stop playing around and clear it up if it gets ugly. If you HATE that, then let me know and I'll tone it down (if enough folks want me to). Otherwise get ready for a wild ride. Now remember about potential energy? Remember when I dismissively said, ENERGY IS POSITIVE! I realize I may have come on too strong there. It was really more of an incredulous question than an answer; i.e. what do you mean that ENERGY is negative!?!?!?!? Can you have negative mass (E = mc^2) !?!?!?!!? What's going on here!?!?!?!?!? So the question to you is: Is potential energy ALWAYS NON-NEGATIVE? Certainly kinetic energy is non-negative (the zero reference point is always a mass at rest in an inertial frame). However, is this always true for potential energy where you choose the reference as the zero force point? More importantly did I give away 50 cents / head in class or did I save 50 cents/head? Let's say I was goign to wager $50 a head. Would I have changed my answer? I'm not telling :) Just trying to make it interesting .... :) If it takes money... :) The ONE THING I'M NOT GOING TO MISLEAD YOU ON is that potential energy is almost ALWAYS referenced to the zero force point. At the zero force point we have zero potenial energy. The potential energy stored is the amount of work done when an object is moved from a given point to the zero force point. Remember how work is defined... integral F dot ds a contour integral of the dot product of the force vector F and the displacement path tangent ds Now, can WORK be negative or must it always be positive????? :) :) :) I JUST LOVE THIS JOB!!!!!!!! :) :) :) :) ***************************** Now as for system analogies. Let's look at the constitutive relationships of various physical components: F = ma = m x_dot_dot F = Bv = B x_dot F = Kx I = C v_dot = phi_dot_dot I = V/R = phi_dot/R I = phi/L For the way things were written here, we have capacitance analogous to mass, resistors analogous to dash pots and inductors analogous to springs (force -> current displacement -> flux (integral voltage) ) But LOOKY HERE! We could also have V = Q/C V = Q_dot R V = L Q_dot_dot in which case we have capacitance analogous to springs, resistors ARE STILL ANALOGOUS TO DASH POTS and inductors analogous to mass (force -> voltage displacement -> charge) So going back to the example in class we had a diffeq in VOLTAGE of Rv + L v_dot + RLC v_dot_dot = blah blah And OH MY GOODNESS! The terms don't seem to match up!!!!!!! Well, let's divide by RL v/L + v_dot/R + C v_dot_dot = blah blah2 OH MY GOODNESS AGAIN! This is just the same as phi/L + phi_dot/R + C phi_dot_dot = int(blah blah2) dt after we integrate both sides. (our first option of mass=capacitance and inductance = spring and I -> force and flux (integral v) -> displacement). The bottom line is you ALWAYS map energy storage elements to energy storage elements and dissipative elements to dissipative elements (like dashpots to resistors). For thermodynamic systems... Let Q be the heat flux and T the temperature. An insulator has Q = TR where R is the insulation coeff A mass of stuff has T_dot = QC where C is the thermal capacity There are no alternate energy storage elements in thermo... if you want temperature oscillations you have to use active elements. Cheers, Chris Rose PS: By the way I'd really love to see a workup of Hamiltonians for dissipative systems (HINT HINT). I've not found one simple enough to teach as part of a lecture. From crose@localhost.localdomain Thu Oct 16 23:42:33 1997 Return-Path: Received: from localhost.localdomain (ppp-19.ts-2.nyc.idt.net) by boom.rutgers.edu (4.1/SMI-4.1) id AA02337; Thu, 16 Oct 97 23:42:31 EDT Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id XAA03929; Thu, 16 Oct 1997 23:30:04 -0400 Date: Thu, 16 Oct 1997 23:30:04 -0400 From: Christopher Rose Message-Id: <199710170330.XAA03929@localhost.localdomain> To: 330_501@mogli.rutgers.edu Subject: quiz solutions Cc: crose@boom.rutgers.edu Status: RO Hi Folks, It seems that I hid the quiz solutions on the web page. I've now put them under the problem set and exams section (after the problem set 4 statement). It contains both the exam statement and the solutions (in italics). Cheers, Chris Rose From cwrice@att.com Fri Oct 17 11:22:29 1997 X-UIDL: d21fc0a27f887a7527da43498cb3d6f0 Return-Path: Received: from att.com (kcgw1.att.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA29654; Fri, 17 Oct 97 11:21:41 EDT Received: by kcgw1.att.com; Fri Oct 17 09:21 CDT 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by kcig1.att.att.com (AT&T/GW-1.0) with SMTP id JAA05307 for <330_501@mogli.rutgers.edu>; Fri, 17 Oct 1997 09:13:53 -0500 (CDT) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA06249; Fri, 17 Oct 97 10:26:58 EDT Message-Id: <9710171426.AA06249@hoccson.ho.att.com> Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id <4WKYB2S0>; Fri, 17 Oct 1997 10:23:35 -0400 From: "Rice, Chris" To: 330_501@mogli.rutgers.edu Subject: Mech-Elec Equivalents and Potential Energy Date: Fri, 17 Oct 1997 10:23:29 -0400 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: RO Dr. Rose and Class, I want to thank Dr. Rose for giving me two items in class to do - Elec/Mech Equivalents and derivation of Potential Energy/direction of force - and then doing them for me. However, he was a little too late. I had already done some work; so, here it is. As Dr. Rose gave in his E-mail, here are the Elec/Mech Equivalents: MECHANICAL: 1) F=ma=m*x_dot_dot (Force due to accelerated mass) 2) F=B*v=B*x_dot (Force due to dash-pot or piston that is moving) 3) F=k*x (Force due to compression or expansion of Spring) ELECTRICAL: 1) V=L*I_dot=L*Q_dot_dot (Voltage across an inductor with an accelerated charge) 2) V=R*I=R*Q_dot (Voltage across a resistor with a moving charge) 3) V=Q/C (Voltage across a charged capacitor) (Note: equivalence between position, x, and charge, Q) The equation in class for the electrical circuit was: A) V + L/R*V_dot = LC*Vc_dot_dot + L/R*Vc_dot + Vc, where V is the driving voltage and Vc is the voltage across the capacitor. Using Q=C*Vc and putting equation A) in terms of charge (Q), we get: B) V + L/R*V_dot = L*Q_dot_dot + L/(RC)*Q_dot + Q/C Putting equation B) into mechanical equivalent gives, C) (Drive Terms) = m*x_dot_dot + (mk)/B*x_dot + k*x = forces (Note: m=>kg, k=>kg/(sec^2), B=>kg/(sec); therefore, (mk/B)=>kg/(sec) and units are correct) POTENTIAL ENERGY: USUALLY, potential energy is referenced to a ground point (i.e. the earth's surface). Since the Earth has a radius of ~3,950 miles or ~6,360 km, and its CENTER is used for gravitational calculations {(F = G*M1*M2/(R^2), where G is the gravitational constant of 6.670*10^(-11) Newton*(meter^2)/(kg^2), M1 is the mass of object 1 (kg), M2 is the mass of object 2 (kg), R is the distance from the CENTER of object 1 to the CENTER of object 2 (meters)}. With the earth's surface as a reference, the pull of gravity is ~ constant for heights up to a 19 miles (less than one percent (1%) error). Therefore, WORK required to move an object from the earth's surface to a height (< 19 miles) above ground is m*g*h (m=> mass, g=> gravitational acceleration {9.8 meters/(sec^2)}, h=> height above ground). This is the work required to act against gravity over a distance h. A good question to ask about our class problem: can a point source (infinitesimal size) have a mass? Doesn't this violate one of Newton's LAWS (i.e. wouldn't this be energy, not mass, if it had no size?). Even with these questions, we continue. In the satellite problem in class, the two masses attract one another from the gravitational pull. In a free body diagram, we would need a force in the POSITIVE radial direction to stop the movement of the masses toward one another. This force would be G1/(r^2)*r_hat (force in the POSITIVE radial direction). Since we have REFERENCED the potential energy to r -> infinity, we need to calculate the WORK required to move the mass of the satellite, on a radial path {r_hat*dr}, from some point, r0, to infinity. This would be the {INTEGRAL from r0 to infinity of {K/(r^2)*r_hat-dot product-(r_hat*dr)}. The solution of this integral gives us the WORK or POTENTIAL ENERGY. The answer is the SAME answer as in class: K/r0, just arrived at in a slightly different manner. Chris Rice Sincerely, Christopher W. Rice AT&T, Advanced Communications Laboratory RF and Antenna Technology, Group Manager, HA6222500 67 Whippany Road, WH 15F-215 Whippany, NJ 07981 P: (973) 386-4488 F: (973) 386-7831 E: rice@ustad.att.com From crose Fri Oct 17 13:22:56 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA29796; Fri, 17 Oct 97 13:21:16 EDT Date: Fri, 17 Oct 97 13:21:16 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710171721.AA29796@MOGLI.rutgers.edu> To: 330_501@mogli.rutgers.edu, cwrice@att.com Subject: Re: Mech-Elec Equivalents and Potential Energy Cc: 330_501 Status: RO THANKS CHRIS! Mor grist for the mill! Cheers, Chris ROse From jzheng@biomed.rutgers.edu Fri Oct 17 13:46:50 1997 Return-Path: Received: from biomed.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA29934; Fri, 17 Oct 97 13:46:49 EDT Received: (from jzheng@localhost) by biomed.rutgers.edu (8.6.12+bestmx+oldruq+newsunq+grosshack/8.6.12) id MAA12922 for crose@MOGLI.rutgers.edu; Fri, 17 Oct 1997 12:34:16 -0400 Date: Fri, 17 Oct 1997 12:34:16 -0400 From: Jian Zheng Message-Id: <199710171634.MAA12922@biomed.rutgers.edu> To: crose@MOGLI.rutgers.edu Subject: Re: potential energy Status: RO Hi, If we consider the zero force point, where r = infinity, is the zero potential energy point, then at any place where r = R < infinity, an object has a negative potential energy. Think of this, if we move this object from R to infinity, we have to consume some energy, in order to counteract the force of gravity. So, we increased the potential energy of the object to zero. That means, at r = R, the object has negative potential energy. Cheers, Jian From crose Fri Oct 17 13:55:12 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA29949; Fri, 17 Oct 97 13:54:40 EDT Date: Fri, 17 Oct 97 13:54:40 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710171754.AA29949@MOGLI.rutgers.edu> To: jzheng@biomed.rutgers.edu Subject: Re: potential energy Cc: 330_501 Status: RO Thanks Jian, I'm reposting your comment: __________________________________________ Hi, If we consider the zero force point, where r = infinity, is the zero potential energy point, then at any place where r = R < infinity, an object has a negative potential energy. Think of this, if we move this object from R to infinity, we have to consume some energy, in order to counteract the force of gravity. So, we increased the potential energy of the object to zero. That means, at r = R, the object has negative potential energy. Cheers, Jian ______________________________________ I think this is at odds with what Chris Rice wrote. Chris, or anyone else, care to comment!?!??!? :) Wish I knew how to draw a devil horns smiley ! :) Also, Chris Rice graciously provided analogies between the mechanical and electrical systems. Anyone care to comment (you can look at my submission too if you'd like) on that as well? I hope you can all become professors! The job is really a blast. You stir dissention and then watch it settle in a sea of increasing understanding! In a business, you'd incur backstabbing and treachery and bad blood. here, it's all in a day's work..... :) From smajumde@caip.rutgers.edu Fri Oct 17 23:45:51 1997 Return-Path: Received: from caipfs.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA00869; Fri, 17 Oct 97 23:45:50 EDT Received: from grogg.rutgers.edu (grogg.rutgers.edu [128.6.19.59]) by caipfs.rutgers.edu (8.8.5/8.8.5) with ESMTP id WAA12030 for ; Fri, 17 Oct 1997 22:48:10 -0400 (EDT) From: Subhashis Majumder Received: (smajumde@localhost) by grogg.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.12) id WAA10820 for crose@MOGLI.rutgers.edu; Fri, 17 Oct 1997 22:48:09 -0400 Date: Fri, 17 Oct 1997 22:48:09 -0400 Message-Id: <199710180248.WAA10820@grogg.rutgers.edu> To: crose@MOGLI.rutgers.edu Subject: Re: potential energy Status: RO Dear Prof. Rose, I am taking the chance to put some comments as you asked us to do so. First of all, in the mech-electrical analogy the final equation to which Chris Rice arrived C) (Drive Terms) = m*x_dot_dot + (mk)/B*x_dot + k*x = forces has the coefficient of x_dot as mk/B, but when you derive the force equations for mechanical system this equation is simply m*x.. + b*x. + k*x . So we really did not arrive at the same equations from the two system. The actual analogy is much more simple than this. L stands for mass, R stands for damping constant and 1/C stands for spring constant K. It is derived very clearly in Kreysiz's book in the 2nd Chapter. The old version has it in section 2.12 and 2.13 called Forced oscillations. Now why did we arrive at a different solution in the class. It is because Kreyzig's book considers R, L and C in series. But we considered R and L in parallel in the class. I guess because you had drawn the damping system in parallel to the spring ( not in the conventional way as drawn in Halliday-Resnick or Kreyzig books, where the mass is directly connected to the dashpot at the other end to where the spring is connected.) (* Remember you already had some analogy in mind when you did that, as you put two specific items in parallel. Strange!!! Chicken and Egg problem *) Now the final question is whether the electrical ckt. considered in the class was right or not. I am afraid that it was not. This is because though the spring and the dashpot was in parallel, the force exerted by them simply adds up and gives the necessary resistance to the mass being moved. IT would have been the same resistance being offered if you had drawn the picture in the conventional way. But the same is not true for the electrical system. Proof - Trivial. Q.E.D. Lesson - We have to be careful when comparing between apples (mech.) and oranges (elec.) I am sorry if I have confused more. For the other problem, I think the only fault was that we did not consider the correct definition of Potential energy which is P(x) = Integral of (-F)dx and not of (Fdx) The force F = - K/(r^2) ( the -ve sign as the force is attractive, a common convention) So now P(x) = Integral of K/(r^2) which is (-K/r), Integrating from infinity to r0 we get (-K/r0). So as r0 increases the -ve value decreases and hence the potential energy increases, that's what we want as we are working against the gravitational force. If purists like Bogdan is not happy about potential energy getting negative lets add a huge positive number to bias the potential energy, doesn't really matter as P.E. is relative. Best Regards, Subhashis. P.S. Sorry for the spelling mistakes of Kreyszig, and this sentence refers to all sentences above and also to itself. From crose Sat Oct 18 03:35:28 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA01019; Sat, 18 Oct 97 03:34:45 EDT Date: Sat, 18 Oct 97 03:34:45 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710180734.AA01019@MOGLI.rutgers.edu> To: crose@MOGLI.rutgers.edu, smajumde@caip.rutgers.edu Subject: Re: potential energy Cc: 330_501 Status: RO Hi Subhashis, I'm going to repost your message to the group AND respond as well. First: If you have not already done so, take a peek at the mail I sent out before Chris Rice's message on the analogies between physical systems. That message is correct (and the example in class worked just fine under the proper assumptions... it's just that the analogy is NOT with respect to which derivatives but with respect to the state variable used). However, I agree with your moral: we need to be careful when comparing different system types! Second: I am now formally stating that potential energy CAN be negative and that your workup is ALMOST CORRECT. The expression for work is correct (the one I gave) and not int -Fdx. The issue is where your zero ref is. IN our case the ref is at infinity so P(r) = int_infty^r k/r^2 dr since we have to apply a force of k/r^2 in the r direction to move the mass (without acceleration) from infinity to position r. That is, if we just let the mass go (did not hold it back by applying force in the positive r direction) the mass would accelerate toward the r=0 point. The results is P(r) = -k/r WHICH IS NEGATIVE just as you pointed out. So, you got the right answer, but for what I consider the wrong reason :) The bottom line: everyone will be paid two quarters! It was a price I decided to pay for stirring up discussion. Hey class, how about I pay it in coca cola cans? Now, I don't want this to end discussion folks, but rather focus it. Please read and comment as you see fit. Cheers Chris Rose SUBASHIS WROTE: Dear Prof. Rose, I am taking the chance to put some comments as you asked us to do so. First of all, in the mech-electrical analogy the final equation to which Chris Rice arrived C) (Drive Terms) = m*x_dot_dot + (mk)/B*x_dot + k*x = forces has the coefficient of x_dot as mk/B, but when you derive the force equations for mechanical system this equation is simply m*x.. + b*x. + k*x . So we really did not arrive at the same equations from the two system. The actual analogy is much more simple than this. L stands for mass, R stands for damping constant and 1/C stands for spring constant K. It is derived very clearly in Kreysiz's book in the 2nd Chapter. The old version has it in section 2.12 and 2.13 called Forced oscillations. Now why did we arrive at a different solution in the class. It is because Kreyzig's book considers R, L and C in series. But we considered R and L in parallel in the class. I guess because you had drawn the damping system in parallel to the spring ( not in the conventional way as drawn in Halliday-Resnick or Kreyzig books, where the mass is directly connected to the dashpot at the other end to where the spring is connected.) (* Remember you already had some analogy in mind when you did that, as you put two specific items in parallel. Strange!!! Chicken and Egg problem *) Now the final question is whether the electrical ckt. considered in the class was right or not. I am afraid that it was not. This is because though the spring and the dashpot was in parallel, the force exerted by them simply adds up and gives the necessary resistance to the mass being moved. IT would have been the same resistance being offered if you had drawn the picture in the conventional way. But the same is not true for the electrical system. Proof - Trivial. Q.E.D. Lesson - We have to be careful when comparing between apples (mech.) and oranges (elec.) I am sorry if I have confused more. For the other problem, I think the only fault was that we did not consider the correct definition of Potential energy which is P(x) = Integral of (-F)dx and not of (Fdx) The force F = - K/(r^2) ( the -ve sign as the force is attractive, a common convention) So now P(x) = Integral of K/(r^2) which is (-K/r), Integrating from infinity to r0 we get (-K/r0). So as r0 increases the -ve value decreases and hence the potential energy increases, that's what we want as we are working against the gravitational force. If purists like Bogdan is not happy about potential energy getting negative lets add a huge positive number to bias the potential energy, doesn't really matter as P.E. is relative. Best Regards, Subhashis. P.S. Sorry for the spelling mistakes of Kreyszig, and this sentence refers to all sentences above and also to itself. From crose@localhost.localdomain Sat Oct 18 17:35:33 1997 Return-Path: Received: from localhost.localdomain (ppp-18.ts-1.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA01618; Sat, 18 Oct 97 17:35:00 EDT Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id QAA01393 for 330_501@mogli.rutgers.edu; Sat, 18 Oct 1997 16:27:05 -0400 Date: Sat, 18 Oct 1997 16:27:05 -0400 From: Christopher Rose Message-Id: <199710182027.QAA01393@localhost.localdomain> To: 330_501@mogli.rutgers.edu Subject: averages Status: RO Hi Folks, The class average was 74 (+- 26) with a high of 117 and a low of 10. I'm reasonably pleased with the outcome, but it could be better. If I had to give out grades today, class average would be a low B or possibly a C+ at the downside. I think the next section where we consider more practical stuff will be much easier and you'll blow the next exam out (I hope!) Cheers, Chris Rose From bonnzhu@eden-backend.rutgers.edu Sat Oct 18 16:46:28 1997 Return-Path: Received: from eden-backend.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA01585; Sat, 18 Oct 97 16:45:24 EDT Received: from tst001 (til216.rutgers.edu [128.6.143.71]) by eden-backend.rutgers.edu (8.8.5/8.8.5) with SMTP id PAA03646 for <330_501@mogli.rutgers.edu>; Sat, 18 Oct 1997 15:47:37 -0400 (EDT) Message-Id: <3449124F.773B@email.eden.rutgers.edu> Date: Sat, 18 Oct 1997 15:47:28 -0400 From: bonnzhu Organization: Rutgers University X-Mailer: Mozilla 3.03Gold (Win95; I) Mime-Version: 1.0 To: 330_501@mogli.rutgers.edu Subject: quiz1 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Hi 330_501, There were 33 students who participated in the QUIZ1. The mean grad is 74.3. Five are above 100, fourteen between 99 to 71 and the rest are below 70. Good luck! Bonnie From crose@localhost.localdomain Sat Oct 18 17:48:53 1997 Return-Path: Received: from localhost.localdomain (ppp-18.ts-1.nyc.idt.net) by boom.rutgers.edu (4.1/SMI-4.1) id AA02511; Sat, 18 Oct 97 17:48:51 EDT Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id RAA01633; Sat, 18 Oct 1997 17:36:22 -0400 Date: Sat, 18 Oct 1997 17:36:22 -0400 From: Christopher Rose Message-Id: <199710182136.RAA01633@localhost.localdomain> To: 330_501@mogli.rutgers.edu Subject: exam and no-class dates Cc: crose@boom.rutgers.edu Status: RO hi Folks, You already know you have an exam coming up on 10/30 in class. However, the no-class day has been CHANGED from 10/28 to 11/4 (tuesday after your exam). Please make note of this. There will be NO CLASS on TUESDAY NOVEMBER 4, 1997. Why, because 330:543 will be having their exam during your class period! Cheers, Chris Rose From 76546.2535@compuserve.com Mon Oct 20 14:31:01 1997 Return-Path: <76546.2535@compuserve.com> Received: from dub-img-4.compuserve.com by MOGLI.rutgers.edu (4.1/25-eef) id AA04010; Mon, 20 Oct 97 14:30:59 EDT Received: (from root@localhost) by dub-img-4.compuserve.com (8.8.6/8.8.6/2.7) id NAA28416 for crose@MOGLI.rutgers.edu; Mon, 20 Oct 1997 13:32:51 -0400 (EDT) Date: Mon, 20 Oct 1997 12:52:00 -0400 From: Alexandra Jacinto <76546.2535@compuserve.com> Subject: potential energy Sender: Alexandra Jacinto <76546.2535@compuserve.com> To: Christopher Rose Message-Id: <199710201254_MC2-2483-EA01@compuserve.com> Mime-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Status: RO Hi Professor Rose & Everybody, How is everybody? Regarding the question on the potential energy being positive and negative, here is what I think. I actually consulted my Physics book, under Gravitational Potential Energy (GPE), and it says that the change in GPE associated with a given displacement is defined as negative of the work done by gravitational force during that displacement. For example, we have a mass m in space and you want to move this mass from point P to Q with respect to the earth of mass Me. Let ri also be the radius from the center of the earth to mass m at point P (initial) and rf be the radius from the center of the earth to mass m at point Q (final), so the change in potential energy is delta(U) = Uf - Ui = - integral of F(r) dr from ri to rf where F = -G*Me*m/r^2 with r unit vector and the negative sign indicates that the force is attractive. Substituting, Uf - Ui = G*Me*m * integral (dr/r2) from ri to rf = -G*Me*m*[1/rf - 1/ri] The choice of a reference point for the potential energy is completely arbitrary. However, the book says that it is customary to choose the reference point where the force is zero. So taking Ui = 0 at ri = infinity, the result is U(r) = -G*Me*m/r The potential energy is negative since the force is attractive and we assume that the potential energy is zero when the particle separation is infinity. -Alexandra P.S. Prof, is this worth at least 25 cents now? :) From crose Mon Oct 20 17:10:34 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA04184; Mon, 20 Oct 97 17:08:26 EDT Date: Mon, 20 Oct 97 17:08:26 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710202108.AA04184@MOGLI.rutgers.edu> To: 76546.2535@compuserve.com Subject: Re: potential energy Cc: 330_501 Status: RO Yup, you get your 25 cents! :) Cheers, Chris Rose From erikawagner@HOTMAIL.COM Mon Oct 20 19:12:50 1997 Received: from outbound.Princeton.EDU by MOGLI.rutgers.edu (4.1/25-eef) id AA04358; Mon, 20 Oct 97 19:07:47 EDT Received: from IDENT-NOT-QUERIED@alumni.Princeton.EDU (port 57828 [204.153.50.12]) by outbound.Princeton.EDU with SMTP id <541456-15711>; Mon, 20 Oct 1997 18:08:27 -0400 Return-Path: erikawagner@hotmail.com Received: from 128.112.69.44 (comserv-dialup44.Princeton.EDU [128.112.69.44]) by alumni.Princeton.EDU (8.6.9/8.6.12) with ESMTP id SAA27640 for <330_501@MOGLI.rutgers.edu>; Mon, 20 Oct 1997 18:07:39 -0400 Message-Id: <344BD113.92B137A7@hotmail.com> Date: Mon, 20 Oct 1997 17:45:55 -0400 From: Erika Wagner Reply-To: wolfgang@alumni.Princeton.EDU Organization: Princeton '94 X-Mailer: Mozilla 4.01 (Macintosh; U; 68K) Mime-Version: 1.0 To: "330_501@MOGLI.rutgers.edu" <330_501@MOGLI.rutgers.edu> Subject: Lagrangian for non-cons. syst X-Priority: 3 (Normal) Content-Type: text/plain; charset=us-ascii; x-mac-type="54455854"; x-mac-creator="4D4F5353" Content-Transfer-Encoding: 7bit Status: RO Hi! Here's my understanding of how Lagrange's equation works for non-conservative forces: Lagrange's equation is simply an application of Newtonian equations of motion subject where a constant force of constraint, normal to the surface of motion (such as gravity) is disregarded. In the nonconservative case, the Lagrangian becomes equal to the force term, rather than zero. I have a problem I found in a book that gives the Lagrangian for a double pendulum, including a term for air friction in the solution. It's much too involved to show on E-mail, but the important feature one must remember in solving this problem is that the resistive force on a particle is proportional to its velocity, so: d/dt{dL/dx(dot)}-dL/dx = -(mu)x(dot) where mu is the coefficient of friction in air for the moving body. From jzheng@biomed.rutgers.edu Mon Oct 20 21:28:47 1997 Return-Path: Received: from biomed.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA04445; Mon, 20 Oct 97 21:28:43 EDT Received: (from jzheng@localhost) by biomed.rutgers.edu (8.6.12+bestmx+oldruq+newsunq+grosshack/8.6.12) id UAA19314; Mon, 20 Oct 1997 20:15:18 -0400 Date: Mon, 20 Oct 1997 20:15:18 -0400 From: Jian Zheng Message-Id: <199710210015.UAA19314@biomed.rutgers.edu> To: 76546.2535@compuserve.com, crose@MOGLI.rutgers.edu Subject: Re: potential energy Cc: 330_501@MOGLI.rutgers.edu Status: RO Dear Dr. Rose: Thank you. But why a discount? :) Cheers, Jian From crose Tue Oct 21 00:12:37 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA04654; Tue, 21 Oct 97 00:10:34 EDT Date: Tue, 21 Oct 97 00:10:34 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710210410.AA04654@MOGLI.rutgers.edu> To: 330_501@MOGLI.rutgers.edu, wolfgang@alumni.Princeton.EDU Subject: Re: Lagrangian for non-cons. syst Cc: crose@MOGLI.rutgers.edu Status: RO Thanks Wolfgang! I'd just found this exact form (the usual Hamiltonian description with the Lagrangian) with the addition of the appropriate loss term. maybe we'll try one in class or on the exam! Cheers, Chris Rose From crose Tue Oct 21 00:16:15 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA04671; Tue, 21 Oct 97 00:14:39 EDT Date: Tue, 21 Oct 97 00:14:39 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710210414.AA04671@MOGLI.rutgers.edu> To: jzheng@biomed.rutgers.edu Subject: Re: potential energy Cc: 330_501 Status: RO Oh yeah... it was 50 cnts right??????? Good because I just bought you all soda tonite! Cheers, Chris Rose From Becky.Xie@mci.com Tue Oct 21 10:30:05 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA05097; Tue, 21 Oct 97 10:30:04 EDT Received: from alpha.mcit.com (alpha.mcit.com [199.249.18.143]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id JAA02448 for ; Tue, 21 Oct 1997 09:27:08 -0400 Received: from omzrelay.mcit.com (omzrelay.mcit.com [166.37.204.49]) by alpha.mcit.com (8.8.7/) with ESMTP id JAA09168 for ; Tue, 21 Oct 1997 09:31:13 -0400 (EDT) Received: from imeid03.mcit.com.mci.com (imeid03.mcit.com [166.37.221.15]) by omzrelay.mcit.com (8.8.5/) with ESMTP id IAA23740 for ; Tue, 21 Oct 1997 08:31:12 -0500 (CDT) Received: from localHost ([166.44.16.164]) by imeid03.mcit.com.mci.com (Intermail v3.1 117 223) with SMTP id <19971021133110.FFSM14145@[166.44.16.164]> for ; Tue, 21 Oct 1997 08:31:10 -0500 Date: Tue, 21 Oct 1997 09:35 -0400 (EDT) From: YUQING XIE To: crose@ece.rutgers.edu Subject: Examination Solution X-Mailer: MailRoom v2.1e Message-Id: <19971021133110.FFSM14145@[166.44.16.164]> Status: RO Dr. Rose, sorry I am so far behind my intelligent classmates, always use those old problem to bother you. I have question on the solution: 2.(a).i: How do you get (x_n)^h=C(a^n) and the solution (x_n)^p=b/(1-a). 2.(d): How does form(7) <1/2(|x_1-x_2|)e^r> come from form(6) <1/2(|e^(-x_1)-e^(-x_2)|) 3.(b): I just could not understand why x(t)=(2t+1)^(1/2)? Best regards Becky (Yuqing) Xie From crose Tue Oct 21 13:38:10 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA05277; Tue, 21 Oct 97 13:37:19 EDT Date: Tue, 21 Oct 97 13:37:19 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710211737.AA05277@MOGLI.rutgers.edu> To: Becky.Xie@mci.com Subject: Re: Examination Solution Cc: 330_501, crose@MOGLI.rutgers.edu Status: RO Hi Becky, on 2a, it's a homogenous and particular solution. The homogeneous is a constant times a^n. The particular is found by assuming a solution in the same form as the input (a constant in this case) and solving for the value. on 2d, you use the mean value theorem, take a peek at chapter 1 example 1.6. On 3b you HAVE to use variable separability to get the right answer since contraction mapping won't work (the function does not satisfy the Leinitz ... sorry Lipschitz condition). HOpe that helps CHeers, CHris Rose ********************** 2.(a).i: How do you get (x_n)^h=C(a^n) and the solution (x_n)^p=b/(1-a). 2.(d): How does form(7) <1/2(|x_1-x_2|)e^r> come from form(6) <1/2(|e^(-x_1)-e^(-x_2)|) 3.(b): I just could not understand why x(t)=(2t+1)^(1/2)? ********************** From abei@us.ibm.com Wed Oct 22 00:37:10 1997 Return-Path: Received: from lms03.us.ibm.com (lms03.ny.us.ibm.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA05896; Wed, 22 Oct 97 00:37:09 EDT Received: from US.IBM.COM (d01lms03.pok.ibm.com [9.117.30.8]) by lms03.us.ibm.com (8.8.7/8.8.7) with SMTP id XAA83636 for ; Tue, 21 Oct 1997 23:36:20 -0500 Received: by US.IBM.COM (Soft-Switch LMS 2.0) with snapi via D01AU031 id 5010300010901190; Tue, 21 Oct 1997 23:38:39 -0400 From: Abe Ittycheriah To: Abe Ittycheriah , Subject: potential energy Message-Id: <5010300010901190000002L002*@MHS> Date: Tue, 21 Oct 1997 23:38:39 -0400 Mime-Version: 1.0 Content-Type: text/plain Status: RO >From Halliday&Resnick, 2nd edition pp. 109: changeInPotential = - Work = - integral from x0 to x of F dx No mention of direction of F but in general, W = integral from x0 to x of F dx , and this is positive if F lies in the direction of the path from x0 to x. "If the particle on which a force acts has a displacement opposite to the direction of the force, the work done by that force is negative". Abe From crose Wed Oct 22 12:20:43 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA06316; Wed, 22 Oct 97 12:16:13 EDT Date: Wed, 22 Oct 97 12:16:13 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710221616.AA06316@MOGLI.rutgers.edu> To: abei@us.ibm.com Subject: Re: potential energy Cc: 330_501 Status: RO Thanks Abe! Here's my version (I'll include yours as an attachment) 1) Work = int_{x_0}^x F dot dr where dr is the path differential, x_0 is the initial position and x is the final position. This is sconsonant with your equation 2) Now, the issue with potential is one of convention. The potential energy equation that H&R derive is referenced to the foce on the particle AS A FUNCTION OF IT'S POSITION. It is not considering HOW the particle is actually moved. What I showed you in class is the WORK DONE BY THE THING MOVING THE PARTICLE. What H&R show is the integral of the forces on a body as you move it (in an imaginary sense) from one point to another. So for the gravity problm (with which we're all familiar), the H&R force is downward while the displacement is upward. Thus, PE = -int_{x_0}^x (-mg) dx However, if you look at it as the work you actually have to do to lift the mass to height x from x_0 (very slowly with vanishing force imbalance) you get my expression: PE = int_{x_0}^x (mg) dx Now, you ask WHO IS RIGHT!?!?!?!?!? Well, we both are, except that you will probably get into less trouble with H&R when things get complicated. WHY? Because potential is defined IN TERMS OF A POTENTIAL FIELD (the graviatational field in this case). So you will never go wrong calculating the potential energy with the H&R method. However, if you use what I showed you blindly you could just equate work with PE no matter what. In that case, you might think that moving a block across asurface with friction stores up energy (because you do work to move it). Or as another example, if you were moving the mass through a viscous medium very rapidly from point A to point B my method (again blindly applied) would fail since part of the force you record would be frictional and not due to the force ONLY as a function of position. So to be safe, you might want to use the H&R definition (which is tried and true on undergtraduates over what must be almost half a century!). However, as long as ou move slowly (infinitessimal force imbalance) to get the mass wher you want it, you can use what I showed you. For me, the actual work you put into the object (and which gets stored) is a more intuitive way to look at it. Cheers, Chris Rose ****************************>From Halliday&Resnick, 2nd edition pp. 109: changeInPotential = - Work = - integral from x0 to x of F dx No mention of direction of F but in general, W = integral from x0 to x of F dx , and this is positive if F lies in the direction of the path from x0 to x. From crose Wed Oct 22 17:26:59 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA06679; Wed, 22 Oct 97 17:26:59 EDT Date: Wed, 22 Oct 97 17:26:59 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710222126.AA06679@MOGLI.rutgers.edu> To: jsucec@ece.rutgers.edu Subject: Re: Lagrangian and Polar Coordinates Cc: crose@MOGLI.rutgers.edu Status: RO Hi John, I still think you may be being too literal when using the word force. A force in theta IS a torque no matter how you cut it. The better way to have tought about the sattelite problem would have been to think of the mass as attached to the r=0 point though a massless infinitely extensible rod. The rod then exerts radial force on the mass and torque is applied to rotate the mass about the center point. The idea is that you have to match up the forces to the dimension of the units you're using. I thihk Chris Rice said it best when he talked about d/dtheta being unitless. Cheers, Chris Rose From jsucec@tomsriver.rutgers.edu Wed Oct 22 18:50:02 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA06810; Wed, 22 Oct 97 18:50:01 EDT Received: from tomsriver.rutgers.edu (tomsriver.rutgers.edu [128.6.214.55]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id RAA27008 for ; Wed, 22 Oct 1997 17:46:56 -0400 Received: from localhost by tomsriver.rutgers.edu (SMI-8.6/SMI-SVR4) id RAA05373; Wed, 22 Oct 1997 17:48:07 -0400 Date: Wed, 22 Oct 1997 17:48:06 -0400 (EDT) From: John Sucec To: Christopher Rose Subject: Re: Lagrangian and Polar Coordinates In-Reply-To: <9710222126.AA06679@MOGLI.rutgers.edu> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Prof. Rose, thanks for the reply. I feel comfortable now with this particular example. I still think our text should have a caveat posted next to the Lagrange's equation expressed on page 85, but the important thing for me at least, is that I now see where we have to be wary when using the non-Cartesian coordinate representations. By the way, I think the analogy I cited last night between the gradient operator for cylindrical coordinates and our satellite Lagrangian example was valid, but I may have recalled incorrectly how the r*(delta_theta) estimate is employed in the derivation of the gradient expression. That is, the r*(delta_theta) estimate may have nothing to do with the approximation of a line integral as I stated in my E-Mail (I may have been confusing the gradient derivation with the derivation of some other vector operator). I think it is safe to say, however, that the derivation of the cylindrical coordinate gradient expression uses r*(delta_theta) as an estimate of an arbitrarily small displacement in the direction of increasing theta in an analogous fashion as our expression of kinetic energy in the theta direction uses r*(theta-dot) for the satellite example. Hence, both the gradient operator and Lagrange equation require 1/r scaling factor for the term in the theta direction. Again, thanks. (A 2nd reply from you on this matter is not anticipated) ...John On Wed, 22 Oct 1997, Christopher Rose wrote: > Hi John, > > I still think you may be being too literal when using the word force. > A force in theta IS a torque no matter how you cut it. The better way > to have tought about the sattelite problem would have been to think of > the mass as attached to the r=0 point though a massless infinitely > extensible rod. > > The rod then exerts radial force on the mass and torque is applied > to rotate the mass about the center point. > > The idea is that you have to match up the forces to the dimension of > the units you're using. I thihk Chris Rice said it best when he > talked about d/dtheta being unitless. > > Cheers, > > Chris Rose > From crose Fri Oct 24 07:29:00 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA08998; Fri, 24 Oct 97 07:28:11 EDT Date: Fri, 24 Oct 97 07:28:11 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710241128.AA08998@MOGLI.rutgers.edu> To: 330_501 Subject: whoops Cc: crose@MOGLI.rutgers.edu Status: RO Hi FOlks, You can safely ignore the discussion of sorting. I posted that letter to the wrong class! Then again, I COULD put a Babbage mechanical computation engine on the linear systems (nonlinear) quiz and ... well you get the picture (just kidding). Cheers, Chris Rose From yuqing@er5.rutgers.edu Fri Oct 24 10:29:59 1997 Return-Path: Received: from er5.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA09206; Fri, 24 Oct 97 10:29:27 EDT Received: from localhost (yuqing@localhost) by er5.rutgers.edu (8.8.5/8.8.5) with SMTP id JAA09850 for <330_501@mogli.rutgers.edu>; Fri, 24 Oct 1997 09:30:40 -0400 (EDT) Date: Fri, 24 Oct 1997 09:30:39 -0400 (EDT) From: Yuqing Xie To: 330_501@mogli.rutgers.edu Subject: Only for Hongju Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Dear Hongju, could you please mail your phone number to . I want return your exam as soon as possible. Thanks Yuqing ---Sorry to bother others. From abei@us.ibm.com Fri Oct 24 22:38:33 1997 Return-Path: Received: from lms02.us1.ibm.com (lms02.ny.us.ibm.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA09799; Fri, 24 Oct 97 22:37:47 EDT Received: from d01lms03.pok.ibm.com by lms02.us1.ibm.com (AIX 4.1/UCB 5.64/4.03) id AA07710; Sat, 25 Oct 1997 01:41:51 GMT Received: by US.IBM.COM (Soft-Switch LMS 2.0) with snapi via D01AU031 id 5010300011047492; Fri, 24 Oct 1997 21:38:54 -0400 From: Abe Ittycheriah To: <330_501@Mogli.Rutgers.Edu> Subject: Re: potential energy Message-Id: <5010300011047492000002L022*@MHS> Date: Fri, 24 Oct 1997 21:38:54 -0400 Mime-Version: 1.0 Content-Type: text/plain Status: RO To all: Does anyone know why problem 2, HW#3, the solution doesn't have the property phi(t0, t0) != I where phi[t,t0] = | t 0 | from the solutions. | 0 t | Some of the other properties of fundamental matrices are also hard to check with this solution. I believe solution should be phi[t,t0] = | t-t0+1 0 | | 0 t-t0+1 | which I got by doing e ^ I * int_t0_t 1/q dq . However this solution doesn't seem to satisfy phi(t,0) = phi(t,1)*phi(1,0). Help! Abe From crose Fri Oct 24 23:23:49 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA09830; Fri, 24 Oct 97 23:23:46 EDT Date: Fri, 24 Oct 97 23:23:46 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710250323.AA09830@MOGLI.rutgers.edu> To: abei@us.ibm.com Subject: Re: potential energy Cc: crose@MOGLI.rutgers.edu Status: RO Hi Abe, If the solution does not have the property phi(t,t) = I then IT'S WRONG!!!!!!! I'll check the page and get back to you. Funny, but I JUST turned off my browser from home! :) I'll fire it up again and let you know unless someone beats me to the punch... Cheers, Chris Rose From crose Fri Oct 24 23:41:01 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA09855; Fri, 24 Oct 97 23:39:37 EDT Date: Fri, 24 Oct 97 23:39:37 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710250339.AA09855@MOGLI.rutgers.edu> To: 330_501 Subject: problem 2 ch 2 Status: RO Hi Folks, Te solution is misleading (if not wrong). The correct solution is phi(t,t_0) = [t/t_0 0] [ 0 t/t_0] The TA two years ago must have simply substituted t_0 = 1 for this case and I did not catch the error until you pointed it out. Thanks! The way you find the solution by the way is to solve for the two initial conditions x_0 = [1,0] and [0,1] (just the way you find transition matrices in the proof about properties of transition matrices). We know the solutions for x_1 and x_2 will be of the form At (by variable separability as the solution says). For an initial condition at t_0 (can't be zero in case you did not realize this :) A MUST be 1/t_0, and the solution follows from there. If you check you'll see that the matrix satisfies all the properties we know and love. Cheers, Chris Rose From abei@us.ibm.com Sat Oct 25 11:51:55 1997 Return-Path: Received: from lms02.us1.ibm.com (lms02.ny.us.ibm.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA10319; Sat, 25 Oct 97 11:51:54 EDT Received: from d01lms03.pok.ibm.com by lms02.us1.ibm.com (AIX 4.1/UCB 5.64/4.03) id AA08060; Sat, 25 Oct 1997 14:55:52 GMT Received: by US.IBM.COM (Soft-Switch LMS 2.0) with snapi via D01AU031 id 5010300011062575; Sat, 25 Oct 1997 10:52:52 -0400 From: Abe Ittycheriah To: Subject: Re: problem 2 ch 2 Message-Id: <5010300011062575000002L052*@MHS> Date: Sat, 25 Oct 1997 10:52:52 -0400 Mime-Version: 1.0 Content-Type: text/plain Status: RO Dr. Rose, Sorry to bother again, but the problem I previously mentioned also occurs in Midterm 1995, problem 2, part b, you get (though I am a bit confused about why left side of solution says phi_n+1 (t), I think it should be phi_n+1(t,t0) = ...)) phi(t,t0) = e^(A(t^2)/2) I believe again some assumption was made about t0 = 0 but in general the transition matrix should be phi(t,t0) = e^(A(t^2 - t0^2)/2) which can be found from the part c solution phi(t,t0) = exp^(int_t0_t A(tau) d(tau)) and observing when this can be applied (ie, A and int_t0_t A(tau)d(tau) have to commute). Is this correct? Abe From crose Sat Oct 25 22:08:58 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA10751; Sat, 25 Oct 97 22:08:25 EDT Date: Sat, 25 Oct 97 22:08:25 EDT From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710260208.AA10751@MOGLI.rutgers.edu> To: abei@us.ibm.com, crose@MOGLI.rutgers.edu Subject: Re: problem 2 ch 2 Cc: 330_501 Status: RO Hi , Not quite. I think in that problem the answer is in terms of (t -t_0) as opposed to t^2 - t_0^2. I'll check on monday 9no time right now) and get back toyou. Cheers, Chris Rose From matei@caip.rutgers.edu Sun Oct 26 12:54:22 1997 Return-Path: Received: from caipfs.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA11404; Sun, 26 Oct 97 12:54:21 EST Received: from ikura.rutgers.edu (ikura.rutgers.edu [128.6.43.2]) by caipfs.rutgers.edu (8.8.5/8.8.5) with ESMTP id LAA20646 for ; Sun, 26 Oct 1997 11:55:13 -0500 (EST) Received: (matei@localhost) by ikura.rutgers.edu (8.7.6/8.6.9) id LAA11382 for crose@MOGLI.rutgers.edu; Sun, 26 Oct 1997 11:55:12 -0500 (EST) From: "Bogdan Matei" Message-Id: <9710261155.ZM11380@ikura.rutgers.edu> Date: Sun, 26 Oct 1997 11:55:12 -0500 In-Reply-To: Christopher Rose "Re: problem 2 ch 2" (Oct 25, 10:08pm) References: <9710260208.AA10751@MOGLI.rutgers.edu> X-Mailer: Z-Mail (3.2.0 06sep94) To: Christopher Rose Subject: Re: problem 2 ch 2 Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Status: RO Dear Dr. Rose, I think that your solution to problem 2 ch.2 is correct because: t_0 = 1 in the expression you gave. Obviously phi(t,1) = [t 0; 0 t], satisfies all the requirements: phi(1,1) = [1 0; 0 1] = I_2; d phi(t,1) ----------- = [ 1 0 = [1/t 0 * [t 0 dt 0 1] 0 1/t] 0 t] ^ ^ | | | | A(t) phi(t,1) So the relations are verified Also the solution is x(dot) = [ t t] , which verifies the equation. When I've seen the discussions I thought that you were wrong, because my matrix was [ exp (ln(t) 0; 0 exp(ln(t)]. I was ashamed to realize that exp(ln(t) = t and in the rush I was carring that expression with me. This is happening when you apply mechanically some relations. Cheers, Bogdan -- --------------------------------------------------------| Bogdan MATEI | | OFFICE: | HOME : | CAIP | BPO 23805 PO Box 1119 | PO Box 1390 | Piscataway,NJ 08855-1119 | Piscataway, NJ 08855-1390 | (Tel) (908) 7430806 | (Tel) (908)4454268 |---------------------------| E-mail: matei@caip.rutgers.edu | Web page: http://www.caip.rutgers.edu/~matei | --------------------------------------------------------| From jsucec@ece.rutgers.edu Sun Oct 26 13:53:40 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA11452; Sun, 26 Oct 97 13:53:40 EST Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id MAA03701 for ; Sun, 26 Oct 1997 12:49:52 -0500 Date: Sun, 26 Oct 1997 12:49:52 -0500 (EST) From: John Sucec To: crose@MOGLI.rutgers.edu Subject: Sorting Network Issue (543) Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Prof. Rose, thanks for pondering the point I made at the end of 543, on Thursday, that sorting the inputs based on the desired outputs effectively eliminates the need of a subsequent shuffle exchange network for the case where all N inputs are active. The issue you cited about output conflicts not being properly processed by sorting, was an excellent counterexample. Well, I was happy to observe this morning while reading my text, that the author had the same line of thinking that I had in class! Quoting from the first paragraph of section 6.2, our author writes: "If we have a maximal connection pattern such that each input is connected to a distinct output, a sorting network for these destination requests would effectively perform the function of switching." Although I did not consider the need for output conflict resolution, this is precisely the basis on which I made class statement. Later in chapter 6, the author goes on to describe how the output address conflict for the sorting network can be resolved by adding an acknowledgement handshaking procedure to the network. Again, thanks for taking time out to consider my point. I just send this E-Mail now so it will not be thought that I was off my rocker for raising it. ...John From crose Sun Oct 26 16:11:47 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA11560; Sun, 26 Oct 97 16:11:46 EST Date: Sun, 26 Oct 97 16:11:46 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710262111.AA11560@MOGLI.rutgers.edu> To: matei@caip.rutgers.edu Subject: Re: problem 2 ch 2 Cc: crose@MOGLI.rutgers.edu Status: RO Hi Bogdan, Thanks for double checking anyway! Cheers, Chris Rose From crose Sun Oct 26 16:14:07 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA11565; Sun, 26 Oct 97 16:14:07 EST Date: Sun, 26 Oct 97 16:14:07 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710262114.AA11565@MOGLI.rutgers.edu> To: jsucec@ece.rutgers.edu Subject: Re: Sorting Network Issue (543) Cc: crose@MOGLI.rutgers.edu Status: RO Hi John, NO on will EVER think you're off your rocker. I simply did not understand your point sicne I was in mathematician mode. I'll raise the issue again some time. Please post your previous letter (and this repsonse) to the mail group. I've gotta run right now. Thanks again and ALWAYS question! That's what being a grad student is all about. From bonnzhu@eden-backend.rutgers.edu Sun Oct 26 20:45:31 1997 X-UIDL: 7506f488b8336ac9207a40bdf5566b17 Return-Path: Received: from eden-backend.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA11786; Sun, 26 Oct 97 20:44:40 EST Received: from tst001 (til109.rutgers.edu [128.6.143.34]) by eden-backend.rutgers.edu (8.8.5/8.8.5) with SMTP id TAA07585 for <330_501@mogli.rutgers.edu>; Sun, 26 Oct 1997 19:45:29 -0500 (EST) Message-Id: <3453E427.4F42@email.eden.rutgers.edu> Date: Sun, 26 Oct 1997 19:45:27 -0500 From: bonnzhu Organization: Rutgers University X-Mailer: Mozilla 3.03Gold (Win95; I) Mime-Version: 1.0 To: 330_501@mogli.rutgers.edu Subject: Change of O.H. Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Hi, I want to change the office hours for 501 from 1:10-2:10 Mon to 12:00-1:00 Mon, since I will have several important workshop to attend in the following four weeks. I hope it will not bring any unconvenience to you. Bonnie From elf_pub@email.rutgers.edu Mon Oct 27 19:08:08 1997 Return-Path: Received: from eden-backend.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA12987; Mon, 27 Oct 97 19:05:53 EST Received: from maef02.rutgers.edu (maef02.rutgers.edu [165.230.104.133]) by eden-backend.rutgers.edu (8.8.5/8.8.5) with SMTP id SAA27703 for <330_501@mogli.rutgers.edu>; Mon, 27 Oct 1997 18:06:31 -0500 (EST) Message-Id: <34550C87.23E1@email.rutgers.edu> Date: Mon, 27 Oct 1997 17:50:38 -0400 From: Public ELF Workstation Reply-To: "no reply"@eden.rutgers.edu Organization: Rutgers University Libraries X-Mailer: Mozilla 3.01 (Win16; I) Mime-Version: 1.0 To: 330_501@mogli.rutgers.edu Subject: Ch 2 Problems Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Prof. Rose, When we have degree of the numerator polynomial>= degree of the denominator poly we divide Nr br Dr and then take its Laplace or Z-transforms;don't we? If thats right, we have in Ch 2 (10) and (8) where degree of Nr= degree of Dr.So we get a constant quotient.On inv Laplace or Z-transform; doesn't it become an impulse funtion??? Regards Anagha From elf_pub@email.rutgers.edu Mon Oct 27 19:08:08 1997 Return-Path: Received: from eden-backend.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA12987; Mon, 27 Oct 97 19:05:53 EST Received: from maef02.rutgers.edu (maef02.rutgers.edu [165.230.104.133]) by eden-backend.rutgers.edu (8.8.5/8.8.5) with SMTP id SAA27703 for <330_501@mogli.rutgers.edu>; Mon, 27 Oct 1997 18:06:31 -0500 (EST) Message-Id: <34550C87.23E1@email.rutgers.edu> Date: Mon, 27 Oct 1997 17:50:38 -0400 From: Public ELF Workstation Reply-To: "no reply"@eden.rutgers.edu Organization: Rutgers University Libraries X-Mailer: Mozilla 3.01 (Win16; I) Mime-Version: 1.0 To: 330_501@mogli.rutgers.edu Subject: Ch 2 Problems Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Prof. Rose, When we have degree of the numerator polynomial>= degree of the denominator poly we divide Nr br Dr and then take its Laplace or Z-transforms;don't we? If thats right, we have in Ch 2 (10) and (8) where degree of Nr= degree of Dr.So we get a constant quotient.On inv Laplace or Z-transform; doesn't it become an impulse funtion??? Regards Anagha From crose Mon Oct 27 23:30:38 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA13191; Mon, 27 Oct 97 23:27:00 EST Date: Mon, 27 Oct 97 23:27:00 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710280427.AA13191@MOGLI.rutgers.edu> To: 330_501@mogli.rutgers.edu, no@email.rutgers.edu, reply@eden.rutgers.edu Subject: Re: Ch 2 Problems Cc: crose@MOGLI.rutgers.edu Status: RO Hi Anagha, Yup, when you have the degree of the numerator higher you've got problems doing the residues. The way to see this quickly is to think about something already in residue form (composed of a sum of terms of the form A/(s-b)^k and think abot putting it all over a common denominator. The degree of the numerator CAN NEVER be larger than that of the denominator! So, what will happen as you factor things out is taht some of the terms will have to be of the form A s^m/(s-b)^k But then you just factor out the s^m and you've got residues all over again... The only further problem is that when going to time domain you now have to figure out all thos pesky constants associated with the derivative of the time waveform (multiplication by s does not mean straight differentiation). Hope that helps! Cheers, Chris Rose From crose Mon Oct 27 23:49:32 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA13340; Mon, 27 Oct 97 23:47:12 EST Date: Mon, 27 Oct 97 23:47:12 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710280447.AA13340@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: class on tuesday Status: RO Hi Folks, There is a serious chance that I'll have to cancel class on tuesday (10/28/97). I'll send email as early as possible (probably in the early PM). I'll be at the maternity hospital (in NY) and will laptop-email from there if at all possible. 501 STUDENTS: About the test: it is commulative (covers EVERYTHING from the begnning of the term until what we've done so far and maybe a little more besides). However, it will be heavily skewed towward the systems stuff we've been doing of late with a fair amount of physical modeling and solutions. Don't worry TOO much about the Lagrangian. Anything I give you on that will be heavily guided. But you'll need to know all about linearization, laplace transforms transfer functions (that was tomorrow's lecture among other things) and everything else we've done so far. 543 STUDENTS: Everything up through and including chapter 6 is fair game. I won't have your solutions ready (probably) for the answers some of you handed in via email, but will return them with your graded quiz II at the latest. You should know all about switching and sorting and packet networks etc. I'll also almost certainly spring some probability on you! But I will carefully guide you this time. EVERYONE: if we miss tomorrow we'll have to make up the class. The only day which seems feasible is on a friday late afternoon. We'll cross that bridge (schedule a class) when we come to it if necessary. It's also possible that I might try to give you a web lecture (but don't count on it because I dont' think the technology is quite there yet.... CHEERS ALL! Chris Rose From coslit@ece.rutgers.edu Tue Oct 28 13:10:24 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA13998; Tue, 28 Oct 97 13:09:19 EST Received: (from coslit@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) id MAA10153; Tue, 28 Oct 1997 12:05:11 -0500 Date: Tue, 28 Oct 1997 12:05:11 -0500 From: Dianne Coslit Message-Id: <199710281705.MAA10153@ece.rutgers.edu> To: 330_543@mogli.rutgers.edu, 330_501@mogli.rutgers.edu Status: RO CLASSES ARE CANCELLED FOR TONIGHT. D. COSLIT ECE From crose@localhost.localdomain Tue Oct 28 23:55:32 1997 Return-Path: Received: from localhost.localdomain (ppp-11.ts-3.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA14540; Tue, 28 Oct 97 23:55:08 EST Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id MAA00683; Tue, 28 Oct 1997 12:39:47 -0500 Date: Tue, 28 Oct 1997 12:39:47 -0500 From: Christopher Rose Message-Id: <199710281739.MAA00683@localhost.localdomain> To: 330_501@mogli.rutgers.edu, 330_543@mogli.rutgers.edu Subject: class cancelled for tuesday 10/28 Cc: crose@MOGLI.rutgers.edu Status: RO Hi FOlks, Class is cancelled tonite. Baby seems to be making an entrance. Will contact 501 folks tonite or tomorrow about exam on thursday and further details. We'll need to reschedule class ... probably for a friday later in the term. Cheers, Chris Rose From crose Wed Oct 29 00:22:38 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA14649; Wed, 29 Oct 97 00:21:18 EST Date: Wed, 29 Oct 97 00:21:18 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710290521.AA14649@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: Baby Cc: crose@MOGLI.rutgers.edu Status: RO Hi FOlks, Our baby boy was born today at about 4:40 pm. Mother and baby are resting comfortably. Thanks for your forebearance (sorry I had to miss class). FOr 501 folks, exam is still on for thursday. FOr 543 solks, I'll see if we can get the solutions posted to the PS's by this weekend at the latest (friday is what I mean). Gotta go now... I'm almost asleep as you can probably tell my my typing. Cheers, Chris ROse From crose Wed Oct 29 04:07:42 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA00864; Wed, 29 Oct 97 04:06:05 EST Date: Wed, 29 Oct 97 04:06:05 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9710290906.AA00864@MOGLI.rutgers.edu> To: 330_501, 330_543 Subject: mail problems Cc: crose@MOGLI.rutgers.edu Status: RO hi Folks, I've been having some mailer problems which may have sent some confusing mail. 1) there is NO CLASS for 330_543 on this coming thursday. The exam is on tuesday and I'll have solutions to the last two PS out on the web by friday (actually Wenfeng is working on this now). 2) there is NO CLASS for 330_501 on tuesday next. Thanks for all the well wishes on the new baby. Steph and I really appreciate it. Cheers, Chris Rose From crose Thu Oct 30 01:13:27 1997 Return-Path: Received: by boom.rutgers.edu (4.1/SMI-4.1) id AB03883; Thu, 30 Oct 97 01:13:24 EST Date: Thu, 30 Oct 97 01:13:24 EST From: Mailer-Daemon (Mail Delivery Subsystem) Subject: Returned mail: User unknown Message-Id: <9710300613.AB03883@boom.rutgers.edu> To: crose Status: RO ----- Transcript of session follows ----- Connected to mogli: >>> RCPT To:<330_501@mogli> <<< 550 /usr/crose/system/501: line 44: bonnie@mogli.rutgers.edu... User unknown 550 330_501@mogli... User unknown ----- Unsent message follows ----- Return-Path: Received: by boom.rutgers.edu (4.1/SMI-4.1) id AA03881; Thu, 30 Oct 97 01:13:24 EST Date: Thu, 30 Oct 97 01:13:24 EST From: crose (Christopher Rose) Message-Id: <9710300613.AA03881@boom.rutgers.edu> To: 330_501@mogli >From jsucec@sandyhook.rutgers.edu Tue Oct 28 20:16:32 1997 Return-Path: Received: from zen.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AB00220; Tue, 28 Oct 97 20:16:28 EST Received: from ece.rutgers.edu (ece.rutgers.edu [128.6.46.12]) by zen.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id PAA16646 for ; Wed, 29 Oct 1997 15:48:47 -0500 Received: from sandyhook.rutgers.edu (sandyhook.rutgers.edu [128.6.214.54]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id PAA17190 for ; Wed, 29 Oct 1997 15:45:05 -0500 Received: from localhost by sandyhook.rutgers.edu (SMI-8.6/SMI-SVR4) id PAA09186; Wed, 29 Oct 1997 15:49:32 -0500 Date: Wed, 29 Oct 1997 15:49:31 -0500 (EST) From: John Sucec To: crose@mogli.rutgers.edu Subject: Homework 5 solutions Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Dr. Rose, I was just working on homework set 5, and there appear a couple of typos in the solutions that were posted... Concerning problem #4, Ch3 P20, it appears that an s term in the denominator is missing. This "zero pole" term is introduced at the very end of calculating the xfer function of the block diagram. That is, after deriving the "mini" xfer function of the two feedback loops, this mini-xfer function is multiplied by the xfer functions of the two blocks which sandwich the feedback loops as shown in figure P3.20. These two blocks in series with the feedback loop block contribute (s^2+s)*(s+1) to the denominator of the overall xfer function. Factoring an s out of this contribution, we obtain it in the form s*(s+1)^2, and it appears that the s term on the outside was dropped in the solution posting. Concerning problem #5, Ch3 P21, I believe that the overall xfer function given in the problem statement was simply copied incorrectly into the solution posting... If you look at the xfer function given in equation P21.9, there are no "square brackets" enclosing the product of "K constants", as shown in the solutions. This typo propogates through the rest of the solution and explains why the A matrix given in the solution is singular. Anyway, no big deal. I think I understand what's going on with these problems. If, however, someone else questions the solutions to these problems, feel welcome forward on to them my comments here. ...John PS: I looked at the ebola/AIDS epidemic equations presented in class... I now want to change the vote I made in class, so that we prioritize an AIDS vaccine higher than an ebola vaccine. From crose@localhost.localdomain Sun Nov 2 02:21:07 1997 Return-Path: Received: from localhost.localdomain (ppp-58.ts-7.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA04731; Sun, 2 Nov 97 02:20:40 EST Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id AAA03008; Mon, 3 Nov 1997 00:09:42 -0500 Date: Mon, 3 Nov 1997 00:09:42 -0500 From: Christopher Rose Message-Id: <199711030509.AAA03008@localhost.localdomain> To: 330_543@mogli.rutgers.edu Subject: An excellent Idea! Cc: 330_501@mogli.rutgers.edu Status: RO Hi Folks, A student in my linear systems class brought to my attention that I sometimes use relatively sophisticated English idioms when phrasing problems. It was felt that having a dictionary handy for translation from different languages would be helpful. SO, for those of you whose mother tongue is not English, I invite you to bring a dictionary for translation to the test tomorrow just in case you run across words which you do not understand. For those of you who speak and write English better than I do I apologize in advance for the seeming condescension. That is not my intention. I simply want everyone on equal technical footing. The nice thing about technical courses is that they are, more than many other courses, language-independent. That is, as mathematicians we speak a lovely higher form of language which travels well around the world. It therefore seems particularly distasteful to raise the spectre of plebian language difficulties in a technical course examination when it can be easily avoided. Cheers, Chris Rose PS: For 501 folks, the same rule will apply on the final. PPS: I know I DON'T HAVE TO MENTION THIS TO YOU FOLKS, but unfortunately my avatar of ECE Professor requires it: don't abuse this priviledge by bringing a reference book disguised as a dictionary. Sorrow will be your first, last and middle name :) Think of it this way. Your career is a lovely butterfly emerging from its crysalis, spreading its wings slowly, gently raising and lowering them, readying for flight in a sunlit meadow filled with flowers. A disguised reference book is the same butterfly emerging from its crysalis on a miserable rainy day in the left lane of the NJ Turnpike during rush hour :) From crose Sun Nov 2 14:01:50 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA05394; Sun, 2 Nov 97 13:58:47 EST Date: Sun, 2 Nov 97 13:58:47 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9711021858.AA05394@MOGLI.rutgers.edu> To: 330_501 Subject: NO CLASS Status: RO Remember folks, there is no class on TUesday! The 330_543 exam is taking place during your class period. Cheers From jsucec@ece.rutgers.edu Sat Nov 15 22:18:28 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA21394; Sat, 15 Nov 97 22:18:27 EST Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id WAA11793 for ; Sat, 15 Nov 1997 22:12:04 -0500 Date: Sat, 15 Nov 1997 22:12:03 -0500 (EST) From: John Sucec To: crose@MOGLI.rutgers.edu Subject: Lyapunov Class Example Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Prof. Rose, I agree with you that the selection of the energy function is not a good choice for the Lyapunov function of the spring-dashpot system. I believe, however, that your selection of V(x(t)) = (2-norm(x))^2 as the Lyapunov function is a suitable choice. Clearly, V is continuous and it also has a global minimum at x=0. The only remaining question is whether it is non-increasing in t... The solution of the system derived in class was of the form: x(t) = A*e^(a*t) + B*e^(b*t) [Eq.1] where a = e'value "1" = (-B-sqrt(B^2-4*K*m))/(2*m) [Eq.2] b = e'value "2" = (-B+sqrt(B^2-4*K*m))/(2*m) [Eq.3] B = -A [Eq.4] --> x(t) = A*(e^(a*t) - e^(b*t)) [Eq.5] Now, V(x(t)) = A^2*(e^(2*a*t) - 2*e^(a*b*t) + e^(2*b*t)) [Eq.6] Next, calculate V_dot to verify that V_dot < 0 for all t: V_dot = 2*A^2*(a*e^(2*a*t) - a*b*e(a*b*t) + b*e(2*b*t)) [Eq.7] * Since Re(a) < 0 and Re(b) < 0 when K > 0, the terms a*e^(2*a*t) and b*e^(2*b*t) will be less than 0 for all t. * Now, the only term to check is -a*b*^(a*b*t). * But, a*b = K/m > 0 --> -a*b*e(a*b*t) = -(K/m)*e^(K*t/m) < 0 * Clearly, all 3 terms of [Eq.7] are less than 0 --> V_dot<0 for all t. Since V(x(t)) is also non-increasing with respect to t, the choice of (2-norm(x))^2 is, therefore, a suitable Lyapunov function for the spring-dashpot system. This selection of the 2-norm as the Lyapunov function is similar to Ch6P12 of the 6th homework set, except that the homework set applies the 2-norm to a system described in state-space notation, instead of a system described as a differential equation as is our class example. ...John From crose Sun Nov 16 15:47:08 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22099; Sun, 16 Nov 97 15:45:40 EST Date: Sun, 16 Nov 97 15:45:40 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9711162045.AA22099@MOGLI.rutgers.edu> To: 330_501 Status: RO >From jsucec@ece.rutgers.edu Sat Nov 15 22:18:28 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA21394; Sat, 15 Nov 97 22:18:27 EST Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id WAA11793 for ; Sat, 15 Nov 1997 22:12:04 -0500 Date: Sat, 15 Nov 1997 22:12:03 -0500 (EST) From: John Sucec To: crose@MOGLI.rutgers.edu Subject: Lyapunov Class Example Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: R Prof. Rose, I agree with you that the selection of the energy function is not a good choice for the Lyapunov function of the spring-dashpot system. I believe, however, that your selection of V(x(t)) = (2-norm(x))^2 as the Lyapunov function is a suitable choice. Clearly, V is continuous and it also has a global minimum at x=0. The only remaining question is whether it is non-increasing in t... The solution of the system derived in class was of the form: x(t) = A*e^(a*t) + B*e^(b*t) [Eq.1] where a = e'value "1" = (-B-sqrt(B^2-4*K*m))/(2*m) [Eq.2] b = e'value "2" = (-B+sqrt(B^2-4*K*m))/(2*m) [Eq.3] B = -A [Eq.4] --> x(t) = A*(e^(a*t) - e^(b*t)) [Eq.5] Now, V(x(t)) = A^2*(e^(2*a*t) - 2*e^(a*b*t) + e^(2*b*t)) [Eq.6] Next, calculate V_dot to verify that V_dot < 0 for all t: V_dot = 2*A^2*(a*e^(2*a*t) - a*b*e(a*b*t) + b*e(2*b*t)) [Eq.7] * Since Re(a) < 0 and Re(b) < 0 when K > 0, the terms a*e^(2*a*t) and b*e^(2*b*t) will be less than 0 for all t. * Now, the only term to check is -a*b*^(a*b*t). * But, a*b = K/m > 0 --> -a*b*e(a*b*t) = -(K/m)*e^(K*t/m) < 0 * Clearly, all 3 terms of [Eq.7] are less than 0 --> V_dot<0 for all t. Since V(x(t)) is also non-increasing with respect to t, the choice of (2-norm(x))^2 is, therefore, a suitable Lyapunov function for the spring-dashpot system. This selection of the 2-norm as the Lyapunov function is similar to Ch6P12 of the 6th homework set, except that the homework set applies the 2-norm to a system described in state-space notation, instead of a system described as a differential equation as is our class example. ...John From crose Sun Nov 16 15:47:13 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AB22101; Sun, 16 Nov 97 15:45:40 EST Date: Sun, 16 Nov 97 15:45:40 EST From: Mail Delivery Subsystem Full-Name: Mail Delivery Subsystem Message-Id: <9711162045.AB22101@MOGLI.rutgers.edu> Subject: Returned mail: User unknown To: crose Status: RO ----- Transcript of session follows ----- Connected to eden-backend.rutgers.edu: >>> RCPT To: <<< 550 ... User unknown 550 hengwang@eden.rutgers.edu... User unknown 550 log... User unknown ----- Unsent message follows ----- Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22099; Sun, 16 Nov 97 15:45:40 EST Date: Sun, 16 Nov 97 15:45:40 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9711162045.AA22099@MOGLI.rutgers.edu> To: 330_501 >From jsucec@ece.rutgers.edu Sat Nov 15 22:18:28 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA21394; Sat, 15 Nov 97 22:18:27 EST Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id WAA11793 for ; Sat, 15 Nov 1997 22:12:04 -0500 Date: Sat, 15 Nov 1997 22:12:03 -0500 (EST) From: John Sucec To: crose@MOGLI.rutgers.edu Subject: Lyapunov Class Example Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: R Prof. Rose, I agree with you that the selection of the energy function is not a good choice for the Lyapunov function of the spring-dashpot system. I believe, however, that your selection of V(x(t)) = (2-norm(x))^2 as the Lyapunov function is a suitable choice. Clearly, V is continuous and it also has a global minimum at x=0. The only remaining question is whether it is non-increasing in t... The solution of the system derived in class was of the form: x(t) = A*e^(a*t) + B*e^(b*t) [Eq.1] where a = e'value "1" = (-B-sqrt(B^2-4*K*m))/(2*m) [Eq.2] b = e'value "2" = (-B+sqrt(B^2-4*K*m))/(2*m) [Eq.3] B = -A [Eq.4] --> x(t) = A*(e^(a*t) - e^(b*t)) [Eq.5] Now, V(x(t)) = A^2*(e^(2*a*t) - 2*e^(a*b*t) + e^(2*b*t)) [Eq.6] Next, calculate V_dot to verify that V_dot < 0 for all t: V_dot = 2*A^2*(a*e^(2*a*t) - a*b*e(a*b*t) + b*e(2*b*t)) [Eq.7] * Since Re(a) < 0 and Re(b) < 0 when K > 0, the terms a*e^(2*a*t) and b*e^(2*b*t) will be less than 0 for all t. * Now, the only term to check is -a*b*^(a*b*t). * But, a*b = K/m > 0 --> -a*b*e(a*b*t) = -(K/m)*e^(K*t/m) < 0 * Clearly, all 3 terms of [Eq.7] are less than 0 --> V_dot<0 for all t. Since V(x(t)) is also non-increasing with respect to t, the choice of (2-norm(x))^2 is, therefore, a suitable Lyapunov function for the spring-dashpot system. This selection of the 2-norm as the Lyapunov function is similar to Ch6P12 of the 6th homework set, except that the homework set applies the 2-norm to a system described in state-space notation, instead of a system described as a differential equation as is our class example. ...John From crose Sun Nov 16 15:47:12 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22089; Sun, 16 Nov 97 15:45:20 EST Date: Sun, 16 Nov 97 15:45:20 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9711162045.AA22089@MOGLI.rutgers.edu> To: jsucec@ece.rutgers.edu Subject: Re: Lyapunov Class Example Cc: 330_501 Status: RO John, I'm posting your solution for perusal by the class. Thanks for finding it. However, th energy function SHOULD be a good Lyapunov function since it's always decreasing, even if I was unable to show it quickly :0 Cheers, Chris Rose From crose Sun Nov 16 15:47:16 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AB22092; Sun, 16 Nov 97 15:45:20 EST Date: Sun, 16 Nov 97 15:45:20 EST From: Mail Delivery Subsystem Full-Name: Mail Delivery Subsystem Message-Id: <9711162045.AB22092@MOGLI.rutgers.edu> Subject: Returned mail: User unknown To: crose Status: RO ----- Transcript of session follows ----- Connected to eden-backend.rutgers.edu: >>> RCPT To: <<< 550 ... User unknown 550 hengwang@eden.rutgers.edu... User unknown 550 log... User unknown ----- Unsent message follows ----- Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22089; Sun, 16 Nov 97 15:45:20 EST Date: Sun, 16 Nov 97 15:45:20 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9711162045.AA22089@MOGLI.rutgers.edu> To: jsucec@ece.rutgers.edu Subject: Re: Lyapunov Class Example Cc: 330_501 John, I'm posting your solution for perusal by the class. Thanks for finding it. However, th energy function SHOULD be a good Lyapunov function since it's always decreasing, even if I was unable to show it quickly :0 Cheers, Chris Rose From crose@localhost.localdomain Mon Nov 17 11:11:06 1997 Return-Path: Received: from localhost.localdomain (ppp-38.ts-10.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA22931; Mon, 17 Nov 97 11:08:05 EST Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id LAA00947 for 330_501@mogli.rutgers.edu; Mon, 17 Nov 1997 11:55:07 -0500 Date: Mon, 17 Nov 1997 11:55:07 -0500 From: Christopher Rose Message-Id: <199711171655.LAA00947@localhost.localdomain> To: 330_501@mogli.rutgers.edu Subject: test II Status: RO Hi Folks, Just entered the results of quiz II. NO SODA FOR YOU!!!!! :) However, I am taking orders now for the final :) Here's the average stuff: mean sd Hi Lo 79.8214 37.8711 157 0 Here's the specific stuff. For those of you who did not opt out of the second exam (because of graduate orals for instance), your grades are included here for both exams you've taken. Check your student ID (last 4 digits) against the list and ALSO check the grade you received on the first quiz (just to make sure we have no recording errors). You might like to know who XXXX is. Well, if you've never provided your SSN, then you know who you are! Of course, you realize I'll have to have it to assign what looks like it's going to be a rather nice final grade :) Cheers ALL! SSN Q1 Q2 __________________ 0786 35 15 6752 79 75 1171 117 65 3106 20 0 2271 84 60 5407 71 100 9782 67 49 4920 100 120 2564 75 42 2586 99 97 0831 85 79 2244 114 157 xxxx 95 145 9910 83 105 9930 79 62 5992 74 95 8931 60 75 4974 63 49 0258 105 120 4667 47 40 0373 37 15 2537 112 80 0486 97 95 1439 63 55 1368 80 110 I'll post a picture later showing how I'd assign grades if I had to do so today (scatterplot with the grades). From crose Mon Nov 17 12:58:28 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA23091; Mon, 17 Nov 97 12:56:09 EST Date: Mon, 17 Nov 97 12:56:09 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9711171756.AA23091@MOGLI.rutgers.edu> To: 330_501 Subject: grading errors Status: RO Hi Folks, Please check your grades (both of them) against your new exam (tomorrow) and old exam (quiz I). There's been at least one error and another suspected error in the grade compilations. Below is a COMPLETE LIST of grades from the first quiz: SSN Q1 Q2 6281 37 X 0786 35 15 6752 79 75 1171 117 65 3106 20 0 2271 84 60 5407 71 100 9782 67 49 4920 100 120 2564 75 42 2586 104 97 8621 115 X 0831 85 79 2244 114 157 xxxx 95 145 9910 83 105 7915 64 X 9930 79 62 5992 74 95 8931 60 75 4974 63 49 1318 76 X 0258 105 120 4667 47 40 xxxx 58 X 0373 37 15 2537 112 80 0486 97 95 4657 85 X 5405 65 X 1439 63 55 1368 80 110 From crose@localhost.localdomain Mon Nov 17 21:22:09 1997 Return-Path: Received: from localhost.localdomain (ppp-38.ts-10.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA23742; Mon, 17 Nov 97 21:20:37 EST Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id WAA03086 for 330_501@mogli.rutgers.edu; Mon, 17 Nov 1997 22:07:33 -0500 Date: Mon, 17 Nov 1997 22:07:33 -0500 From: Christopher Rose Message-Id: <199711180307.WAA03086@localhost.localdomain> To: 330_501@mogli.rutgers.edu Subject: solutions Status: RO hi Folks, The exam solutions are out (in case I forgot to tell you) on the web page. From cwrice@att.com Wed Nov 19 09:00:31 1997 X-UIDL: 89dd729a661012f7943200635cd89173 Return-Path: Received: from zen.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA25464; Wed, 19 Nov 97 09:00:30 EST Received: from att.com (kcgw1.att.com [192.128.133.151]) by zen.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id IAA11330 for ; Wed, 19 Nov 1997 08:53:48 -0500 Received: by kcgw1.att.com; Wed Nov 19 07:55 CST 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by kcig1.att.att.com (AT&T/GW-1.0) with SMTP id HAA02403 for ; Wed, 19 Nov 1997 07:47:29 -0600 (CST) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA14268; Wed, 19 Nov 97 09:02:43 EST Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id ; Wed, 19 Nov 1997 08:58:15 -0500 Message-Id: From: "Rice, Chris" To: crose@ece.rutgers.edu Cc: "Dodley, JP" Subject: ECE542 in the Spring Date: Wed, 19 Nov 1997 08:57:51 -0500 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: RO Dr. Rose, Two questions: 1) Will you be teaching the ECE542 Informaton Theory and Coding Class in the Spring?, and 2) If so, what is the book that you will be using? I sent this to you directly because I felt it was not of general interest to the class. Please feel free to post this message with your answer if you think the class would be interested. Sincerely, Chris Rice From crose@ece.rutgers.edu Wed Nov 19 15:52:30 1997 X-UIDL: 0c5e3a94ca784b92384d1b0d9bcf0e58 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA25911; Wed, 19 Nov 97 15:52:29 EST Received: from localhost.localdomain (root@ppp-10.ts-5.nyc.idt.net [169.132.97.154]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id PAA16887 for ; Wed, 19 Nov 1997 15:45:23 -0500 Received: from ece.rutgers.edu (localhost [127.0.0.1]) by localhost.localdomain (8.8.5/8.8.5) with ESMTP id QAA00933; Wed, 19 Nov 1997 16:32:43 -0500 Sender: crose@mogli.rutgers.edu Message-Id: <34735AFB.22C469CF@ece.rutgers.edu> Date: Wed, 19 Nov 1997 16:32:43 -0500 From: Christopher Rose Organization: Rutgers.University X-Mailer: Mozilla 4.03 [en] (X11; I; Linux 2.0.30 i586) Mime-Version: 1.0 To: "Rice, Chris" , 330_501@mogli.rutgers.edu, 330_543@mogli.rutgers.edu Subject: Re: ECE542 in the Spring References: Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Rice, Chris wrote: > > Dr. Rose, > > Two questions: > > 1) Will you be teaching the ECE542 Informaton Theory and Coding Class > in the Spring?, and > 2) If so, what is the book that you will be using? > > I sent this to you directly because I felt it was not of general > interest to the class. Please feel free to post this message with your > answer if you think the class would be interested. > > Sincerely, > > Chris Rice Hi Chris, (Great Name!) Unfortunately, I'm on sabbatical next term and won't be teaching anything. However, I plan to offer IT in spring 1999. It think you'd LOVE the course since it's analytic but tells you a lot about the way the world operations. For example, in the networks course there was a problem on sorting which is intimately related to IT concepts. The book (WHICH I ABSOLUTELY LOVE) is Tom Cover's (Stanford) book (and Joy Thomas, one of Tom's old students) entitled Elements of Information Theory (WILEY) it's only "flaw" is that it has NO error correction coding. But for me, that's a benefit as opposed to a liability since it allows the freedom to explore the many ramifications of IT (statistics, stock market, thermodynamics among others). Cheers, Chris Rose -- ********************************************************************** * Dr. Christopher Rose * * * Associate Professor of * \ / -----------> \ / * * Electrical & Computer Engineering * | | * * Rutgers University -- WINLAB * | | * * (732) 445-5250 * * * crose@ece.rutgers.edu ******************************** * http://winwww.rutgers.edu/pub/about/people/staff/crose/crose.html * ********************************************************************** From crose@ece.rutgers.edu Mon Dec 1 15:49:56 1997 X-UIDL: 1c8d4d0df5e33660ddf6c67909cbce1a Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA08798; Mon, 1 Dec 97 15:49:56 EST Received: from localhost.localdomain (root@ppp-26.ts-1.nyc.idt.net [169.132.96.26]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with ESMTP id PAA17351 for ; Mon, 1 Dec 1997 15:40:37 -0500 Received: from ece.rutgers.edu (localhost [127.0.0.1]) by localhost.localdomain (8.8.5/8.8.5) with ESMTP id QAA00943; Mon, 1 Dec 1997 16:33:41 -0500 Sender: crose@mogli.rutgers.edu Message-Id: <34832D34.5ACE6CCE@ece.rutgers.edu> Date: Mon, 01 Dec 1997 16:33:40 -0500 From: Christopher Rose Organization: Rutgers.University X-Mailer: Mozilla 4.03 [en] (X11; I; Linux 2.0.30 i586) Mime-Version: 1.0 To: Anagha Kelkar Cc: 330_501@mogli.rutgers.edu Subject: Re: Fixed points References: Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Status: RO Anagha Kelkar wrote: > > Prof. Rose, > > What is the difference between fixed point and limit points? > When are they the same?? > > Regards > Anagha HI, Fixed point is any point where the system is stationary (mapping maps to the same point ---> this means xdot = 0 for diff eqs and x(n+1) = x (n) for discrete maps). A Limit point is a fixed point which is approached through state evolution. So for example, in the inverted pendulum problem you have two fixed points but only one limit point ( when there is damping that is). Cheers -- ********************************************************************** * Dr. Christopher Rose * * * Associate Professor of * \ / -----------> \ / * * Electrical & Computer Engineering * | | * * Rutgers University -- WINLAB * | | * * (732) 445-5250 * * * crose@ece.rutgers.edu ******************************** * http://winwww.rutgers.edu/pub/about/people/staff/crose/crose.html * ********************************************************************** From anagha@er7.rutgers.edu Wed Dec 3 18:50:49 1997 Return-Path: Received: from er7.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA11792; Wed, 3 Dec 97 18:48:32 EST Received: (from anagha@localhost) by er7.rutgers.edu (8.8.5/8.8.5) id SAA02913 for 330_501@MOGLI.rutgers.edu; Wed, 3 Dec 1997 18:43:56 -0500 (EST) Date: Wed, 3 Dec 97 18:43:55 EST From: Anagha Kelkar To: 330_501@MOGLI.rutgers.edu Subject: Controllability Gramian Message-Id: Status: R Prof Rose, How do we find the controllability Gramian for a non-linera system? Do we linearise the equation always? what if it cannot be linearised??? Regards Anagha From crose Wed Dec 3 19:23:05 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA11845; Wed, 3 Dec 97 19:21:29 EST Date: Wed, 3 Dec 97 19:21:29 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9712040021.AA11845@MOGLI.rutgers.edu> To: anagha@eden.rutgers.edu Subject: Re: Controllability Gramian Cc: 330_501 Status: R We've not defined controllability for nonlinear systems. Too hard. Just linearize as you suggest From crose@localhost.localdomain Fri Dec 5 00:22:47 1997 Return-Path: Received: from localhost.localdomain (ppp-56.ts-6.nyc.idt.net) by boom.rutgers.edu (4.1/SMI-4.1) id AA04080; Fri, 5 Dec 97 00:22:41 EST Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id BAA03185; Fri, 5 Dec 1997 01:08:12 -0500 Date: Fri, 5 Dec 1997 01:08:12 -0500 From: Christopher Rose Message-Id: <199712050608.BAA03185@localhost.localdomain> To: 330_501@mogli.rutgers.edu Subject: ARRRGGGGGGGHHHHH! Cc: crose@boom.rutgers.edu Status: R r is not the rank of A!!!! It's the rank of the controllability matrix K!!!!! I remember vaguely writing r as rank of A on the board when I meant to write K AAAARRRRRRGGGGGGHHHH! Sorry for the inconvenience. Cheers From bahl@microsoft.com Fri Dec 12 14:49:20 1997 Return-Path: Received: from mail5.microsoft.com by MOGLI.rutgers.edu (4.1/25-eef) id AA22491; Fri, 12 Dec 97 14:49:19 EST Received: by mail5.microsoft.com with Internet Mail Service (5.5.1960.3) id ; Fri, 12 Dec 1997 11:37:50 -0800 Message-Id: <01A42EDE8A6CCF118F3E00805FD4AC53031A961E@red-76-msg.dns.microsoft.com> From: Victor Bahl To: Nomadic Communications Cc: 'Imrich Chlamtac' , "'Dave B. Johnson'" , 'Chris Rose' , 'On-Ching Yue' , 'Ramon Caceres' , 'Lisette Burgos' , 'Jason Redi' Subject: FYI: New IEEE Wireless Communications and Networking Conference Date: Fri, 12 Dec 1997 11:38:35 -0800 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.5.1960.3) Content-Type: text/plain; charset="ISO-8859-1" Status: R IEEE ComSoc Agrees to Link '99 Wireless Conference to PCIA Event Contact: Jack Howell, (212) 705-8421, j.howell@comsoc.org NEW YORK, 1 December 1997 -- The IEEE Communications Society has signed an agreement with the Personal Communications Industry Association to hold the IEEE Wireless Communications and Networking Conference (WCNC) in conjunction with PCIA's Personal Communications Showcase '99 (PCS '99) in New Orleans, 22-27 Sept 1999. The official agreement was signed by IEEE Communications Society President Steve Weinstein; Tom Plevyak, president-elect; Jack Howell, executive director; and PCIA President Jay Kitchen " The partnering provides a great opportunity for both the IEEE and the PCIA to broaden their reach," said Weinstein. "Together WNCN and PCS '99 provide a forum that will enable conference participants to draw from the full spectrum of information -- from technical development to product delivery -- required to maintain a competitive edge " With the addition of WCNC's programming, technical depth is assured for show attendees according to technical program chair Jerry Gibson, Southern Methodist University EE department chair and well-known editor and author in the mobile communications field. "Our call for papers and tutorials will feature the following wireless topics: ATM, Internet, multimedia, networking, and standards. It also will cover smart antennas, channel assignment schemes, compression, handoff algorithms, mobility, modulation and coding, multiple access techniques, power control, security and field studies," said Gibson. IEEE Communications Society technical committees to be directly involved are Personal Communications, Communications Theory, Computer Communications, Radio Communications, and Satellite and Space Communication. The IEEE Wireless Communications and Networking Conference (WCNC), an expanded format of the IEEE International Conference on Universal Personal Communication (ICUPC), is the world's foremost international technical conference for engineers and researchers at the forefront of development and deployment of digital cellular, PCS and the full spectrum of supporting wireless technologies. The Personal Communications Showcase is the world's largest wireless exhibition and conference to date. Produced annually by PCIA, PCS offers an unmatched combination of quality educational programming and a cutting-edge exhibition. # # # Version For Leadership Wire/Society Sentinel The IEEE Communications Society has signed an agreement with the Personal Communications Industry Association to hold the IEEE Wireless Communications and Networking Conference (WCNC) in conjunction with PCIA's Personal Communications Showcase '99 (PCS '99) in New Orleans, 22-27 Sept 1999. This brings together the world's foremost international technical conference for engineers and researchers in the field, and the world's largest wireless exhibition and conference to date. The WCNC is an expanded format of the IEEE International Conference on Universal Personal Communication (ICUPC). Jerry Gibson, Southern Methodist University EE department chair, and well-known editor and author in the mobile communications field, will chair the IEEE technical program. Papers and tutorials will feature numerous wireless topics including ATM, Internet, multimedia, networking and standards. They also will cover smart antennas, channel assignment schemes, compression, handoff algorithms, mobility, modulation and coding, multiple access techniques, power control, security and field studies. IEEE ComSoc technical committees to be directly involved are Personal Communications, Communications Theory, Computer Communications, Radio Communications, and Satellite and Space Communication. From crose Fri Dec 12 14:48:55 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA22484; Fri, 12 Dec 97 14:45:42 EST Date: Fri, 12 Dec 97 14:45:42 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9712121945.AA22484@MOGLI.rutgers.edu> To: abei@us.ibm.com, crose@MOGLI.rutgers.edu Subject: Re: final Cc: 330_501, 330_543 Status: R Hi Abe, I've never had an open book final. And yest, you can have thre sheets both sides of notes! Cheers, Chris ROse From abei@us.ibm.com Sat Dec 13 12:48:06 1997 Return-Path: Received: from smtp4.ny.us.ibm.COM by MOGLI.rutgers.edu (4.1/25-eef) id AA23549; Sat, 13 Dec 97 12:48:05 EST Received: from relay1.server.ibm.com (relay1.server.ibm.com [9.14.2.98]) by smtp4.ny.us.ibm.COM (8.8.7/8.8.7) with ESMTP id MAA12880; Sat, 13 Dec 1997 12:43:00 -0500 Received: from US.IBM.COM (d01lms03.pok.ibm.com [9.117.30.8]) by relay1.server.ibm.com (8.8.7/8.7) with SMTP id MAA71570; Sat, 13 Dec 1997 12:41:25 -0500 Received: by US.IBM.COM (Soft-Switch LMS 2.0) with snapi via D01AU032 id 5010300013427775; Sat, 13 Dec 1997 12:40:52 -0500 From: Abe Ittycheriah To: , <330_501@MOGLI.rutgers.edu> Subject: Trajectory Control Message-Id: <5010300013427775000002L052*@MHS> Date: Sat, 13 Dec 1997 12:40:52 -0500 Mime-Version: 1.0 Content-Type: text/plain Status: R Dr. Rose, You set up the problem: If K is full rank, is the system always trajectory controllable? You said no it wasn't and started the proof. I tried to continue from there: since from the state space relations: X(s) = (sI - A)^-1 B U(s) and we know the X(s) we need, we can find U(s) = B^-1 (sI-A) X(s) However, K being full rank doesn't imply B^-1 exists. Only that there are n independent vectors in K = [B BA BA^2 ...]. Is this the gist of the proof? Abe From crose Sat Dec 13 16:11:34 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA23766; Sat, 13 Dec 97 16:10:46 EST Date: Sat, 13 Dec 97 16:10:46 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9712132110.AA23766@MOGLI.rutgers.edu> To: abei@us.ibm.com Subject: Re: Trajectory Control Cc: 330_501@mogli.rutgers.edu Status: R Yup, that's the gist! Except you need a funny sort of inversion when B is not square (as it often is not). Ie, left inverse. That was too complicated to go into given half the class has not had a formal linear algebra course. Cheers, Chris Rose From wougk@worldnet.att.net Mon Dec 15 10:20:41 1997 Return-Path: Received: from mtigwc04.worldnet.att.net by MOGLI.rutgers.edu (4.1/25-eef) id AA25432; Mon, 15 Dec 97 10:20:41 EST Received: from LOCALNAME ([12.68.157.175]) by mtigwc04.worldnet.att.net (post.office MTA v2.0 0613 ) with SMTP id AAA7427 for ; Mon, 15 Dec 1997 15:14:05 +0000 X-Sender: wougk@postoffice.worldnet.att.net (Unverified) X-Mailer: Windows Eudora Light Version 1.5.2 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: Christopher Rose From: Harald Wougk Subject: Final Exam Date: Mon, 15 Dec 1997 15:14:05 +0000 Message-Id: <19971215151403.AAA7427@LOCALNAME> Status: R Hello Professor Rose, I would just like to review with you why I am attending your 501 class and taking the exams. I am preparing for the master's comprehensive exam in the spring. When I took the class some three years ago Dr. Puri taught the course. Since you are preparing the 501 portion of the exam I understand it would be a good idea to be familiar with the material you present. (There are differences in the material taught between you and Dr. Puri. Dr. Puri included complex integration while you do not and you present measure theory and linearization where Dr. Puri did not). If you do not object I would like to take the final exam. This will help my preparation for the comprehensive exam. Thanks, Harry From jsucec@ece.rutgers.edu Tue Dec 16 02:10:58 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA26199; Tue, 16 Dec 97 02:10:27 EST Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id BAA18514; Tue, 16 Dec 1997 01:58:33 -0500 Date: Tue, 16 Dec 1997 01:58:33 -0500 (EST) From: John Sucec To: crose@MOGLI.rutgers.edu Cc: 330_501@MOGLI.rutgers.edu Subject: Want your 50 cents back? Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO Prof. Rose, earlier this evening I was reading the 501 discussion group E-Mails from October on the debate of whether potential energy can be negative or not. A lot of fascinating comments were offered. However, I am convinced that it is NOT possible for potential energy to be negative. Call me closed minded, but here is my reasoning... You can obtain the potential energy of an object at position x and acted on by a force F, by applying a line integral of the force, "in the direction of the force", between position x and the zero energy point. What I mean by "in the direction of the force", is that if the vector valued function is negative, as in the case of the restorative force of a spring and for the attractive force of gravity, then the line integral will be evaluated from b to a, where b > a. That is, the limits of integration for the line integral of the spring constant force will be from x to 0 (or to whatever happens to be the rest position of the spring) and from infinity (the zero energy point for the gravitional field) to x in the case of the line integral of the gravitational force. The potential energy (PE) integrals thus derived are as follows: PE(spring) = INT(from x to 0){-k*w}dw = -(1/2)*k*w^2 (evaluated at 0 and at x) = -(1/2)*k(0)^2 - (-(1/2)*k*x^2) = (1/2)*k*x^2 > 0 QED PE(gravity) = INT(from infinity to x){-G*m1*m2/(r^2)}dr = G*m1*m2/r (evaluated at x and at infinity) = G*m1*m2/x - G*m1*m2/(infinity) = G*m1*m2/x > 0 as x being a radius is > 0 QED I think the arguments for energy being negative were based on the concept of WORK, which is not the same concept as energy. That is, work can be evaluated to a negative value because it is a special application of energy. In other words, we have the notion of being able to inject energy into a system (positive work) and of being able to harness energy from a system (negative work). Potential energy, on the other hand is an absolute concept, as per the specification of the potential energy line integral given above. So, if you want to recover the 50 cents you spent on soda for me, earlier this semester, just let me know. ...John From cwrice@att.com Tue Dec 16 09:03:48 1997 Return-Path: Received: from att.com (kcgw2.att.com) by MOGLI.rutgers.edu (4.1/25-eef) id AA26449; Tue, 16 Dec 97 09:01:54 EST Received: by kcgw2.att.com; Tue Dec 16 07:39 CST 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by kcig2.att.att.com (AT&T/GW-1.0) with SMTP id HAA01593 for <330_501@mogli.rutgers.edu>; Tue, 16 Dec 1997 07:44:09 -0600 (CST) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA01185; Tue, 16 Dec 97 08:59:49 EST Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id ; Tue, 16 Dec 1997 08:55:15 -0500 Message-Id: From: "Rice, Chris" To: 330_501@mogli.rutgers.edu Subject: Exam Questions Date: Tue, 16 Dec 1997 08:55:25 -0500 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: R Dr. Rose, Two questions: 1) In class we said, if Re(Lambdai)<0, then asymptotically stable. Should this not be GLOBALLY ASYMPTOTICALLY STABLE? If not, why not? 2) Again in class, THM: Using the characteristic eqn (SUM(pk*sk), k=0 to n) If matrix A has Re(Lambdai)<0, then Pk>0. SHOULD this not be Pk>=0. If not, why not? That's all for now. Thanks, > Christopher W. Rice > AT&T, Advanced Communications Laboratory > 67 Whippany Road, WH 15F-215 > Whippany, NJ 07981 > P: (973) 386-4488 > F: (973) 386-7831 > E: cwrice@att.com > > From abei@us.ibm.com Tue Dec 16 10:59:11 1997 Return-Path: Received: from smtp4.ny.us.ibm.COM by MOGLI.rutgers.edu (4.1/25-eef) id AA26580; Tue, 16 Dec 97 10:59:10 EST Received: from relay1.server.ibm.com (relay1.server.ibm.com [9.14.2.98]) by smtp4.ny.us.ibm.COM (8.8.7/8.8.7) with ESMTP id KAA41732 for ; Tue, 16 Dec 1997 10:53:27 -0500 Received: from US.IBM.COM (d01lms03.pok.ibm.com [9.117.30.8]) by relay1.server.ibm.com (8.8.7/8.7) with SMTP id KAA36416 for ; Tue, 16 Dec 1997 10:51:35 -0500 Received: by US.IBM.COM (Soft-Switch LMS 2.0) with snapi via D01AU032 id 5010300013543928; Tue, 16 Dec 1997 10:51:30 -0500 From: Abe Ittycheriah To: Subject: transition matrix question Message-Id: <5010300013543928000002L082*@MHS> Date: Tue, 16 Dec 1997 10:51:30 -0500 Mime-Version: 1.0 Content-Type: text/plain Status: R In the Fall 1995 midterm, in question 2, part b, we are given system x' = tAx(t) where x' is derivative of x. We are asked to use the convergence property of the mapping x_n+1 (t) = x_n (t0) + int_t0_t f(x,sigma) dsigma to find the transition matrix. Looking at your solutions, you chose t0 = 0, but in general if you keep the t0 and try to work it, the math gets really ugly. So is there a trick to consider the general case where t0 is not 0? Abe From crose Tue Dec 16 12:31:26 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA26675; Tue, 16 Dec 97 12:31:24 EST Date: Tue, 16 Dec 97 12:31:24 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9712161731.AA26675@MOGLI.rutgers.edu> To: abei@us.ibm.com Subject: Re: transition matrix question Cc: crose@MOGLI.rutgers.edu Status: R Abe, Try posting that question to the group. But the answer is that YES it gets ugly for t != 0 :) From jsucec@ece.rutgers.edu Tue Dec 16 13:44:15 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA26773; Tue, 16 Dec 97 13:42:43 EST Received: from localhost (jsucec@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id NAA07334; Tue, 16 Dec 1997 13:30:43 -0500 Date: Tue, 16 Dec 1997 13:30:43 -0500 (EST) From: John Sucec To: Christopher Rose Cc: 330_501@MOGLI.rutgers.edu Subject: Re: Want your 50 cents back? In-Reply-To: <9712160744.AA26230@MOGLI.rutgers.edu> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: R Prof. Rose, thanks for replying to my E-Mail. Concerning the expression mgh, I contend that it does not represent the potential energy for any natural system of which I am aware. I think what it represents is an approximation of the amount of Work done in moving an from some arbitrary reference point 0 (e.g., surface of the Earth) to a point h. That is, per the E-Mail of Chris Rice back on 17-Oct-97, this linear approximation of the force of gravity is a valid approximation of the net change in potential energy (i.e., Work) to within 1% when moving an object in the range bounded by the Earth's surface up to 19 miles in altitude. I am not certain if I can explain adequately why h<0 for mgh is not a valid expression for potential energy, so I will simply ask this question: What natural system has a potential energy equation that is represented by mgh where h can be < 0 (being careful here not to confuse Work with potential energy)? For example, suppose for the sake of argument we let h=-1. Then, h=-1 becomes the true zero reference where h'=0 <--> h=-1. Therefore, we can always shift the zero reference point such that we have no h'<0. Anyway, sorry I can not provide at this time a killer argument for why mgh represents only another expression contrived for calculating Work. Maybe someone else has a concise and complete explaination already formulated that can be shared with the class... I am afraid, however, there may be little time left for that. ...John On Tue, 16 Dec 1997, Christopher Rose wrote: > HI John, > > Consider a ball at height h=0. You get the usual mgh as it's potential energy. > > So what happens when the ball is lower than h=0? > > PE is usually referenced to the zero force point, but can be referenced anywhere > as long as you keep track of where. > > SO, I think taht soda is long gone and you earned it! > > Cheers, > > Chris Rose > From abei@us.ibm.com Wed Dec 17 22:41:33 1997 X-UIDL: 0a184394a338ac98722a4dfa4b0647e5 Return-Path: Received: from smtp3.ny.us.ibm.com by MOGLI.rutgers.edu (4.1/25-eef) id AA28002; Wed, 17 Dec 97 22:41:32 EST Received: from relay1.server.ibm.com (relay1.server.ibm.com [9.14.2.98]) by smtp3.ny.us.ibm.com (8.8.7/8.8.7) with ESMTP id WAA21542 for ; Wed, 17 Dec 1997 22:32:36 -0500 Received: from US.IBM.COM (d01lms03.pok.ibm.com [9.117.30.8]) by relay1.server.ibm.com (8.8.7/8.7) with SMTP id WAA31676 for ; Wed, 17 Dec 1997 22:33:49 -0500 Received: by US.IBM.COM (Soft-Switch LMS 2.0) with snapi via D01AU032 id 5010300013638612; Wed, 17 Dec 1997 22:33:31 -0500 From: Abe Ittycheriah To: Subject: final and grade Message-Id: <5010300013638612000002L022*@MHS> Date: Wed, 17 Dec 1997 22:33:31 -0500 Mime-Version: 1.0 Content-Type: text/plain Status: RO Dr. Rose, Can you send me my final score and the grade in the class? Can I pick up my final from somewhere - a dept. secretary or if you are around? Abe From srinis@ece.rutgers.edu Mon Dec 22 11:03:23 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA00554; Mon, 22 Dec 97 11:03:22 EST Received: (from srinis@localhost) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) id KAA05022 for crose@ece; Mon, 22 Dec 1997 10:50:19 -0500 Date: Mon, 22 Dec 1997 10:50:19 -0500 From: Suchitra Srinivasan Message-Id: <199712221550.KAA05022@ece.rutgers.edu> To: crose@ece.rutgers.edu Subject: 330:501 Content-Length: 627 Status: R Dear Dr. Rose, I have been watching the course web page for a grade announcement for 330:501 ( Systems Analysis ) but haven't caught it yet. I am leaving town today in the evening for India for a vacation and will be back on 22 Jan. If you have the grades finalized in any format, I would be really grateful if you could email me my grade if it is at all possible...it would be one whole month of suspense otherwise!! However if they have not yet been finalized, I apologize for causing you any inconvenience. My name: Suchitra Srinivasan SSN: 135 02 5992. Hope you have a very Happy Holidays, Thanking you, Suchitra. From crose Mon Dec 22 12:28:53 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA00629; Mon, 22 Dec 97 12:28:53 EST Date: Mon, 22 Dec 97 12:28:53 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9712221728.AA00629@MOGLI.rutgers.edu> To: srinis@ece.rutgers.edu Subject: Re: 330:501 Cc: crose@MOGLI.rutgers.edu Status: R No grades yet. Soon. From estock@rci.rutgers.edu Tue Dec 23 07:17:06 1997 Return-Path: Received: from amenti.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA00855; Tue, 23 Dec 97 07:17:06 EST Received: (from estock@localhost) by amenti.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.12) id HAA00802 for crose@mogli.rutgers.edu; Tue, 23 Dec 1997 07:09:12 -0500 Date: Tue, 23 Dec 1997 07:09:12 -0500 From: Richard Estock Message-Id: <199712231209.HAA00802@amenti.rutgers.edu> To: crose@mogli.rutgers.edu Subject: 2nd edition of F&A's Linear System Theory Book Cc: +rose@rci.rutgers.edu Status: R Prof. Rose, I understand that the second edition of Linear Systems Theory by Ferenc Szidarovszky and A. Terry Bahill is now available from CRC Press. (At least it was supposed to be as of 12/1/97!) Have you seen it? I was wondering if you could tell me what major changes may have been made to its contents. I would consider purchasing the 2nd edition if the chapters on stability (4), controllability (5) and observability (6) have been expanded, all topics in which I have become more interested. Kindest regards. Richard Estock (estock@rci.rutgers.edu) From cwrice@att.com Tue Dec 23 11:28:05 1997 Return-Path: Received: from ece.rutgers.edu by MOGLI.rutgers.edu (4.1/25-eef) id AA00914; Tue, 23 Dec 97 11:28:04 EST Received: from att.com (kcgw1.att.com [192.128.133.151]) by ece.rutgers.edu (8.6.12+bestmx+oldruq+newsunq/8.6.6) with SMTP id LAA04022 for ; Tue, 23 Dec 1997 11:14:48 -0500 Received: by kcgw1.att.com; Tue Dec 23 10:16 CST 1997 Received: from hoccson.ho.att.com (hoccson.ho.att.com [135.16.2.30]) by kcig1.att.att.com (AT&T/GW-1.0) with SMTP id KAA00402 for ; Tue, 23 Dec 1997 10:08:28 -0600 (CST) Received: from nj-mailnet.ho.att.com (mailnet.ho.att.com) by hoccson.ho.att.com (4.1/EMS-1.1.1 SunOS) id AA03035; Tue, 23 Dec 97 11:24:35 EST Received: by mailnet.ho.att.com with Internet Mail Service (5.0.1458.49) id ; Tue, 23 Dec 1997 11:19:39 -0500 Message-Id: From: "Rice, Chris" To: crose@ece.rutgers.edu Subject: Exam Solutions and Grades Date: Tue, 23 Dec 1997 11:20:11 -0500 X-Priority: 3 Mime-Version: 1.0 X-Mailer: Internet Mail Service (5.0.1458.49) Content-Type: text/plain Status: R Dr. Rose, Two questions: 1) Did you post the solutions to ECE330:501 final exam? I thought you finished them the night of the exam and were going to post them. I did not see them on the Web page. 2) Also, are you going to post the grades on the Web site? I remember you said Christmas was the deadline. I can almost hear those sleigh bells jingling! Thanks and have a happy holiday, Chris Rice From crose Tue Dec 23 12:53:27 1997 Return-Path: Received: by MOGLI.rutgers.edu (4.1/25-eef) id AA00965; Tue, 23 Dec 97 12:52:29 EST Date: Tue, 23 Dec 97 12:52:29 EST From: Christopher Rose Full-Name: Christopher Rose Message-Id: <9712231752.AA00965@MOGLI.rutgers.edu> To: cwrice@att.com Subject: Re: Exam Solutions and Grades Cc: 330_501, 330_543 Status: R Hi Chris, Lots happened since tuesday last. I'll have to disappoint and get grades in by official Jan 5 deadline (SORRY!). If sooner I'll post of course. So try to have a happy and a merry and all that without the grades. Cheers (ALL) Chris Rose From MAILER-DAEMON Sun Jan 4 22:35:21 1998 Return-Path: Received: from localhost.localdomain (ppp-29.ts-3.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA03233; Sun, 4 Jan 98 22:35:18 EST Received: from localhost (localhost) by localhost.localdomain (8.8.5/8.8.5) with internal id XAA01497; Sun, 4 Jan 1998 23:12:27 -0500 Date: Sun, 4 Jan 1998 23:12:27 -0500 From: Mail Delivery Subsystem Message-Id: <199801050412.XAA01497@localhost.localdomain> To: crose@localhost.localdomain Mime-Version: 1.0 Content-Type: multipart/report; report-type=delivery-status; boundary="XAA01497.883973547/localhost.localdomain" Subject: Returned mail: User unknown Auto-Submitted: auto-generated (failure) Status: RO This is a MIME-encapsulated message --XAA01497.883973547/localhost.localdomain The original message was received at Sun, 4 Jan 1998 23:12:19 -0500 from crose@localhost ----- The following addresses had permanent fatal errors ----- 330_501@mogli.rutgers.edu ----- Transcript of session follows ----- ... while talking to mogli.rutgers.edu.: >>> RCPT To:<330_501@mogli.rutgers.edu> <<< 550 /usr/crose/system/501: line 44: bonnie@mogli.rutgers.edu... User unknown 550 330_501@mogli.rutgers.edu... User unknown --XAA01497.883973547/localhost.localdomain Content-Type: message/delivery-status Reporting-MTA: dns; localhost.localdomain Arrival-Date: Sun, 4 Jan 1998 23:12:19 -0500 Final-Recipient: RFC822; 330_501@mogli.rutgers.edu Action: failed Status: 5.1.1 Remote-MTA: DNS; mogli.rutgers.edu Diagnostic-Code: SMTP; 550 /usr/crose/system/501: line 44: bonnie@mogli.rutgers.edu... User unknown Last-Attempt-Date: Sun, 4 Jan 1998 23:12:27 -0500 --XAA01497.883973547/localhost.localdomain Content-Type: message/rfc822 Return-Path: Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id XAA01495 for 330_501@mogli.rutgers.edu; Sun, 4 Jan 1998 23:12:19 -0500 Date: Sun, 4 Jan 1998 23:12:19 -0500 From: Christopher Rose Message-Id: <199801050412.XAA01495@localhost.localdomain> To: 330_501@mogli.rutgers.edu SSN Q1 Q2 F Grade 0786 81 81 100 C+ 6752 79 75 150 C+ 1171 117 65 175 B+ 3106 20 0 60 F 2271 84 65 210 B 5407 71 100 165 B 9782 67 49 150 C 4920 100 120 290 A 2564 75 42 255 B 2586 99 97 230 A 0831 85 79 195 B+ 2244 114 157 280 A xxxx 95 145 290 A 9910 83 105 205 A 9930 79 62 200 B 5992 74 95 270 A 8931 60 75 265 B+ 4974 63 49 205 C+ 0258 105 120 240 A 4667 47 40 150 C 0373 37 15 130 C 2537 112 80 300 A 0486 97 95 260 A 1439 63 55 195 C+ 1368 80 110 275 A --XAA01497.883973547/localhost.localdomain-- From crose@localhost.localdomain Wed Jan 7 18:34:43 1998 Return-Path: Received: from localhost.localdomain (ppp-50.ts-10.nyc.idt.net) by MOGLI.rutgers.edu (4.1/25-eef) id AA03252; Wed, 7 Jan 98 18:31:58 EST Received: (from crose@localhost) by localhost.localdomain (8.8.5/8.8.5) id TAA17782 for 330_501@mogli.rutgers.edu; Wed, 7 Jan 1998 19:08:19 -0500 Date: Wed, 7 Jan 1998 19:08:19 -0500 From: Christopher Rose Message-Id: <199801080008.TAA17782@localhost.localdomain> To: 330_501@mogli.rutgers.edu Status: R SSN Q1 Q2 F Grade 0786 81 81 100 C+ 6752 79 75 150 C+ 1171 117 65 175 B+ 3106 20 0 60 F 2271 84 65 210 B 5407 71 100 165 B 9782 67 49 150 C 4920 100 120 290 A 2564 75 42 255 B 2586 99 97 230 A 0831 85 79 195 B+ 2244 114 157 280 A xxxx 95 145 290 A 9910 83 105 205 A 9930 79 62 200 B 5992 74 95 270 A 8931 60 75 265 B+ 4974 63 49 205 C+ 0258 105 120 240 A 4667 47 40 150 C 0373 37 15 130 C 2537 112 80 300 A 0486 97 95 260 A 1439 63 55 195 C+ 1368 80 110 275 A