Long Chen 陳龍

Brief CV

2017-09-03T17:00:00.000-07:00

Please visit my new home page: http://math.uci.edu/~chenlong/

Employment

2007 - . Assistant Professor, Department of Mathematics, University of California, Irvine

2006 - 2007. Postdoc, Department of Mathematics, University of Maryland.
Advisor: Professor Ricardo Nochetto

2005 - 2006. Postdoc, Department of Mathematics, UCSD.
Advisor: Professor Michael Holst

Education

Ph.D Applied Mathematics (Aug. 2000 - Dec.2005)
Pennsylvania State University Advisor: Prof. Jinchao Xu

M.S Mathematics (Sept. 1997 - July.2000) Peking University

B.S Mathematics (Sept. 1993 - July. 1997) Nanjing University

Award

2005 Alumni Association Dissertation Award of The Pennsylvania State University.

Service

2002-2003 The President of Chinese Friendship Association of The Pennsylvania State University.

Contact

2017-09-02T20:50:00.000-07:00

Office: 271 MSTB
Tel: (301)367-9667
Email: chenlong@math.uci.edu

迷路

2011-05-07T01:34:00.000-07:00

陈龙

一个男人终将遇上一个女人，这是必然，而我遇上了你，这就是偶然。这就是宏观的必然和微观的偶然，这就是世界的构成规律。

我喜欢这样的一个男子，他斜靠在路边的护栏，饶有兴趣地观看着周围的这个世界。蓝的天白的云，金色的阳光，黑色的体恤，年轻的身躯和过往的车辆行人。他燃起了一根烟，感受着时间的流逝，一分一秒，生活在按其自身的逻辑发展，我们无能为力。四周不停变化着，他安静地靠在那，在烟雾中迷茫和陶醉。

小丁时不时就会这样靠在路边，因为他经常迷路，以至于每到十字路口，他都会怀疑自己的选择，他不知道怎样才能走到自己想去的地方。红灯亮了，公交停了，窗口是一位年青小伙，低头看了一下表。他也许在赶赴一个约会，也许这会儿已经迟到了，也许悲惨的结果已经在等着他，但无论如何，小丁还是很羡慕那些车上的人，一旦上了车，剩下的只是等待而已。

烟雾在眼前上升，迅速的散去。人的一生大抵如此，恍然如烟，变幻无常，然后散去，就象烟雾一样散去，然后消失。小丁感伤地看着四周聚散的男男女女，一个称之为缘分的东西，让他们在这个地方，在这一刻，相遇，相知，相恋，或是相离，分分合合，就像一堆实验室里的粒子随机的运动，靠拢，碰撞，分离。

他想起曾对小艾讲起过的关于缘分的一些话：什么是缘分？缘分在我看来是世界的一种偶然存在。每一件事情发生之后，每一个状态到达之后，如果回溯以往你都能看到很多偶然，很多时间和空间的分岔小径，我们永远不会知道如果当初选择的是左而不是右，如果遇到的是她而不是你，世界又将会是怎样，也许我们会去设想，设想世界的另一种可能的存在方式，也许会问，为什么我遇上的是你？其实问题的答案便是问题本身，因为我们已经立足了世界的这样一种存在。

烟抽完了，小丁转过身。背后是一个有名的广场和购物中心，很多时尚女子出入的场合，那些女子远远看来还颇有风韵和气质，大胆的穿着，暴露的身材，在阳光下把小丁晒得火辣火辣的。

恋恋风尘影评

2011-05-07T01:16:00.000-07:00

陈龙

一个恋是怀恋，对过去的怀恋，一个恋是爱恋，已逝去的爱恋。

风尘。韵味实足的汉语。扬起的风与尘，是一段路途，也见证了走过的一段岁月。

恋恋风尘。短短四字，一段可待追忆的往事跃然纸上。

那还是两个在读中学的孩子，一起在回家的车上温书。是火车，穿梭于山洞之间。忽明忽暗。

“你怎么了？”

“明天要考数学，还都不会。”

“不会？怎么不早问我。”

这个对话，是那么的熟悉，连口吻也是一般。女孩的事似乎已成了男孩的一份责任。他们在回家的路上，并肩地走着。

成为一种习惯，保护和被保护。责任 ─ 要命的青春期的责任感。

那是一个含蓄的时代，一对含蓄的少年情侣。没有表白，只是默认。依赖和守护都已成为习惯。含蓄地象隔着一只弹簧，距离的接近，压缩后产生了张力。

似乎没有欢快的大笑，连玩笑似乎也不适合。责任的体现方式是严肃。男孩看着女孩，却有一种守护的满足感。两人都是含蓄的人。和朋友在一起唱歌，也无法大声。

放不开。这是性格使然。

女孩子，学人家喝酒。男孩象丈夫一样轻叱着，女孩低着头，没有言语。也不需要言语。他们是一对，是一家人。

男孩是关心女孩的，女孩也是一样。只是方式有些窒息。

齐耳的短发，干净的白衬衣，黑裙子，如同衣服一样朴素的脸。

然后到了台北。

生活并不容易。终于，安排两个孩子去逛商场，买皮鞋，回家的礼物。似乎放了轻松。却不然。送货的摩托不见了。

于是更加的窒息。窒息到男孩病倒在床上。

女孩来了，象个好妻子一般，关心着病床上的男孩。似乎是一种从小就定下的契约。目送着自己心爱的女人转过街角，男孩感到的是一种满足。这算是他们距离最近的一次。

衣服仍然是白色，只是多了些花样。头发在不知不觉中变长，开始有些式样，发带。朴素依然，多了一丝甜美。

开始有了颜色，淡雅的绿色，发带也更漂亮，衬着微微的卷发。不再象个孩子，而是一个漂亮的lady。

还有衣服。作为裁缝店的学徒工，女孩给自己的男朋友做了一件花花的衬衣。刚开始并不合身。改了再改。男孩一如既往地去探望。隔壁楼房失火。

如此种种，便是那点点滴滴的风尘往事。　

再然后男孩去当了兵。弹簧被拉长，张力便成为引力。频繁的鸿雁传书，分享着两边的生活。还有３７０天。一种无奈。女孩的事却只是信中代出，因为这是一个男人的怀恋，对初恋的怀恋。

最后，女孩和送信的邮差结婚了。男孩终于忍不住痛苦，失声饮泣。

阿公说，这是缘分，不能勉强的。青山白云，山不动，云飘过。

恋恋风尘的歌。注定了和一个女孩有关，注定了和一段青春的悸动相连。

诗歌分析之一：阳光打在地上

2011-05-07T01:09:00.000-07:00

陈龙

文本

海子歌：阳光打在地上

阳光打在地上

并不见得

我的胸口在疼

疼又怎样

阳光打在地上

注：此为该首诗歌的第一节，全文请在google查询

第一句描述一个客观的事实：有阳光在地上。这里我省略了动词，一般用“照”，而诗人在此选用“打”，从而含有“无情，责难，惩罚”等意，更为重要的是，“打”字和第三句的“疼”字构成字面的因果关系，从而联系起客观的事实和主观的感受，让人猜测是否因为阳光而触动诗人的心事，然而诗人却刻意否认“并不见得”，这是一种欲盖弥彰的修辞手段，旨在强化而非否定命题。当然还不局限于此，这种否认呈现了诗人的惊恐和逃避，缘何否认，实在“疼”非得己。下面一句“疼又怎样”，则从正面进一步肯定了命题：因为阳光打在地上，所以我的心在疼。（“胸口”显然是指心，而做为“打”的受动者， “胸口”要比抽象的“心”更适合）。此时诗人情绪已然变化，痛到极处，自然反弹，反正是躲不掉，不如直面这份心疼。同时在句式上构成一句问语（反问，设问皆有），很自然引出本节中最为悲怆，凄惨的一句，“阳光打在地上”。

句式上这是对上一句问语“疼又怎样”的回答。“疼”并不能换来怜悯，阳光依然这样无情地打在地上，继而依然作用于我的心疼，无能为力，无奈无助的感觉呼然纸上。其次，两句“阳光打在地上”构成形式和内容上的呼应，在两次“阳光打在地上”，流逝过去的除了心疼，还有“时间”（注意到“光”正是“时间”最自然的表象），因此时间的维度就在句式的反复中自然被引入，而对时光无情流逝，世间沧桑变化的唏嘘感伤正是诗歌永恒的话题之一。

Tips for Mail

2007-05-17T20:13:00.000-07:00

Apple's Mail + MailTags, Act-On is a wonderful solution for mail. Here is my usage.

1. Stop Folders. People is used to put emails into different mailboxes. This is a traditional way for organization. Gmail changes the way. Use one folder for all emails (and never delete emails) and SEARCH to organize your emails. To maintain a clear inbox, you Archive mails to All Mail box.

2. Stop Archive. You can also Archive in the Apple's Mail. With Act-On, you can use keyboard shortcut. Looks like a good solution. But wait a second. You will move every email into another mailbox. One hit for one email. Not a big deal. But why not treat your inbox as Archive?

Here is my solution. I will create a smart box , Current Message, using rule: Date Received in 2 days. (You can configure rules to exclude certain emails (junk, newsletter).) My default mailbox will be this one. I read new message in this mail box only.

3. Cost + Priority. For the explanation, it is better to draw a coordinate with cost as x-axis and priority as y-axis (Picture is coming soon) . Several critical values of cost is: 5 minutes, 1 hour, days. For Priority: Urgent, High, Mid, Low. I will sort my emails as the following class:

P=Urgent, C <= 10 min
P>=High, 10 min < = C < = hours OR P <= Mid, C < = 10 min
P <= Low, C < = 10 min OR P >= Mid, 10 min < = C < = hours
Others.

For class 1, when I read this email, I will deal with it immediately. If you even don't have 10 minutes, treat as class 2.

For class 2, C-q set the due date is in 2 days. Create a smart box To Do in 2 days with rule: MailTags Due Date --- is within --- 3 days from today.

For class 3, C-a set the due date is in 5 days. Create a smart box To Do in a Week with rule: MailTags Due Date --- is within --- 7 days from today +
MailTags Due Date --- is after --- 3 days from today.

For class 4, C-z set the due date is in 10 days. Create a smart box To Do Later with rule: MailTags Due Date --- is after --- 7 days from today.

Everyday you only need to work on the emails in the mail box To Do in 2 days. After you are done with the selected email, C-x to set the due date is off. Then it won't be in this smart box. Mails in other boxes will be moved to this box automatically (thanks to smart box). If you cannot finish it, you can use C-q, a , or z to reset it. If the box To Do in 2 days is already empty, you can start to look at To Do in a Week.

* All the shorcut C-q,a,z, x etc are set by Act-On

Math Department of UMD, College Park

2007-04-17T19:43:00.000-07:00

Please visit my new home page: http://math.uci.edu/~chenlong/

PEOPLE

RESEARCH

TEACHING

Topic 4

2006-08-01T16:30:00.000-07:00

Andrea Bonito. Convergence of adaptive discontinuous Garlerkin methods.

ABSTRACT:
To prove the consistency, the coercivity, and the first upper bound. Another upper bound, a quasi Galerkin orthogonality, and the convergence.

Topic 3

2006-08-01T16:00:00.000-07:00

Chen-Song Zhang. A posteriori error estimation for integro-differential operators.

ABSTRACT:
A posteriori error estimation for integro-differential operators including the upper and lower bound

Topic 2

2006-08-01T15:00:00.000-07:00

Ricardo H. Nochetto. AFEM for the Laplace-Beltrami Operator on Surfaces.

ABSTRACT: We first introduce an AFEM for the Laplace-Beltrami operator on C1 graphs in R^d (d>=2). We derive a posteriori error estimates that account for boththe energy error in H1 and the geometric error in W^{1,1} due to approximation of the surface by a polyhedral one. We devise a marking strategy to reduce the energyand geometric errors as well as the geometric oscillation. We prove that AFEM is a contraction on a suitably scaled sum of these three quantities as soon as the geometric oscillation has been reduced beyond a threshold. The resulting AFEM converges without knowing such threshold or any constants, and starting from anycoarse initial triangulation. Several numerical experiments illustrate the theory. Finally, we introduce and analyze an AFEM for the Laplace-Beltrami operatoron parametric surfaces, thereby extending the results for graphs. Note that, due to the nature of parametric surfaces, the geometric oscillation is now measured in terms of the differences of tangential gradients rather than differences of normals as for graphs. Numerical experiments with closed surfaces are provided to illustrate the theory.

Topic 1

2006-08-01T14:25:00.000-07:00

Long Chen. Convergence and Optimality of Adaptive Mixed Finite Element Methods.

ABSTRACT: The convergence and optimality of adaptive mixed finite element methods for second order elliptic partial differential equations is established in this paper. The main difficulty for the mixed finite element method is the lack of minimization principle and thus the failure of orthogonality. A quasi-orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace, while the part of the error containing divergence can be bounded by data oscillation.

Math 462 Info

2006-07-31T19:39:00.000-07:00

Lecture: T Th 2:00 pm - 3:15 pm (MTH 0401)
Instructor: Long Chen lyc102@gmail.com
Ofice Hours: M W F 2:00 pm -- 3:00 pm (MTH 4108)
Syllabus: Click Here.

Math 462 Quiz Exam

2006-07-28T19:32:00.000-07:00

Quiz 1: Chapter 2;
Quiz 2: Chapter 4, 5;
Mid Exam: Ch 6.1, 6.3; Ch 7.1, 7.2, 7.3, 7.4; Ch 11.1, 11.2, 11.3, 11.6
Final Exam: May 16, Wednesday, 10:30 am - 12:30 pm. Room: 0401 (the same classroom)
You can bring your textbook and notes to the final.
Review of Math 462.

Math 462 Homework

2006-07-01T20:37:00.000-07:00

Matlab Project (you may work in teams of up to 3 students with each team handing in one paper):

Write a program to verify the calculation in Figure 2 (p. 192) and Example 1 (p. 193).
Write a program to reproduce Figure 1 (p. 201), 2 (p. 202), 3 (p. 203). (Hint: using (6) in p. 202 to set up the first two rows of the computation.)
Exercise 8.4: 1. Write a program to verify Figure 2(a), (b).

Homework will not be collected; your homework will be evaluated by your performance on periodic quizzes and midterm exams.

Section 1.2: 1, 3, 9;

Section 2.1: 1, 2, 5, 6

Section 2.2: 3, 6;

Section 2.3: 1, 4, 6

Section 2.4: 3, 6;

Section 4.1: 1;

Section 4.2: 2;

Section 5.1: 2, 8;

Section 5.2: 1, 2, 7;

Section 5.3: 2;

Section 6.1: 5, 6;

Section 6.2: Reading Assignment.;

Section 6.3: 1.

Section 7.1: 1, 2, 5;

Section 7.2: 1.

Section 11.1: 2, 3.

Section 11.2: 1, 4.

Section 11.3: 3.

Section 9.1: 6(a), 8

Section 8.4: 5

Math 462 Calendar

2006-07-01T20:32:00.000-07:00

Spring Semester 2007
Note: This calendar is subject to revision during the term.

Week	Tuesday	Thursday
1	Jan. 23	Jan. 25 1.1 - 1.2, 2.1
2	Jan. 30 2.2, 2.3	Feb. 1 2.3, 2.4
3	Feb. 6 2.5, 4.1	Feb. 8 4.1, 4.2
4	Feb. 13 Quiz 1, 5.1,5.2	Feb. 15 5.3
5	Feb. 20 6.1	Feb. 22 6.3
6	Feb. 27 6.3	Mar. 1 7.1
7	Mar. 6 Quiz 2; 7.2	Mar. 8 7.3, 7.4
8	Mar. 13 11.1	Mar. 15 11.3, 11.6
9	Mar. 20 Spring Break	Mar. 22 Spring Break
10	Mar. 27 11.2	Mar. 30 9.4
11	Apr. 3 9.2	Apr. 5 Mid Exam I
12	Apr. 10 8.1	Apr. 12 8.2
13	Apr. 17	Apr. 19 Quizz 3
14	Apr. 24	Apr. 26
15	May 1	May 3
16	May 8 Quiz 4	May 10 Matlab Project

Math 462 Syllabus

2006-07-01T10:26:00.000-07:00

MATH 462 (Differential Equations for Scientists and Engineers)

Course Decription:This course is an introduction to partial differential equations (PDE). We will discuss first order equations, the heat equation, the wave equation and the Poisson equation, the last three being the prototype of second order equations. We will also discuss nonlinear equations of each type. We will develop the method of separation of variables and eigen-function expansions, which lead to Fourier analysis. Qualitative properties and numerical methods will also be studied. This corresponds to Chapters 1 to 8. MATLAB will be used mostly for graphical purposes and illustrative computation.

Prerequisite: Calculus MATH 240, 241 and Elementary ODE MATH 246 (or equivalent).

Textbook: Partial Differential Equations: An Introduction,., by Walter A. Strauss. Published by Wiley and Sons.
Reference for the MATLAB material:
Introduction to Partial Differential Equations with MATLAB, by Jeffery M. Cooper Published by Bikhauser.

Homework: Homework (not including MATLAB projects) will be assigned on the course homework page and should be completed by the indicated due date. Homework will not be collected; your homework will be evaluated by your performance on periodic quizzes and midterm exams. You should make every effort to complete the homework assignments and seek help with problems you have not been able to solve.

Reading: Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment and it will be expected that you read the assigned material in advance of each lecture. You are responsible for material in the assigned reading whether or not it is discussed in the lecture.

Quizzes: There will be four (4) quizzes given during the discussion section on certain Tuesday; please see the course calendar for the dates of the quizzes. Each quiz will consist of two problems similar to the assigned homework and you will be allowed twenty (20) minutes to complete each quiz. Your cumulative quiz grade will be based on the best 3 of the 4 quizzes. No notes (or books) or calculators will be allowed during the quizzes. There will be no makeup quizzes.

Matlab Projects: There will be one (1) Matlab project. You may work in teams of up to 3 students with each team handing in one paper.

Exams: There will be one midterm exams and one final exam. See the course calendar for the dates of the midterm exams.There will be no make up exams.

Grading: Your course grade will be determined by your cumulative average at the end of the term:
20% Quizzes, 25% Midterm Exam, 20% Matlab Projects, 35% Final Exam

Presentation

2006-06-24T14:21:00.000-07:00

Please visit my new home page: http://math.uci.edu/~chenlong/

Mathematical and Computational Sciences Division Seminar Series, National Institute of Standards and Technology (NIST), June 5, 2007.

NSF-CBMS Regional Research Conference, University of Iowa, May 23, 2007.

Finite Element Circus, University of Maryland, April 21, 2007.

Numerical Analysis Seminar, University of Maryland, January 30, 2007.

University of California, Irvine (Special Recruitment Colloquium), January 19, 2007.

Finite Element Circus, The Pennsylvania State University, November 4, 2006.

Academy of Mathematics and System Sciences, Chinese Academy of Sciences. July 21, 2006.

2006 Summer School on the Multiscale Adaptive Method, Beijing University, July 17-21, 2006.

Numerical Analysis Seminar, UCSD, May 23, 2006.

Tech Report, National Biomedical Computation Resource, UCSD, Apr. 27, 2006

Numerical Analysis Seminar, UCSD, Oct. 11, 2005.

8th US National Congress on Computational Mechanics Austin, Texas, July 24-28, 2005

Midwest Numerical Analysis Conference, May 22, 2005

University of California, San Diego (Special Recruitment Colloquium), Jan 6, 2005.

University of Delaware (an Invited Talk), Dec 13, 2004.

Wayne State University (an Invited Talk), Dec 8, 2004.

University of Maryland (an Invited Talk), Nov 30, 2004.

Finite Element Circus. Syracuse University, Oct 15, 2004.

CAM Luncheon Seminar in Penn State, Sept 24, 2004.

13th International Meshing Roundtable. Williamsburg, VA. Sept. 20 2004.

Beijing University, China, June 21, 2004.

Superconvergence and A Posteriori Error Estimates (an Invited Talk), Changsha, China, May 31-Jun 2, 2004.

Recent Advances in Adaptive Computation (an Invited Talk), Hangzhou, China, May 24-28, 2004.

Finite Element Circus, University of Pittsburgh, April 17 2004.

Finite Element Circus. Cornell University, Nov 8, 2003.

CAM Luncheon Seminar in Penn State, Nov 14, 2003

Numerical Analysis RIT

2006-05-31T20:57:00.000-07:00

Focus of the RIT in Fall 2006: Adaptive Multilevel FEM for PDE
Meeting schedule: Monday 4:30 -- 5:30, Math 1313
Other RIT

Week 10 (Dec 11)

2006-05-31T20:04:00.000-07:00

Chensong Zhang. Rate of convergence for some constraint decomposition methods for nonlinear variational inequalities.

ABSTRACT: General subspace correction algorithms are proposed for a constrained convex minimization problem by Tai. General results on the convergence rates of these algorithms are derived. We discuss the application of this general framework to the solution of obstacle problems by multilevel subspace decompostions.

Week 9 (Dec 4)

2006-05-31T19:59:00.000-07:00

Manel Cascon. The completion of newest vertex bisection

Week 7,8 (Nov 20,27)

2006-05-31T06:53:00.000-07:00

Manel Cascon. Convergence and Optimality of an AFEM for General Second Order Linear Elliptic PDE

ABSTRACT: Despite the overwhelming computational evidence that AFEM lead to optimal meshes, the mathematical theory started very recently with Binev et al [1] and Stevenson [3]. Paper [1] discusses geometric properties of bisection which turn out to be crucial for optimality; The AFEM in [1]
includes a coarsening step which is not necessary in practise for linear elliptic PDE. Stevenson presents in [3] an algorithm with optimal complexity without coarsening, but it does not work with general linear elliptic operator and is unpractical.

In this work, we modify the Morin-Nochetto-Siebert algorithm [2] with a new procedure for oscillation reduction relative to error estimator. We prove that the resulting AFEM is a contraction for the total error between two consecutive adaptive loops. This strict error reduction property then leads to the optimality of AFEM, that is the total error decays in terms of number of degrees of freedom as predicted by the best approximation. This work is joint with R. H. Nochetto.

Bibliography

[1] P. Binev, W. Dahmen, and R. DeVore Adaptive finite element methods with convergence rate, Numer. Math., 97(2), pp.~219-268 (2004).

[2] P. Morin, R.H. Nochetto, and K.G. Siebert, Data Oscillation and Convergence of adaptive FEM. SIAM J. Numer. Anal. 38, pp.~466--488 (2000).

[3] R. Stevenson, Optimality of a standard adaptive finite element method Found. Comput. Math. Online. DOI 10.1007/s10208-005-0183-0, (2006).

Week 6 (Nov 13, 14)

2006-05-30T08:08:00.000-07:00

Long Chen. Uniform Convergence of Multigrid Methods on Adaptive Grids obtained by Newest Vertex Bisection

ABSTRACT: We finished proof by proving a stable decomposition. In 2-D, we show that hierarchical basis MG is robust with respect to the jump of coefficients.

Week 5 (Nov 6)

2006-05-30T07:27:00.000-07:00

Long Chen. Uniform Convergence of Multigrid Methods on Adaptive Grids obtained by Newest Vertex Bisection

ABSTRACT: We shall prove multigrid method for solving Poisson equation on adapted grids obtained by newest vertex bisection will converges uniformly with respect to the size of unknowns. Furthermore we shall show the computational cost is also optimal. This is a generalization of the result in \cite{Wu.H;Chen.Z2003} to higher dimensions with a simplified and more straightforward proof.

Week 4 (Oct 30)

2006-05-29T22:31:00.000-07:00

Long Chen. New Chaeracterization on Adaptive Grids obtained by Newest Vertex Bisection

ABSTRACT: We give a decomposition of adaptive grids obtained by newest vertex bisection. This decomposition is new and crucial for developing multigrid.

Week 3 (Oct 23)

2006-05-29T22:28:00.000-07:00

Long Chen. X-Z identity for successive subspace correction method.

ABSTRACT: We shall report a sharp estimate of the convergence rate of multgird methods. Indeed it is an identity on the contraction number for general successive subspace correction methods. The main reference is

[1] J. Xu and L. Zikatanov. The method of alternating projections and the method of subspace corrections in Hilbert space. Journal of The American Mathematical Society, 15:573–597, 2002.

We shall give a simple proof for a special but the most important case of this identity. It will be our basic tools for the analysis of multigrid on adapted grids.

Week 2 (Oct 16)

2006-05-16T12:27:00.000-07:00

Long Chen. Subspace correction method.

ABSTRACT: We present iterative methods in the frame work of subspace correction method. We discuss in details the space decompoistion and several inner product structures introduced by the decomposition.

Week 1 (Oct 9)

2006-05-09T21:13:00.000-07:00

Long Chen. Convergence analysis of classical iterative methods.

ABSTRACT: We give theories for the quantitative analysis of classical iterative methods for sovling algebraic system. In the analysis, the new inner product defined by the SPD matrix plays an important role.

Math 246 Quiz & Exam

2006-04-21T14:25:00.000-07:00

Mid Exam I
Quiz 2: 2-nd order homogeneous equation with constant coefficients (3.1, 3.4, 3.5)
Quiz 3: using Laplace transform to solve 2-nd order equation (6.1 -- 6.4)
Mid Exam II: Ch 3.1 -- 3.8; Ch 6.1 -- 6.4.
Quiz 4: Ch 7.1 --7.4
Final Exam: Saturday, May 12,1:30-3:30. Because there will be many students requesting an alternate final for religious reasons, we have scheduled a uniform alternate final on Sunday, May 13, 1:30-3:30.
NOTICE for alternate final on Sunday: Send me an email with your name and UID by Friday. Place: ARM 0126,0135.
Place for Final Exam: Qiwen Chen's sections: MMH 1400, Kostas Spiliopoulos' section : ARM 0126.
Review for the final exam. You can find detailed description of material covered in the final.
Practice Exams: You can find all old exams from Testbank. You are recommended to do the following old exams: Fall 2006, Spring 2006, Fall 2005, Spring 2005.
Since there is no available solution for old exams, this file collect solutions for selected problems which are relatively difficult. It does NOT imply that problems in this file will be in the final. You are recommended to do the following old exams: FALL 2006, SPRING 2006, FALL 2005, and SPRING 2005.
NOTICE: We are sorry for the late notice but we want all instructors andstudents to be aware that UMUC will have commencement ceremonies on Saturday (05/12/07). There are two ceremonies starting at 10am and 4pm and they will occur at the Comcast Center. Please note that there may be heavy traffic conditions on and around campus; and allow adequate traveltime in order to reach your destinations. Please distribute this information to your instructors allowing them to notify their students of the potential congestion on campus this Saturday.

Math 246 Info

2006-04-20T23:50:00.000-07:00

Lecture: T Th 11:00 am - 12:15 pm (ARM 0135)
Instructor: Long Chen lyc102@gmail.com
Ofice Hours: M W F 2:00 pm -- 3:00 pm (MTH 4108)
Syllabus: Click Here.
Teaching Assistant:

Kostas Spiliopoulos. Office Hours: TuTh 8:35-9:35 (MATH 4423).

Qiwen Chen;

Math 246 Calendar

2006-04-20T23:39:00.000-07:00

Spring Semester 2007
Note: This calendar is subject to revision during the term.

Week	Tuesday	Thursday	Friday
1	Jan. 23	Jan. 25 2.1	Jan. 26 Basic of Matlab;
2	Jan. 30 2.2-2.3	Feb. 1 2.4	Feb. 2
3	Feb. 6 2.5	Feb. 8 2.6	Feb. 9 Quiz 1
4	Feb. 13 2.7, 8.1	Feb. 15 8.2, 8.3	Feb. 16
5	Feb. 20 3.1, 3.4	Feb. 22 3.2, 3.5	Feb. 23 Matlab Project 1
6	Feb. 27 Mid Exam I	Mar. 1 3.2, 3.3	Mar. 2
7	Mar. 6 3.6	Mar. 8 3.7	Mar. 9 Quiz 2
8	Mar. 13 3.8	Mar. 15	Mar. 16 Matlab Project 2
9	Mar. 20 Spring Break	Mar. 22 Spring Break	Mar. 23 Spring Break
10	Mar. 27 6.2	Mar. 30 6.3	Mar. 31
11	Apr. 3 6.4	Apr. 5 7.1, 7.2	Apr. 6 Quiz 3
12	Apr. 10 7.3	Apr. 12 7.3, 7.4	Apr. 13
13	Apr. 17 Mid Exam II	Apr. 19 7.4	Apr. 20 Matlab Project 3
14	Apr. 24 7.6	Apr. 26 7.8	Apr. 27 Quiz 4
15	May 1 7.7	May 3 9.1-9.2	May 4 Matlab Project 4
16	May 8 9.3/Review	May 10 Review	May 11

Math 246 Homework

2006-04-20T23:30:00.000-07:00

Homework will not be collected; your homework will be evaluated by your performance on periodic quizzes and midterm exams.

Section 2.1 (Due Feb. 8): 1, 3, 6, 13, 15, 28;

Section 2.2 (Due Feb. 8): 1, 4, 7, 11, 21, 23;

Section 2.3 (Due Feb. 8): 1, 4, 7, 9;

Section 2.4 (Due Feb. 8): 1, 3, 5, 8, 13, 15;

Section 2.5 (Due Feb. 8): 1, 3, 5, 20;

Section 2.6 (Due Feb. 27): 1, 3, 13, 19, 21;

Section 2.7 (Due Feb. 27): 1;

Section 8.2 (Due Feb. 27): 1;

Section 8.3 (Due Feb. 27): 3;

You are welcome to try and modify my matlab files: example1.m, myeuler.m, myheun.m, myRK.m

Section 3.1 : 9, 11, 13;

Section 3.2 : 1, 2, 3, 7, 9, 13;

Section 3.3 : 1, 2, 3, 10, 15;

Section 3.4 : 1, 2, 3, 17, 19;

Section 3.5 : 1, 3, 11;

Section 3.6 : 1, 4, 7, 19;

Section 3.7 : 1, 3

Section 3.8 : 1, 3, 5, 9;

Section 6.1 : 1, 2, 5, 7, 9;

Section 6.2 : 1, 4, 7, 12, 15, 18;

Section 6.3 : 1, 4, 7, 9, 13, 16;

Section 6.4 : 1, 3;

Section 7.1 : 1, 3, 17;

Section 7.2 :6, 8, 9, 11;

Section 7.3 : 1, 3, 6, 7, 8, 10, 15, 16;

Section 7.4 : 4, 6;

Section 7.5 : 1, 3, 7, 15;

Section 7.6 : 1, 2, 15, 17;

Section 7.7 : 1, 4, 14;

Section 7.8: 1, 7, 15;

Section 9.1 : 1, 2, 6, 8, 12;

Math 246 Matlab

2006-04-20T23:15:00.000-07:00

Project 3: Set D: 11, 15

Project 4: Set F: 1.

Formate: we shall follow the formate used by Prof. Tobias von Petersdorff. Click This page and look for "How to Hand in Matlab Homework".

Matlab is available in many computer labs on campus

Quick Start: Read chapters 2, 3, 4, 8 in "Differential Equations with Matlab" and try the commands on the computer.

Tutoring: Matlab Tutoring from Math department

Help: Ask your TA.

Common Problems with Matlab given by Prof. Tobias von Petersdorff.

Math 246 Syllabus

2006-04-20T23:08:00.000-07:00

MATH 246 (Differential Equations for Scientists and Engineers)

Course Decription:This course is an introduction to ordinary differential equations. The course introduces the basic techniques for solving and/or analyzing first and second order differential equations, both linear and nonlinear, and systems of differential equations. The course will follow Chapters 1, 2, 3, 6, 7, 8, and 9 of Boyce and Diprima and Chapters 1-8 and 11-13 of Hunt et al. The use of mathematical software system is an integral and substantial part of the course. All sections of the course will use the software system MATLAB.

Prerequisite: MATH 141 or equivalent

Textbook: Elementary Differential Equations - 8th ed., by Boyce & DiPrima. Published by Wiley and Sons. and for the MATLAB material:
Differential Equations with MATLAB, 2nd Edition, by Hunt, Lipsman, Osborn, and Rosenberg. Published by J. Wiley.

Quizzes: There will be four (4) quizzes given during the discussion section on certain Friday; please see the course calendar for the dates of the quizzes. Each quiz will consist of two problems similar to the assigned homework and you will be allowed twenty (20) minutes to complete each quiz. Your cumulative quiz grade will be based on the best 3 of the 4 quizzes. No notes (or books) or calculators will be allowed during the quizzes. There will be no makeup quizzes.

Matlab Projects: There will be four (4) Matlab projects due on certain Friday; please see Math 246 Matlab for details. You may work in teams of up to 3 students with each team handing in one paper. Different teams may not work together or share their work. Members of a team must have the same TA. Matlab assignments must be handed in in the discussion session. Late assignments will not be accepted. Matlab homework must be prepared in the format explained on the web page.

Exams: There will be two (2) midterm exams and one final exam. See the course calendar for the dates of the midterm exams. The final exam will be held on Saturday, May 12. No calculators will be allowed during the exams. There will be no make up exams.

Grading: Your course grade will be determined by your cumulative average at the end of the term:
20% Quizzes, 30% Two Midterm Exams, 20% Matlab Projects, 30% Final Exam

Teaching Experience

2006-04-01T01:02:00.000-08:00

Math 20C: Calculus and Analytic Geometry for Science and Engineering. Winter 2006.

Instructor for Math 20A: Calculus for Science and Engineering. Fall 2005. Department of Mathematics. University of California at San Diego.

Instructor for Math 230: Multivariate and Vector Calculus. Fall 2003 and Spring 2004. Department of Mathematics. The Pennsylvania State University.

Graduate Assistant. Aug. 2000 - Aug. 2005. Department of Mathematics. The Pennsylvania State University.

AFEM@matlab

2006-03-13T14:42:00.000-08:00

Please visit my new home page: http://math.uci.edu/~chenlong/

This package is developed with Chen-Song Zhang at Univesity of Maryland.

AFEM@matlab is a MATLAB package of adaptive finite element methods (AFEMs) for stationary and evolution partial differential equations in two spatial dimensions. It contains robust, efficient, and easy-following codes for the main building blocks of AFEMs. This will benefit not only the education of the methods but also future research and algorithmic development.

Our package can be useful for education, communication, and research. More precisely, it will (1) speed up program development; (2) facilitate comparisons of ideas and results; (3) improve academic publications. We summarize and emphasis the main features of our package as the following:
• It includes newest development of AFEMs.
• It is concise and easy to follow.
• It can be easily modified for other problems and languages

REFERENCES:

Please acknowledge your use of AFEM@matlab by citing

Long Chen. Short bisection implementation in MATLAB .
Long Chen and Chensong Zhang. A coarsening algorithm and multilevel methods on adaptive grids by newest vertex bisection.
Long Chen and Chensong Zhang. AFEM@matlab: a MATLAB package of adaptive finite element methods.

DOWNLOAD: Matlab Central or Matlab Database

Research Interest

2006-02-17T14:50:00.000-08:00

Please visit my new home page: http://math.uci.edu/~chenlong/

My main research interest is the theoretical analysis and practical application of Adaptive Finite Element Methods (AFEMs). The numerical experiments using FEM need high accuracy to get reliable results. However high accuracy will increase the computation effort including the physical memory as well as cpu time. To speed up the simulation, AFEM is introduced to reduce the size of the computation while keeping optimal accuracy and thus now widely used in scientific computation. While these methods have been shown to be very successful, the theory ensuring the convergence of the algorithm and the advantages over non-adaptive methods is still under development. My main research goal is to to investigate a more complete integration of adaptive and multilevel algorithms, in terms of algorithm design, convergence and complexity theory, and application to important problems in science and engineering.

Multilevel Adaptive Finite Element Methods.

One of my current projects is to apply ideas from multigrid methodology to further improve the efficiency of existing adaptive methods. Existing AFEM algorithms start from a coarse grid and then repeatedly refine without returning to the coarse grid. This successive localized approach is reminiscent of cascade multigrid, which is usually not as efficient, as robust or as widely applicable as the the classic V-cycle or W-cycle multigrid methods. Motivated by our understanding of the different performance of classic multigrid versus cascade multigrid, we propose to develop V-cycle-multigrid-like AFEM to improve the the efficiency and robustness of the classic cascade-multigrid-like AFEM, and, as a result, to develop and analyze AFEM with error indicators and moving mesh methods with monitor functions in a common framework.

Nonlinear Approximation Theory.

Classic linear approximation theory uses Soblev smoothness to characterize the approximability of functions on quasi-uniform grids. The lack of Soblev smoothness of the solution will result a deteriorate of convergent rate if one insists on quasi-uniform grids. Adaptive finite element methods use Besov spaces which is much weaker requirement, to improve the convergence rate. Nonlinear approximation theory characterizes the Besov smoothness in terms of approximability. A new trend is to rely the adaptive finite element methods on the nonlinear approximation theory.
Along this direction, I have done several work. One is to study best approximation of functions with anisotropic singularities. The upper bound and lower bound appeared in [8] using a new fractional norm of second derivatives of object function which could lead to a new class of function spaces. In [10, 11], a kind of Besov norm is used in the theoretical analysis of a 1-D convection-dominated problem and a uniform second order convergence result is obtained for functions with boundary layers. In those papers we also show that an unstable scheme on uniform grid can be made stable on a properly adapted grid and the accuracy of the adapted scheme may depend on (perhaps surprisingly) the uniformity on the grid where the solution is smooth [10, 11]).

Superconvergence.

Another related approximation problem is the superconvergence between solution and its interpolation. It can be used to construct efficient a posterior error estimator for adaptive finite element methods. In [12], we give a simple proof of classic superconvergence result in a symmetric mesh. Also in [4] we give a superconvergence result in 3-D for grid with small perturbation. In [9], we show in an optimal mesh, we may have an exact gradient recovery scheme which can be thought as a preliminary example on the nonlinear superconvergence theory on adaptive grids.

Mesh Generation and Improvement.

By the study of approximation theory, we give cretier of optimal mesh by the approximation error and developed a class of new methods for the mesh improvements. We proposed a new concept Optimal Delaunay Triangulation [9] and develop mesh adaptation schemes based on this concept [7, 2]. In this approach, we are able to combine local refinement and moving mesh methods to get a new and more efficient methods. A preliminary result is reported in [7, 2]. We note that in [1] another research group use this approach to successfully generate 3-D meshes which has better quality than other methods.

Multigrid on Adaptive Grids.

After we get the discrete equation, we need to solve a large algebraic system in the form Ax = b. In most cases the matrix obtained by finite element methods is sparse and thus iterative methods is better than direct methods. An most efficient iterative method is Mutligrid methods. Now I am working on the multigrid on adaptive refined grids and have obtained some preliminary results.

Convergence of Adaptive Finite Element Methods.

There are basically two questions on the AFEM. Does it converge? If yes, how good it is? Those two questions have confirmative answers for Poisson equation. Recently we extend the convergence and optimality of AFEM to mixed finite element methods [5] and a nonlinear Poisson-Boltzmann equation [6].

Applications.

Now I am developing and maintaining a software AFEM@matlab which is a MATLAB package of adaptive finite element methods for stationary and evolution partial differential equations in two spatial dimensions [13, 3]. This package contains robust, efficient, and easy-following codes for the main building blocks of AFEMs. It will (1) speed up program development; (2) facilitate comparisons of ideas and results; (3) improve academic publications. In spite of its brevity, the package is by no means a “toy” software. All the codes are written and optimized using MATLAB’s vectored addressing and built-in functions. Preliminary numerical tests show that our program can solve a middle size problem in seconds on a desktop PC.
Another application project is related to math biology. A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in [6]. This article apparently gives the first rigorous convergence result for a numerical discretization technique for the nonlinear Poisson-Boltzmann equation with delta-function sources, and it also introduces the first provably convergent adaptive method for the equation. This last result is currently one of only a handful of existing convergence results of this type for nonlinear problems.

天上，人间

2006-01-20T10:09:00.000-08:00

李亚伟

我心比天高，文章比表妹还漂亮，曾经在漫长的时光中写作和狂想，试图用诗中的眼睛看穿命的本质。除了喝酒、读书、听音乐是为了享乐，其余时光都反倒被我心目中天上的诗歌之眼看死，且勾去了那些光阴中的魂魄。那时我毫无知觉，自大而又疯狂，以为自己是一个玩命徒。我通常只在初夏和初冬两块时间里写诗，其余时光是人间的，我以为我是天上的人。初夏我内心烂漫、充满喜悦，用语言的听觉倾听人间和海洋的燥动，准备挤进社会，去活；初冬我用词语的耳朵打听命外的消息，准备到很远的地方，也许是天边，也许是眼前，去死。那是80年代，其实那时的雪花和现在没有两样，有时暄闹，有时寂寞。

90年代我完全生活在人间。有时生活在责任感中，有时生活在不负责任中，完全发现自己是一个凡人。我看见与我同辈的80年代诗人群进入90年代后并没写出什么好诗（与我一样），他们开始了再次包装和策划，他们也是凡人，于是出现了后来的各种说法和争吵。我天性反对诗人对自家的诗歌，有一大套说法或一整套理论，反对诗人自负于自家的思想和文笔有正宗的来历（这些常让我好笑得要死），所以那时我认为所有关于诗的说法和争吵都反映了诗人们心目中的阴影。这块阴影很容易紧跟诗人，出现在他们的聚会处，对好诗人来说，这块阴影代表着他们对自己诗歌的没底和不安，对差诗人来说，这块阴影只有一个字：假，这块阴影绝对不是天上投下来的。90年代，马松——我对他的诗佩服之极，他是我心目中最好的诗人——他总是用一个“假”字来搞定酒桌上另一个醉汉兄弟，整个90年代，马松喝醉后就对人比中指。我不知道有多少人想剁他的指头——那写诗和数钱都不方便了，他早已不读当代诗歌，更不知道谁的诗好，谁的诗差，他只知道“假”字很厉害，因为“‘假’字害了你终身”。

那时，诗歌被策划，一群一群的诗人要做策划出来的文化品牌，当我看到策划得比较大的品牌诗人时，我心里常常会冒出一个东北口音“这傻X，啥时候崩盘呢？”，那些日子，我不好意思写诗，想到自己是诗人就害羞，早上起床有时还脸红，出们碰到美女和正派的青年我都低着头，妈个麻花。在整个90年代，只有碰到长头发搞艺术的,我非常不在乎，我也曾蓄长发，后来定定神，剪了。因为我突然明白，艺术家中（画家、诗人、整广告的）凡是没才气的都蓄长发。

如今，已到了21世纪，不知道哪些文化垃圾正被人从古今中外物流过来，但我相信，在北京，不管什么东西，肯定正在被包装，在诗人、艺术家、导演家里正被打着先锋的粉底。其实诗歌从古到今都是先锋的，可我们不嫌累，我们只嫌出名不容易,奶奶个熊！此时我像宋炜——这也是一个天上的人——像他在女人面前说脏话那么有瘾，并且嘴滑，这些日子我极其嘴滑，说的话自己也不知道是真是假。因为整个90年代，实际上我也像我的同辈诗人们一样非常地想做大诗人，而且我还装着X，语不惊人誓不休，同时天天想着吃香的喝辣的。

但我知道，我们不应该对大诗人一词感兴趣，而应该对写作过程感兴趣。因为，即使手术使中国的美女过剩，我们也没什么搞头，她们眉毛、鼻子、乳房越假，极可能她们需要的爱情越真，这东西我们已经不能对付，我们如果再次的策划和包装自己，那会把自己弄成一群过气的二流子。当然，也有牛X的，大师情结弄得他大脑结实，像木头、像橡胶、像铁，在硬东西里面，他会想，妈的X，我是先锋，先锋退回去，成了古典。

前天夜晚，我和张小波、马松、陈琛、宋强等一帮朋友狂饮至夜半，大醉时听到天气预报（天上的声音，东北下雪了），突然想起了诗歌，想起一个孤独的小诗人在东北写诗，他的窗外下起了大雪，这情节深深地弄了我一下，酒中空着的心充满了意境，我突然有所觉悟：我曾经对诗歌无比苛刻，我是因为喜欢好诗、喜欢天外之音才对诗歌如此着迷的吗？不是，这如同世间没有好酒，酒徒们也会造些滥酒喝得幸福不已，那一刻，我的心病和美德，仿佛又被火星上的桃花眼所窥破：我喜欢诗歌，仅仅是因为写诗愉快，写诗的过瘾程度，世间少有。我不愿在社会上做一个大诗人，我愿意在心里、在东北、在云南，在陕西的山里做一个小诗人，每当初冬，在心里看着漫天雪花纷飞而下，推开黑暗中的窗户，眺望他乡和来世, 哦，还能听到人世中最寂寞处的轻轻响动。

2003．10．14

关于语言、杨黎及其它

2006-01-18T22:45:00.000-08:00

文/韩东

1 语言是光线

语言指向的不是事物，是事物间的关系，即事物的意义。

因此，对语言的要求不应是准确对位，而是“看见”。通过语言，我看见事物，而我看见的事物实际上是事物间的关系。

语言，就像光线，而不是模具。

由于看见的需要，语言应该趋向于清明。

准确对位的语言是科学的语言，它注重的是语言和事物间的关系，而不是事物与事物间的关系。它的权威来自于语言和事物相互契合的迷信。科学语言中的数学、逻辑是模具，而非光线。它被用来容纳事物，而非呈现事物。因此，科学有进步，它的语言需要不断地进行修正。这一过程永不可能结束。另一方面，数学和逻辑又可单独地抽离出来演绎，作为某种智力游戏。

叙述的语言是另一回事，它是意义的诞生之地。这意义是由精神和事物的相遇促成的，它的根据既非精神也非事物，乃是二者的相遇。我无法从中抽离出任何单独的东西。光线作为看见和对象之间的媒介，既不属于看见，也不属于对象。

模具是纯粹的人造物。光线则不然，它是看见的条件，也是看不见的条件。

“说什么？”说世界，说事物，但有一个条件，就是必须说我看见的世界或事物。语言可以言说语言，把它作为事物。把它作为语言，则不能言语。叙述语言无论如何不可能成为棋类游戏。

“怎么说？”这里的确有某种分别。由于看见的要求，就是尽量地清明，取消语言的“积垢”。犹如一块玻璃，擦去尘埃污渍，让它透光，就像没有了一样。最后，它真的就没有了。怎么说的极限，就是清明的极限，就是光照的极限。

从此意义上说，杨黎的取消语义是对的。语言传至我的手中，已是一件污染之物。对它的警惕和抗拒都无可厚非。但，“废话”说我却不赞同，就像我不信任棋类游戏一样。我相信语言应是光线，是光明，它使我，或者可能使我看见。2语言的界限

在语言之内言说语言是不可能的，除非，把被言说的语言作为事物，作为言说的对象。

对语言的沉思即对语言的言说，它有别于使用语言。使用语言时，我位于语言中。言说语言时，我在其外，语言作为事物或对象。

一个使用语言的人（如诗人）可以不考虑如何言说语言，这无损于他的作为。但，如果他试图言说语言，必须退至语言之外，并获得看见的距离。尽管我表情丰富，丑陋或俊美，也善于控制，但我看不见自己的脸。若要看见，就得借助镜子，或照片，或别人的目光。在这些情况下，我的脸作为观看的对象，作为事物。

在观看中，语言作为事物，一定如此。所以，存在着对言说的言说，对言说的言说的言说……以至无穷。只有在使用中，语言成为惟一的。

若沉思或言说语言，必然看到它与世间所有的事物一样，它的有限性，它的不能自圆其说，它作为事物在时光中的无常和可悲。语言是世间之物，就像生命体那样的复杂、含混、充满矛盾，并有着生死大限。它不是究竟、目的，只是手段而已。

手段，是被我反复诅咒，而不能摆脱的一个字眼，实际上是我在世惟一可能的处境。我所以为的目的，不过是手段而已，概莫能外。权力，是指挥的手段，但我追求权力。金钱，是购买的手段，但我追求金钱。语言，是看见的手段，但我追求语言。人生，是超越的手段，但我追求人生。这是亘古以来的大骗局。世间万物，宇宙之内，并无合目的性，即没有一物是我的目的，是真正的究竟或绝对。只有一点是真实的，就是我对目的渴望。

但有一点，作为手段的事物，的确处于不同的层次之上。手段，并不一定与投机相关，在一些事情上，它只与界限相关。说语言是手段，并非指“文以载道”，或通过语言获取声名地位金钱权力等等，这是等而下之的，是对语言这种手段的滥用。说语言是手段，是指它与某种超越的绝对之物相联系。在此意义上，将它作为目的本身，关闭通道，一劳永逸地解决问题是一种自欺。说语言是手段，便是划出它的界限。

这样的认识，或许导致语言问题上的虚无主义，或许，经历长期的虚无之后触摸真正的绝对。由于绝对的感召和我对目的渴望，应冒虚无的生死危险。这是值得的。

虚空的虚空

凡事都是虚空
人一切的劳碌
就是他在日光之下的劳碌
有什么益处呢？
一代过去
一代又来
地却永远长存
日头出来
日头落下
急归所出之地
风往南刮
又向北转
不住地旋转
而且返回转行原道
江河都往海里流
海却不满
江河从何处流
仍归何处

万事令人厌烦这是《旧约》“传道书”中的一节，排列成“橡皮体”，以说明我的看法。

3迷雾

语言并非世界，乃是世界之光。在光照下，世界得以呈现、被看见。然而，被看见的并非世界，而是世界中的关系，是它的意义。我看见我愿意看见的东西。看见和语言中的世界共存。世界的意义仅仅是对我而言的，世界的意义对世界并无意义，但它的确又是世界的意义。

世界只有一个，但意义多重。在不同的语言中，不同的看见中，世界破碎、自相矛盾。破碎、自相矛盾正是世界意义的体现。

语言作为看见的媒介，积累了这一切，似乎，它本身也变得有意义。似乎，它本身变成了目的。但这意义是偷窃来的，是从看见中偷窃来的，以吸引我的目光。

清除语言中积垢、含混、意义是可为之事，以使它变得清明，转向世界。

世世代代，语言积累着世界庞杂而含混的意义，当真是迷雾重重。光线被迷雾所取代。世世代代，要求看见的人深受其苦，他们所看见的世界能见度极差，瞪视着变幻莫测的迷雾本身。

所谓的“知识分子诗人”其要害并非是书面语的使用，并非是“殖民地写作”，更非知识炫耀。他们受惑于迷雾，并制造迷雾。他们本能地排斥看见。迷雾奇幻的色彩取代了事物的关系、世界的意义，作为中介的语言成为华丽的屏障。

杨黎的意义即在于清除迷雾，恢复语言的光照。他的写作和言说都说明了这一点。要求看见的人并非绝无仅有，但像杨黎这样坚决、理性、一贯和极端者在我的时代却是惟一。因此，他是一个标志。从实际效果看，正是杨黎的坚持和批评，使“语言生产力”得以巨大地释放。有“橡皮”为证。

我受惠于杨黎，这不可否认。这种受惠源于杨黎的存在。杨黎存在着，这便是支撑。受惠还表现在他顽固的存在迫使我思考，关于语言，关于诗歌的现状等等。

语言是世界之光，是对杨黎的语言即世界思考的结果。语言的清明和光照是对杨黎的取消语义的思考结果。迷雾和光线是我发明的字眼，其灵感依然来自于对杨黎的思考。顺便说一句，于坚的堕落并非在于他的世俗行为，乃是由于他的语言态度。如今，他成为一个迷雾制造者。他的“棕皮”、他的作品都已成为蛊惑人心、虚张声势的范本，其明显标志就是浑浊。这正是迷雾的特征。于坚，已成为他所反对的隐喻的牺牲品。

4看与关注我的思考源于杨黎。正是因为杨黎我才决定动手写这篇文章。但这不等于说我完全赞同杨黎。不赞同和赞同同样是明确的。在对具体诗歌或文学作品的评价上更是如此。

关于“怎么写？”和“写什么？”，我和杨黎在“橡皮”上曾有过认真的讨论，但并未得出一致的结论。杨黎认为怎么写是惟一的，而我认为怎么写和写什么是一体的。双方都未被说服，但通过讨论明白了彼此为什么持这样的观点。我认为，这就是成果。

我不赞同杨黎的还有，他反对将语言与绝对相联系，认为语言是一个封闭的自足体。我不赞成“诗歌教”，虽说这是杨黎的戏言。

我关于语言的“手段”说，定然也会让杨黎大为惊讶。这一问题与上面的问题直接相关。我以为，与超越的存在相比，语言只能是手段。它不是手段（如国家、权力、文化、思想意识、人生、金钱等等）的手段，但它是（在极限处）作为绝对目的手段。

由此，语言之光除了照射世界，还应照射虚无，照向极远处，不可企及之处。条件是净空语言，留出通道。不仅净空语义，最后也将净空语言本身。当然，这是困难的，也是不可能的。但，只有在不可能的向度上，语言才能获得它根本的意义。这一向度不可取消。若取消，在定义上，语言只能是寻常之物。它的不寻常和神秘正是不自称为目的，正是降低到寻常之物之下，降低到微不足道，一无所是，降低到取消自身。当然，这是相对绝对之物而言的。面对世界范围的各种强权、势力、意义，语言则不应卑躬屈膝。

我不赞成杨黎的“废话”说，皆因为此。“废话”把语言当作目的，并不导向有意义的虚无。它并不虚无，因为它保留了自身，保留了“废话”的快感。若坚持这种快感，语言有可能变成某种棋类游戏，无任何意义，但有自得其乐的意义。语言不应成为娱乐。

朱文说过他不写诗的理由，因为，“写诗太有快感了”。此话虽是搪塞，但不无道理。看见的人并不应以看见为炫耀，走马看花和全神贯注的静观是不一样的。面对视力表和极目远眺是不一样。看着车水马龙繁华街市和在人群中认出久别的亲人也是不一样的。看，应提炼成关注。

看，依赖于视力。只有关注，最后导致取消自身。

我爱那些视力良好、尽情浏览的诗人，但更爱那些视力尖锐、全神贯注的诗人，哪怕他的视力稍差。这就是我如此喜欢杨健的理由。在对杨健诗歌的评价上，杨黎和我的观点相左，这也是题中应有之意。

在对杨黎的思考中，我亦有新的发现。他的“语言即世界”、“取消语义”、“废话”说以及“怎么写”高于“写什么”广为传播，为人知晓。但他有一句相对不受重视的话，却让我如获至宝。他曾将我的“诗到语言为止”修正为“诗从语言开始”。首先，我同意这样的修正。无论杨黎怎样理解，我却认为这是一个必然的结论。从语言开始，将导向何处？在我这里便是绝对、真理、超自然，并非任何世间实在之物（包括语言）。在有限的时空内，也许只能体会为虚无。虚无，正是真理在世间的永恒的形象。

2002.7.16

毕业分配

2006-01-17T21:01:00.000-08:00

李亚伟

所有的东西都在夏天
被毕业分配了
哥们都把女朋友留在低年级
留在宽大的教室里读死书读她们自个儿的死信

但是我会主动和你联系，会在信中
向你谈及我的新生活、新环境及有趣的邻居
准时向你报告我的毛病已有所好转的喜讯
逢年过节
我还会给你寄上一颗狗牙齿做的假钻石
寄出山羊皮、涪陵榨菜或什么别的土特产

如果你想我得厉害
就在上古汉语的时候写封痛苦的情书
但鉴于我不爱回信的习惯
你就干脆抽空把你自己寄来
我会把你当一个凯旋的将军来迎接
我要请摄影记者来车站追拍我们历史性的会晤
我绝对不会躲着不见你
不会借故值班溜之大吉
不会向上级要求去很远的下属单位出差什么的
我要把你紧紧搂在怀里
粗声大气地痛哭，掉下大滴的眼泪在你脸上
直到你呼吸发生困难
并且逢人就大声宣布：
“瞧，我的未婚妻!这是我的老婆咧!”

你不要看到我的衣着打扮就大为吃惊
不要过久地打量我粗黑的面容和身着的狐皮背心
要尊重我帽子上的野鸡毛
不要看到我就去联想生物实验楼上的那些标本
不要闻不惯我身上的荷尔蒙味
至少不要表露出来使我大为伤感
走进我的毡房
不要撇嘴，不要捂着你那翘鼻子
不要扯下壁上的貂皮换上世界名画什么的
如果你质问我为什么不回信
我会骄傲地回答：写字那玩意
此地一点也不时兴!
你不必为我的处境搞些喟然长叹、潸然泪下之类的仪式
见了骑毛驴的酋长、族长或别的什么蛮夷
更不能怒气冲冲上前质问
不要认为是他们在迫害我
把我变成了猩猩、野猪或其它野生动物
他们是最正直的人
是我的好兄弟!

如果你感兴趣
我会教你骑马、摔跤，在绝壁上攀沿
教你如何把有夹的猎枪刺在树上射击
教你喝生水吃生肉
再教你跳摆手舞或唱哈达什么的
你和我结婚
我会高兴得死去活来
我们会迅速生下一大打小狗子、小柱子
这些威武的小家伙、小蛮夷
一下地就能穿上马靴和貂皮裤衩
成天骑着马东游西荡
他们的足迹会遍布塞外遍布世界各地
待最后一个小混蛋长大成人
我就亲自挂帅远征
并封你为压寨夫人
我们将骑着膘肥体壮的害群之马
去很远很远的地方戌边

中文系

2006-01-17T20:59:00.000-08:00

李亚伟

中文系是一条撒满钩饵的大河
浅滩边，一个教授和一群讲师正在撒网
网住的鱼儿
上岸就当助教，然后
当屈原的秘书，当李白的随从
当儿童们的故事大王，然后，再去撒网

有时，一个树桩船的老太婆
来到河埠头——鲁迅的洗手处
搅起些早已沉滞的肥皂泡
让孩子们吃下。一个老头
在讲桌上爆炒野草的时候
放些失效的味精
这些要吃透《野草》的人
把鲁迅存进银行，吃他的利息
在河的上游，孔子仍在垂钓
一些教授用成绺的胡须当钓线
以孔子的名义放排钩钓无数的人
当钟声敲响教室的阶梯
阶梯和窗格荡起夕阳的水波
一尾戴眼镜的小鱼还在独自咬钩
当一个大诗人率领一伙小诗人在古代写诗
写王维写过的那些石头
一些蠢鲫鱼或一条傻白鲢
就可能在期末渔汛的尾声
挨一记考试的耳光飞跌出门外

老师说过要做伟人
就得吃伟人的剩饭背诵伟人的咳嗽
亚伟想做伟人
想和古代的伟人一起干
他每天咳着各种各样的声音从图书馆
回到寝室

亚伟和朋友们认真上了三天课以后
就出现各种各样的临床症状
每天睡觉
被盖里都感到地狱之火的熊熊
有时他们未睡着就摆动着身子
从思想的门户游进燃烧着的电影院
或别的不便提及的去处

一年级的学生，那些
小金鱼小鲫鱼还不太到图书馆
及茶馆酒楼去吃细菌常停泊在教室或
老乡的身边有时在黑桃Q的桌下
快活地穿梭

诗人胡玉是个老油子
就是溜冰不太在行，于是
常常踏着自己的长发溜进
女生密集的场所用鳃
唱一首关于晚风吹了澎湖湾的歌
更多的时间是和亚伟
在酒馆的石缝里吐各种气泡
二十四岁的敖歌已经
二十四年都没写诗了
可他本身就是一首诗
常在五公尺外爱一个姑娘
节假日发半价电报
由于没记住韩愈是中国人还是苏联人
敖歌悲壮地降下了一年级，他想外逃
但他害怕爬上香港的海滩会立即
被警察抓去考古汉语

万夏每天起床后的问题是
继续吃饭还是永远
不再吃了
和女朋友卖完旧衣服后
脑袋常吱吱地发出喝酒的信号
他的水龙头身材里拍击着
黄河愤怒的波涛，拐弯处挂着
寻人启示和他的画夹

大伙的拜把兄弟小绵阳
花一个月读完半页书后去食堂
打饭也打炊哥
最后他却被蒋学模主编的那枚深水炸弹
击出浅水区
现已不知饿死在哪个遥远的车站

中文系就是这么的
学生们白天朝拜古人和王力和黑板
晚上就朝拜银幕或很容易地
就到街上去凤求凰兮
这显示了中文系自食其力的能力
亚伟在露水上爱过的那医专
的桃金娘被历史系的瘦猴赊去了很久
最后也还回来了亚伟
是进攻医专的元勋他拒绝谈判
医专的姑娘就有被全歼的可能医专
就有光荣地成为中文系的夫人学校的可能

诗人杨洋老是打算
和刚认识的姑娘结婚老是
以鲨鱼的面孔游上赌饭票的牌桌
这根恶棍认识四个食堂的炊哥
却连写作课的老师至今还不认得
他曾精辟地认为纺织厂
就是电影院就是美味的火锅
火锅就是医专就是知识
知识就是书本就是女人
女人就是考试
每个男人可要及格啦

中文系就这样流着
教授们在讲义上喃喃游动
学生们找到了关键的字
就在外面画上漩涡画上
教授们可能设置的陷阱
把教授们嘀嘀咕咕吐出的气泡
在林荫道上吹到期末

教授们也骑上自己的气泡
朝下漂像手执丈八蛇矛的
辫子将军在河上巡逻
河那边他说“之”河这边说“乎”
遇着情况教授警惕地问口令：“者”
学生在暗处回答道：“也”

根据校规领导命令
学生思想自由命令学生
在大小集会上不得胡说八道
校规规定教授要鼓励学生
创新成果可在酒馆里对女服务员汇报
不得污染期终卷面
中文系也学外国文学
重点学鲍狄埃学高尔基，有晚上
厕所里奔出一神色慌张的讲师
他大声喊：同学们
快撤，里面有现代派

中文系在古战场上流过
在怀抱贞洁的教授和意境深远的月亮
下边流过河岸上奔跑着烈女
那些石洞里坐满了忠于杜甫的寡妇
和三姨太坐满了秀才进士们的小妾
中文系从马致远的古道旁流过
以后置宾语的身份
被把字句提到生活的前面
中文系如今是流上茅盾巴金们的讲台了

中文系有时在梦中流过，缓缓地
像亚伟撒在干土上的小便像可怜的流浪着的
小绵阳身后那消逝而又起伏的脚印，它的波浪
正随毕业时的被盖卷一叠叠地远去

苏东坡和他的朋友们

2006-01-17T20:53:00.000-08:00

李亚伟

古人宽大的衣袖里
藏着纸、笔和他们的手
他们咳嗽
和七律一样整齐

他们鞠躬
有时著书立说，或者
在江上向后人推出排比句
他们随时都有打拱的可能

古人老是回忆更古的人
常常动手写历史
因为毛笔太软
而不能入木三分
他们就用衣袖捂着嘴笑自己

这些古人很少谈恋爱
娶个叫老婆的东西就行了
爱情从不发生三国鼎立的不幸事件
多数时候去看看山
看看遥远的天
坐一叶扁舟去看短暂的人生

他们这些骑着马
在古代彷徨的知识分子
偶尔也把笔扛到皇帝面前去玩
提成千韵脚的意见
有时采纳了，天下太平
多数时候成了右派的光荣先驱

这些乘坐毛笔大字兜风的学者
这些看风水的老手
提着赋去赤壁把酒
挽着比、兴在杨柳岸徘徊
喝酒或不喝酒时
都容易想到沦陷的边塞
他们慷慨悲歌

唉，这些进士们喝了酒
便开始写诗
他们的长衫也像毛笔
从人生之旅上缓缓涂过
朝廷里他们硬撑着瘦弱的身子骨做人
偶尔也当当县令
多数时候被贬到遥远的地方
写些伤感的宋词

红色岁月－第五首

2006-01-16T21:14:00.000-08:00

李亚伟

我心比天高，文章比表妹漂亮
骑马站在赴试的文途上，眺望着革命
犹如一颗心被皮肤包围后成为美色
或者一个意义被嘴唇唱出成为歌声中的丹顶鹤

一颗心率领全部生活夺取天下
它无法统治，种子不能统治花，皇帝不能统治云
诗人占据文字，形成偏安，又骑马治天下
使人民由清一色的服饰到全体戎装，由欠收到饮食单一

爱比恨后发芽，比枣树先结果且红透了脸和决心书
这是强烈要求自杀的身子用她的内心看到了我——
那秋天的远境中纵马的男人，使她甘心被占领
请求用一颗心来消灭
而我已从对她的崇拜发展成为奴役
骑着马朝奴隶社会而去

红色岁月－第十二首

2006-01-15T21:19:00.000-08:00

李亚伟

我看见一个被汉字测出来的美女从偏旁上醒来
右手持剑左手采花
她用象形的一部分吟诗作赋
用会意的一部分兴风作浪
空前的美女!下加一竖是玫瑰
长在树上是妓女
摘下来是格言警句和一年中最后的收成
运回家是不会写的字，最后变成醒目的标语和口号

我只有把她加在表哥的旁边成为表妹
派她到世界各地去捉半字半人的怪物
但加一封回信她又变成了夫人，所以
换其它偏旁她就是妖精，在深山老林中反对世界上的美

如同过去的英雄如今变成隐士或反英雄
城里便派出三个丑男人去打她，打得她变来变去
最后躲在山洞中吃美男子
这打不死的妖精!美得刻骨和极端
已经不能变成现实中的女士或小姐
更使我无法回到最初的字面上去读她

我在双鱼座上给你写信

2006-01-14T21:09:00.000-08:00

李亚伟

我在双鱼座上给你写信
从天上一笔一笔往下写，我是天上的人
我住得太高，爱你有些够不着

我看见平原上走过一条很短的命
在被寂寞刻破的北方的平原上
蟋蟀正无休止地拨着情人的手机

Publication

2005-12-26T13:48:00.000-08:00

Please visit my new home page: http://math.uci.edu/~chenlong/

L. Chen, R.H. Nochetto, and J. Xu. Multilevel methods on graded bisection grids. Preprint. University of Maryland. 2007.
L. Chen and C-S. Zhang. A coarsening algorithm and multilevel methods on adaptive grids by newest vertex bisection. Submitted. 2007.
L. Chen and C-S. Zhang. AFEM.at.matlab: a MATLAB package of Adaptive Finite Element Methods. Technical Report. University of Maryland. 2006.
L. Chen. Short bisection implementation in MATLAB. Submitted to International Workshop on Computational Science and its Education, 2006.
L. Chen and M.J. Holst. Mesh adaptation based on Optimal Delaunay Triangulations. Preprint. University of California, San Diego. 2006.
L. Chen, M.J. Holst, and J. Xu. The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation. Accepted by SIAM Journal on Numerical Analysis, 2006.
L. Chen,M.J. Holst, and J. Xu. Convergence and optimality of adaptive mixed finite element methods. Submitted to Mathematics of Computation, 2006.
J. Jiang, S. Shu, Y. Huang, and L. Chen. A New Adaptive Mesh Method for Two Dimensional Heat Conduction Equations with Three Temperatures. Chinese Journal of Computational Physics, 24(1), 19-28, 2007.
L. Chen and J. Xu. Stability and accuracy of adapted finite element methods for singularly perturbed problems. Submitted to Numerische Mathematik, 2005.
L. Chen, P. Sun, and J. Xu. Optimal anisotropic simplicial meshes for minimizing interpolation errors in Lp-norm. Mathematics of Computation, 76(257):179–204, 2007.
L. Chen and J. Xu. An optimal streamline diffusion finite element method for a singularly perturbed problem. In AMS Contemporary Mathematics Series: Recent Advances in Adaptive Computation, volume 383, pages 236–246, Hangzhou, 2005.
L. Chen. Superconvergence of tetrahedral linear finite elements. International Journal of Numerical Analysis and Modeling, 3(3):273–282, 2006.
L. Chen. New analysis of the sphere covering problems and optimal polytope approximation of convex bodies. Journal of Approximation Theory, 133(1):134–145, 2005.
L. Chen, P. Sun, and J. Xu. Multilevel homotopic adaptive finite element methods for convection dominated problems. In The Proceedings for 15th Conferences for Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 40, pages 459–468. Springer, 2004.
L. Chen. Mesh smoothing schemes based on optimal Delaunay triangulations. In 13th International Meshing Roundtable, pages 109–120, Williamsburg, VA, 2004. Sandia National Laboratories.
L. Chen and J. Xu. Optimal Delaunay triangulations. Journal of Computational Mathematics, 22(2):299–308, 2004.

B4

2005-12-11T18:50:00.000-08:00

Long Chen. Lecture Notes: Subspace Correction and Multigrid Methods.

ABSTRACT:
This is a short introduction to the method of subspace correction [6] on solving algebraic equations. Many iterative methods including multigrid methods can be developed and analyzed in this framework. This notes will emphasis on the theoretical convergence analysis of iterative methods, especially multigrid methods. A new identity [10] for a successive subspace correction method is included to make the analysis of multigrid methods more straightforward. The presentation mainly follows Xu’s work [6, 8, 7, 9].

CONTENTS
1. Introduction 1
2. Basic linear iterative methods 6
3. Convergence analysis of basic iterative methods 8
4. Space decomposition 12
5. Interpolation spaces using multilevel subspaces 16
6. Subspace correction 22
7. PSC: BPX and Hierarchal preconditioner 24
8. SSC: X-Z identity 27
9. Multigrid method and its convergences 32
References 38
Appendix: Matrix Theory 39

B3

2005-12-10T23:37:00.000-08:00

Long Chen. Lecture Notes: Isotropic Adaptivity through Local Refinement.

PERFACE: This is the lecture notes for the 2006 summer school. This part will mainly discuss related topics on adaptive finite element methods (AFEMs). It includes recent development of the convergence and optimality of AFEMs through local refinement, and asymptotically exact a posteriori error estimate based on superconvergence.

B2

2005-12-10T23:36:00.000-08:00

Long Chen and Jinchao Xu. Topics on Adaptive Finite Element Methods.

CONTENT:

1 Convergence of Adaptive Finite Element Methods 2
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Residual type error estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Convergence of an adaptive finite element method . . . . . . . . . . . . . . . . 19
1.5 Optimality of the adaptive finite element method . . . . . . . . . . . . . . . . 24

1 A Posteriori Error Estimator by Post-processing 2
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Linear finite element on patch symmetric grids . . . . . . . . . . . . . . . . . 6
1.3 Linear finite element on mildly structured grids . . . . . . . . . . . . . . . . . 11
1.4 Linear finite element on general unstructured grids . . . . . . . . . . . . . . . 18

B1

2005-12-10T16:18:00.000-08:00

Ph. D Thesis: Robust and Accurate Algorithms for Solving Anisotropic Singularities

This dissertation is focused on the construction of robust and accurate algorithms for mathematical models of physical phenomena that exhibit strong anisotropies, that is, when the quantities have very slow and smooth variations in some directions but have rapid variations in other directions.

Our first result is on the mathematically characterization of optimal or nearly optimal meshes for a general function which could be either isotropic or anisotropic. We give an interpolation error estimate for the continuous and piecewise linear nodal interpolation. Roughly speaking, a nearly optimal mesh is a quasi-uniform triangulation under some new metric defined by the Hessian matrix of the object function. We also prove the error estimate is optimal for strictly convex (or concave) functions.

Based on the interpolation error estimates, we introduce a new concept Optimal Delaunay Triangulation (ODT) and present practical algorithms to construct such nearly optimal meshes. By minimizing the interpolation error globally or locally, we obtain some new functionals for the moving mesh method and several new mesh smoothing schemes.

We then apply our mesh adaptation algorithms to the convection dominated convection-diffusion problems which present anisotropic singularities such as boundary layers. We develop a robust and accurate adaptive finite element method for convection dominated problems by the homotopy of the diffusion parameter.

We give an error analysis of a one dimensional convection dominated convection-diffusion problem that is discretized by the standard finite element method on layer-adapted grids. We find that it is not uniform stable with respect to the perturbation of grid points. We then design a special streamline diffusion finite element method and prove the uniform stability and optimality of our new method.

We also discuss some related concepts and problems on the optimal Delaunay triangulations.

P7

2005-12-10T13:00:00.000-08:00

Long Chen, R.H. Nochetto, and Jinchao Xu. Multilevel methods on bisection grids.

coming soon

ABSTRACT: In this paper, optimal additive and multiplicative multilevel methods are designed and analyzed on adaptive grids obtained by bisections. The analysis relies on a novel decomposition of bisection grids for bridging the results from quasi-uniform grids with locally refined grids.

P6

2005-12-10T11:28:00.000-08:00

Long Chen and Chensong Zhang. A coarsening algorithm and multilevel methods on adaptive grids by newest vertex bisection.

coming soon

ABSTRACT:
In this paper, a new coarsening algorithm is proposed for the adaptive grids obtained by the newest vertex bisection method in two dimensions. One distinguish feature of our approach is that we do not maintain the refinement tree. A new hierarchical basis preconditioner for second order elliptic equations is developed based on the nested grids obtained by the coarsening algorithm. Numerical experiments shows that the proposed coarsening algorithm and preconditioner are very efficient and easy to implement.

P5

2005-12-10T11:27:00.000-08:00

Long Chen and Chensong Zhang. AFEM@matlab: a MATLAB package of adaptive finite element methods.

AFEM@matlab

ABSTRACT:
AFEM@matlab is a MATLAB package of adaptive finite element methods (AFEMs) for stationary and evolution partial differential equations in two spatial dimensions. It contains robust, efficient, and easy-following codes for the main building blocks of AFEMs. This will benefit not only the education of the methods but also future research and algorithmic development.

P4

2005-12-09T23:26:00.000-08:00

Long Chen, Michael Holst, and Jinchao Xu. The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation.

Chen.L;Holst.M;Xu.J2006a

ABSTRACT: A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson-Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson-Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta function sources. {\it A priori} error estimates for the finite element approximation is obtained for the regularized Poisson-Boltzmann equation based on certain quasi-uniform grids in two and three dimensions. Adaptive finite element approximation through local refinement driven by {\it a posteriori} error estimate is shown to converge. The Poisson-Boltzmann equation does not appear to have been previously studied in detail theoretically, and it is hoped that this paper will help provide molecular modelers with a better foundation for their analytical and computational work with the Poisson-Boltzmann equation. Note that this article apparently gives the first rigorous convergence result for a numerical discretization technique for the nonlinear Poisson-Boltzmann equation with delta-function sources, and it also introduces the first provably convergent adaptive method for the equation. This last result is currently one of only a handful of existing convergence results of this type for nonlinear problems.

P3

2005-12-09T21:21:00.000-08:00

Long Chen. Short bisection implementation in MATLAB .

Chen.L2006a.pdf

ABSTRACT: A short MATLAB implementation of the local mesh refinement using newest bisection or longest bisection is presented in this paper. This short implementation is helpful for the teaching of adaptive finite element methods and programming in more advanced languages.

P2

2005-12-08T00:52:00.000-08:00

Long Chen and Michael Holst. Mesh adaptation based on Optimal Delaunay Triangulations.

ABSTRACT: In this paper, a mesh adaptation scheme based on the concept of optimal Delaunay triangulations (ODTs) is developed. The mesh adaptation is obtained by minimizing the interpolation error in the weighted $L^1$ norm. A discrete Laplacian is used as a good preconditioner in the Newton's method to speed up the traditional local smoothing approach.

P1

2005-12-08T00:41:00.000-08:00

Long Chen, Michael Holst, and Jinchao Xu. Convergence and Optimality of Adaptive Mixed Finite Element Methods.

under revision

A6

2005-12-05T15:00:00.000-08:00

Jun Jiang, Shi Shu, Yunqing Huang and Long Chen. A New Adaptive Mesh Method for Two Dimensional Heat Conduction Equations with Three Temperatures. Chinese Journal of Computational Physics, 24(1), 19-28, 2007.

ABSTRACT: Two dimensional heat conduction equations with three temperature is an important model in the simulation of inertial confinement fusion (ICF), which approximately describes the process of radiant energy broadcasting in the quiescent medium and energy exchange of electrons with photons and irons. A symmetric finite volume method (SFVEM) and a new mesh adaptation approach based on the Hessian matrix are proposed for the the numerical simulation in this paper. It is shown that the energy conversation error of our new approach is much better than other adaptive mesh methods using only the gradient of the solution.

A5

2005-12-05T14:54:00.000-08:00

Long Chen and Jinchao Xu. Stability and accuracy of adapted finite element methods for singularly perturbed problems. Technique Report, Department of Mathematics, The Pennsylvania State University, :, 2005.

Chen.L%3BXu.J2005a.pdf

ABSTRACT: The stability and accuracy of a standard finite element method (FEM) and a new streamline diffusion finite element method (SDFEM) are studied in this paper for a one dimensional singularly perturbed connvection-diffusion problem discretized on arbitrary grids. Both schemes are proven to produce stable and accurate approximations provided that the underlying grid is properly adapted to capture the singularity (often in the form of boundary layers) of the solution. Surprisingly the accuracy of the standard FEM is shown to depend crucially on the uniformity of the grid away from the singularity. In other words, the accuracy of the adapted approximation is very sensitive to the perturbation of grid points in the region where the solution is smooth but, in contrast, it is robust with respect to perturbation of properly adapted grid inside the boundary layer. Motivated by this discovery, a new SDFEM is developed based on a special choice of the stabilization bubble function. The new method is shown to have an optimal maximum norm stability and approximation property in the sense that $\|u-u_{N}\|_{\infty}\leq C\inf_{v_{N}\in V^{N}}\|u-v_{N}\|_{\infty},$ where $u_{N}$ is the SDFEM approximation in linear finite element space $V^{N}$ of the exact solution $u$. Finally several optimal convergence results for the standard FEM and the new SDFEM are obtained and an open question about the optimal choice of the monitor function for the moving grid method is answered.

A4

2005-12-04T15:48:00.000-08:00

Long Chen, Pengtao Sun and Jinchao Xu. Optimal anisotropic simplicial meshes for minimizing interpolation errors in ${L}^p$-norm. Mathematics of Computation (In Press), :, 2006.

Chen.L;Sun.P;Xu.J2006.pdf

ABSTRACT: In this paper, we present a new optimal interpolation error estimate in $L^p$ norm ($1\leq p\leq \infty$) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and obtain optimal monitor functions from the view points of minimizing interpolation error in the $L^p$ norm. Some numerical examples are also given to support the theoretical estimates.

A3

2005-12-04T15:21:00.000-08:00

Long Chen. Superconvergence of tetrahedral linear finite elements. International Journal of Numerical Analysis and Modeling, 3:273--282, 2006.

Chen.L2006.pdf

ABSTRACT: In this paper, we show that the piecewise linear finite element solution $u_{h}$ and the linear interpolation $u_{I}$ have superclose gradient for tetrahedral meshes, where most elements are obtained by dividing approximate parallelepiped into six tetrahedra. We then analyze a post-processing gradient recovery scheme, showing that the global $L^2$ projection of $\nabla u_h$ is a superconvergent gradient approximation to $\nabla u$.

A2

2005-12-04T15:10:00.000-08:00

Long Chen. New Analysis of the Sphere Covering Problems and Optimal Polytope Approximation of Convex Bodies. Journal of Approximation Theory, 133:134-145, 2005.

Chen.L2005.pdf

ABSTRACT: In this paper, we show that both sphere covering problems and optimal polytope approximation of convex bodies are related to optimal Delaunay triangulations, which are the triangulations minimizing the interpolation error between function $x^2$ and its linear interpolant based on the underline triangulations. We then develop a new analysis based on the estimate of the interpolation error to get the Coxeter-Few-Rogers lower bound for the thickness in the sphere covering problem and a new estimate of the constant $del_n$ appeared in the optimal polytope approximation of convex bodies.

A1

2005-12-04T15:01:00.000-08:00

Long Chen and Jinchao Xu. Optimal {Delaunay} triangulations. Journal of Computational Mathematics, 22(2):299-308, 2004.

Chen.L%3BXu.J2004.pdf

ABSTRACT: The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in $L^p$-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function $\|\mathbf x\|^2$ among all the triangulations with a given set of vertices. For a more general function, a function-dependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure.
The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-dependent optimal Delaunay triangulation is proved to exist for any given convex continuous function. On an optimal Delaunay triangulation associated with $f$, it is proved that $\nabla f$ at the interior vertices can be exactly recovered by the function values on its neighboring vertices. Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.

C3

2005-12-04T14:30:00.000-08:00

Long Chen and Jinchao Xu. An Optimal Streamline Diffusion Finite Element Method for a Singularly Perturbed Problem. AMS Contemporary Mathematics Series: Recent Advances in Adaptive Computation, 383:236--246, 2005.

Chen.L%3BXu.J2005.pdf

ABSTRACT: The stability and accuracy of a streamline diffusion finite element method (SDFEM) on arbitrary grids applied to a linear 1-d singularly perturbed problem are studied in this paper. With a special choice of the stabilization quadratic bubble function, the SDFEM is shown to have an optimal second order in the sense that $\|u-u_{h}\|_{\infty}\leq C\inf_{v_{h}\in V^{h}}\|u-v_{h}\|_{\infty},$ where $u_{h}$ is the SDFEM approximation of the exact solution $u$ and $V_{h}$ is the linear finite element space. With the quasi-optimal interpolation error estimate, quasi-optimal convergence results for the SDFEM are obtained. As a consequence, an open question about the optimal choice of the monitor function for a second order scheme in the moving mesh method is answered.

C2

2005-12-04T14:03:00.000-08:00

Long Chen. Mesh smoothing schemes based on optimal {Delaunay} triangulations. 13th International Meshing Roundtable, :109-120, 2004.

Chen.L2004.pdf

ABSTRACT: We present several mesh smoothing schemes based on the concept of optimal Delaunay triangulations. We define the optimal Delaunay triangulation (ODT) as the triangulation that minimizes the interpolation error among all triangulations with the same number of vertices. ODTs aim to equidistribute the edge length under a new metric related to the Hessian matrix of the approximated function. Therefore we define the interpolation error as the mesh quality and move each node to a new location, in its local patch, that reduces the interpolation error. With several formulas for the interpolation error, we derive a suitable set of mesh smoothers among which Laplacian smoothing is a special case. The computational cost of proposed new mesh smoothing schemes in the isotropic case is as low as Laplacian smoothing while the error-based mesh quality is provably improved. Our mesh smoothing schemes also work well in the anisotropic case.

This method is sucessfully applied to 3-D mesh generation by Pierre Alliez, David Cohen-Steiner, Mariette Yvinec and Mathieu Desbrun.

C1

2005-12-04T14:00:00.000-08:00

Long Chen and Pengtao Sun and Jinchao Xu. Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems. The Proceedings for 15th Conferences for Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 40:459--468, 2004.

Chen.L%3BSun.P%3BXu.J2004.pdf

ABSTRACT: A multilevel homotopic adaptive methods is presented in this paper for convection dominated problems. By the homotopy method with respect to the diffusion parameter, the grid are iteratively adapted to better approximate the solution. Some new theoretic results and practical techniques for the grid adaptation are presented. Numerical experiments show that a standard finite element scheme based on this properly adapted grid works in a robust and efficient manner.

Introduction

2005-11-18T13:17:00.000-08:00

Please visit my new home page: http://math.uci.edu/~chenlong/

This post contains our solution to the management of references for the following purposes:

Writing paper.
When you are writing paper with Latex, the best solution for the references is to use Bibtex. A quick introduction and usage of Bibdesk is HERE and a more detailed one can be found HERE.

Managing paper.
We use some graphical softwares to manage BibTex databases. For Windows and Unix: JabRef and for Mac: BibDesk.
It is easy to classify, search and edit bib files using those softwares. HERE is a sample page which contains html files generated by BibDesk.

Reading paper.
What we do for this purpose is a small, local, and specialized version of MathSciNet. Most papers in the BibTex database is linked to a pdf file in your local machine or some web sever. A webpage for our current library is HERE (account and password is needed).

Bib Files

2005-11-17T23:14:00.000-08:00

For JabRef, please download umdlib.bib. The configuration of JabRef is HERE.

For BibDesk, please download library.bib. The preference for BibDesk is HERE.
This post is not completed.

Topics

2005-11-17T23:11:00.000-08:00

Long Chen's Publciation

Convergence and Optimality of Adatpvie Finite Element Methods

Bisection

Maxwell equation

Superconvergence

Poisson Boltzmann Equation

Bibtex

2005-11-17T13:29:00.000-08:00

Why Bibtex?

Don't worry about formatting the bibliography.

Avoid retyping the same references.

Mangage your references in an efficient way.

Quick Start

1. Put the following two lines right above the \end{document}
\bibliographystyle{abbrv}
\bibliography{library}

Commonly used bib style: abbrv, alpha, plain, unsrt You can find the examples and difference of those styles HERE.

"library" is the file name of the bib file. You can use directory path here. For example, \bibliography{../Math/Paper/library}. If it doesn't work, which might be the case for Windows, you just copy the library.bib file to your current directory.

2. To refer a paper in your tex file, use command
\cite{Chen.L;Xu.J2004}
where Chen.L;Xu.J2004 is the bib index. The corresponding bib term in library.bib is:

@article{Chen.L;Xu.J2004,
Author = {Long Chen and Jinchao Xu},
Journal = {Journal of Computational Mathematics},
Pages = {299-308},
Title = {Optimal {Delaunay} triangulations},
Volume = {22(2)},
Year = {2004}}

3. Compiling your tex file.

latex yourfile

bibtex yourfile

latex yourfile

Somehow you have to latex your tex file twice after the bibtex command.
More instruction can be found at Google.

读博士与坐牢的惊人相似

2005-10-31T12:40:00.000-08:00

读博士与坐牢的惊人相似

Optimal Stopping

2005-10-30T23:35:00.000-08:00

海外學人相親記李宗元

Evolution

2005-10-30T11:49:00.000-08:00

From http://bessie.che.uc.edu/tlb/

NP vs P

2005-10-29T22:59:00.000-07:00

未來數學家的挑戰--計算量問題楊照崑;楊重駿

You and Your Research

2005-10-28T15:24:00.000-07:00

做大事，成大业 YOU AND YOUR RESEARCH
中文翻译：老马等引自染缸。

韩东文摘

2005-10-18T22:47:00.000-07:00

关于语言、杨黎及其它

李亚伟

2005-10-17T20:14:00.000-07:00

李亚伟是我比较喜欢的一个诗人。文字比较鲜活，具有生活气息和激情，还有四川人的幽默和夸张。“这天空是一片云的叹气，蓝得姓李”。

天上，人间 李亚伟
我心比天高，文章比表妹还漂亮，曾经在漫长的时光中写作和狂想，试图用诗中的眼睛看穿命的本质。除了喝酒、读书、听音乐是为了享乐，其余时光都反倒被我心目中天上的诗歌之眼看死，且勾去了那些光阴中的魂魄。那时我毫无知觉，自大而又疯狂，以为自己是一个玩命徒。我通常只在初夏和初冬两块时间里写诗，其余时光是人间的，我以为我是天上的人。初夏我内心烂漫、充满喜悦，用语言的听觉倾听人间和海洋的燥动，准备挤进社会，去活；初冬我用词语的耳朵打听命外的消息，准备到很远的地方，也许是天边，也许是眼前，去死。那是80年代，其实那时的雪花和现在没有两样，有时暄闹，有时寂寞。

天上，人间
苏东坡和他的朋友们
中文系
毕业分配
我在双鱼座上给你写信
红色岁月－第五首
红色岁月－第十二首

更多文字，请访问下列连接： 李亚伟诗文

Book Wanted

2005-10-16T16:08:00.000-07:00

Those are useful books I don't have.

[1] F. Brezzi and M. Fortin. Mixed and hybrid finite element methods. Springer-Verlag, 1991.
[2] C. M. Chen and Y. Huang. High accuracy theory of finite element methods. Hunan, Science Press, Hunan, China (in Chinese), 1995.
[3] R. A. Devore and G. G. Lorentz. Constructive Approximation. New York, NY:Spring-Verlag, 1993.
[4] V. Girault and P. A. Raviart. Finite element methods for Navier–Stokes equations. Springer-Verlag, Berlin, 1986.
[5] L. B. Wahlbin. Superconvergence in Galkerkin finite element methods. Springer Verlag, Berlin, 1995.
[6] Q. Zhu and Q. Lin. Finite element superconvergence theory. Hunan Science Press, 1989.

科技论文写作

2005-10-09T23:46:00.000-07:00

MIT电子系教授: 如何避免科技论文审稿人的大斧
How to Avoid the Reviewer's Axe

Source Code in LaTeX

2005-10-09T12:42:00.000-07:00

Adding Source Code Listings to LaTeX Documents

围棋文摘

2005-10-05T14:43:00.000-07:00

后,逆手官子的价值问题. 作者：植物老人(dengwixin）来自Tom论坛
官子的基础指南 作者：阿土博来自TOM 棋友论坛
对我围棋帮助最大的一次谈话

轮回

2005-10-04T15:15:00.000-07:00

陈龙

我喜欢这样一个下雪的夜晚，帘子一挑，进来一人，掸掸残雪，然后挑个空地坐了，要上一壶酒，两斤牛肉，讲些武林的奇人轶事，很多事情单是讲讲便很让人向往。

我见到小丁的时候，他就在讲着武林的旧事，那是些传说中的人物，故事也多半在一个下雪的夜晚，在一个可以大碗喝酒，大口吃肉的客栈，帘子一挑，进来一人，掸掸残雪，然后开始杀人。

小丁讲的正是十二年前我接的一笔生意，在一个下雪的夜晚，我用剑挑开了帘子，然后挑开了“一剑封喉”的喉咙，他正在喝酒，剑过去的时候，那酒和着血，喷了出来。

我正在这个客栈大口吃着牛肉，外面的雪下得正紧，旁边有个叫小丁的孩子在讲着我过去的故事。我不认识小丁，他只是一个孩子，我在等另一个人，等着那帘子一挑。

我是一个杀手，所以我没有朋友。帘子一挑的时候，我却非常希望这个人成为我的朋友，我叫他过来，一起喝酒，一起吃肉，他就是小丁，他给我讲着我过去的事情。

帘子终于又动了一下，却没有人。外面的风雪更急了。应该不会有人了。我开始大碗地喝酒，大口地吃肉，剑就这样过来了，酒和着血，喷了出来。

然后小丁掸了掸残血，帘子一挑，消失在风雪之中。

当归，主治鸡肋之症

2005-10-04T14:45:00.000-07:00

《长铗》，许秋汉词曲，取自冯谖客孟尝君，弹剑而歌，归去来兮。

按《新青年》说法，1995年，北京市政府出台一项政策：当年毕业留京的高校学生需交纳城市增容费。许秋汉为当时知识分子的卑微地位而感到屈辱，思冯谖客孟尝君的典故，作歌为当年毕业的90级同学鸣不平。

此曲慷慨悲怆，古风盎然，听之令人嘘唏，惆怅天涯。

长铗，归来乎。

食无鱼，出无车。

两袖清风为谁忙，

国家不用作栋梁。

长铗，归来乎。

无以为家，无可牵挂。

十年寒窗付东流，

壮志未酬回故乡。

天下兴亡事，

在我胸中藏。

叹望世上满目苍凉，

碌碌奔波空悲伤。

长铗，归来乎。

士可杀，不可辱。

从今后对酒当歌，

乐得逍遥回故乡。

台湾民谣

2005-10-04T13:49:00.000-07:00

《秋蝉》，台湾民谣，词曲古朴婉约，“谁道秋下一心愁，烟波林野意幽幽。花落红花落红，红了枫红了枫。” 有次和朋友参加华人聚会，多是台湾同胞，中年居多。卡拉OK时，听他们唱他们年轻时的歌，《秋蝉》便是那时第一次听到。有些歌是更早的，他们在小学就传唱的。比如《兰花草》。“我从山中来,带着兰花草。种在小园中,希望花开早。”《兰花草》的词作者是大名鼎鼎的胡适。《秋蝉》是李子恒。李子恒，台湾的名字都很书面化，象琼瑶小说中的名字。
那些怀旧的民谣，对他们是怀旧，对我倒是有些新鲜。从旋律和歌词，仿佛回到三四十年代。看来，在台湾，文化是沿着原有的那个轨迹在发展，应该算是正统吧。
让我想起另外一次聚会。也是华人为主，也是在饭后开始唱歌。只是这次大陆的居多，也多是中年人。唱的歌，风格迥异。“烽烟滚滚唱英雄，四面青山侧耳听，侧耳听。……为什么战旗美如画，英雄的鲜血染红了她”。便是女士唱来也是慷慨激昂。客人中也有来自宝岛的，初时只能旁听。后来，开了个牌桌，唱歌的地方空闲一点。这个时候，我们便听到了原汁原味的台湾流行歌曲，也比较老一些，王杰前后的。歌很好，都是些经典，比如《一场游戏一场梦》，唱的也好。前面的革命歌曲放到此时，正如苏词与柳词之比。雅的东西，有些偏软；豪放，刚硬，便就多了些粗逛。两岸的文化传统沿行至今，还是略有不同的。
宾客中还有一位意大利教授，夫人是上海人。要陪夫人，不好先行告退。唱歌时便到琴房，弹奏钢琴。

关于台湾民谣的文摘
古月照今尘 —关于台湾民谣的回忆
说说台湾民歌运动

Useful Tips for Blogging

2005-10-03T16:17:00.000-07:00

How can I list my archives by title?

What can I do with CSS?

How do I list the titles of all posts on a page?

How can I make show/hide links for my posts

关于王磊的文摘

2005-10-03T15:12:00.000-07:00

面对王磊面对音乐和面对独立彭洪武
不知道关于不插电和民谣，王磊是否还有兴趣去做？我喜欢听他做民谣，1999年夏天曾听他一个人在Unplugged酒吧排练，每一首歌都很美很动听，有一种叫血的东西在音乐里流动，那时候的王磊有太多的激情，他弹琴的手青筋凹凸，扫落琴弦的划出感人肺腑的旋律，这是中国摇滚后期很少有的，也是王磊先前被传颂的特色之由，在一个没有多少爱的时代浪子真情总是先行的，为何？那首压在箱底没人知的“你永远都不懂”则是一首让有人撕心裂肺之痛的感性之作，它是一首深度与流行度皆佳的好歌，它简单却流畅，淌着这个冷漠时代少有的热忱，呼喊出一个血肉男人的爱和生命……

浪子班头王磊和南方摇滚旗帜颜峻
“我是个普天下郎君领袖，盖世界浪子班头”，关汉卿这样说。倘若他转世投胎，耐不住寂寞，丢开笔墨，上了舞台，恐怕就是我们眼前的王磊——2001年的一天，王磊心血来潮，抱起几千块钱的箱琴跑到广州天河，就地开唱，身边那些专业的卖唱人听说是王磊，登时肃然起敬，因为这就是那个“唱《出门人》的人”。这个时候，《出门人》已经发行了7年，王磊从一个霹雳舞冠军、一个在沙滩上睡觉的流浪汉，已经变成了媒体人熟悉的南方摇滚领袖。但许多不听摇滚乐的、偶然得到那张牛皮纸包装的盒带的普通人，却仍然记得，曾经有一个年轻人唱酸过他们的心。
在中国，最底层的人听的不是布鲁斯或者朋克乐，而是《爱拼才会赢》，或者陈星的《流浪歌》。摇滚乐被认为是艺术，或者理想，要不就是反抗，总之不是生活。因而不甘平庸，摆脱了大众的怀抱。但王磊有幸，曾被底层认可，并且是用民谣摇滚的“前卫”形式，想必有其草根的本性。这便不是做着先锋梦的流浪文艺青年所能体会的了。出门是为了改变生活，解决少年梦想，其动力不过是直觉和本能，其形式也简单得如同10块钱的火车站旅社——你的同屋多半是算命先生、逃债商贩，而不是心怀大志的少年陈独秀。王磊的特别，就在于他和硬座车厢里其他的盲流一样土，而不和文艺青年一样聪明；他的成功，则在于他找到了自己的生存方式，而不是去扛钢筋或者做保镖。至于才华，其实你家楼下的民工小赵，高考落榜前还是个达芬奇呢；命运杀人，并不是为了让王磊幸存下来做精英。


影评：东邪西毒

2005-10-03T14:20:00.000-07:00

陈龙

时间

“很多年之后…”这是马儿克斯魔幻史诗《百年孤独》之开篇句式。此书成于60年代末，80年代中译成中文，甫入中土便奉为圭臬，随者众多，其中尤以此句为甚。传统叙事方式立足此刻，时间的推移借助故事来表现，“多年以后”或“多年以前”此种句式转换叙述角度，以此望彼，两点一线，其中便有了沧海桑田，时空倒置之功效，而完成式的语态又暗含有一种无可奈何的因果宿命。

流风之下，王氏亦不能免俗，只是在他手里，此招已臻化境，以至多年以后，被众多拥趸尊为王氏句法，以此为代表的格言警句式独白功夫更是于古龙之外自称一派，颇得小资青睐。

言归正题，要把东邪西毒这个片名译成英文不是一件易事，直译太过隐晦，老外难以望名揣义，只有意译。因此英文片名便已透出此片主题之一：时间。

情

欧阳锋自负 “很多年之后，我有个绰号叫做西毒。任何人都可以变得狠毒，只要你尝试过什么叫妒忌。我不介意其他人怎样看我，我只不过不想别人比我更开心。”开篇明言欧阳锋因忌而毒，却不言因何而忌，一开场便埋下西毒此条情感主线，并在此之后每场戏中均有话语暗示，这也是王氏的一贯风格：用暧昧的人物关系来呈现出故事的各种可能性。

慕容嫣痴情 东风解冻，春心初动，奈何妾有意而郎无情，黄药师的酒后玩笑却引得慕容燕人格分裂。慕容燕要杀药师，因其引己方寸大乱，乱其示人之强者面目，慕容嫣要杀慕容燕则是女儿本性的自然反抗。最后的结果是“数年后，江湖上出现了一个奇怪的剑客，没有人知道他的来历，只知道他喜欢跟自己的倒影练剑。他有一个很特别的名字，叫独孤求败。”水上练剑一节的惊涛骇浪和声嘶力竭只为表现其内心压抑之深，让我们不得不感慨女人的成功居然要付出压抑人性的代价。

让我们记下这个受伤女子酒后的祈求，它足以让天下所有的痴情女子潸然泪下：

我曾经问过自己，你最爱的女人是不是我，但是我现在已经不想知道。如果有一天我忍不住问你，你一定要骗我，就算你心里多不情愿，也不要告诉，你最爱的人不是我。

盲武士猜忌 因为猜疑自己的妻子爱上了自己最好的朋友（又是那个风流东邪），盲武士落寞江湖。而立之年，双目几近失明，怀念家妻，意欲归乡，却因盘缠命丧马贼之手。此种结局意味着错误的难以挽回，而盲武士在眼瞎之后才想起回家则是在提醒当事人，眼见并非为实，内心明白才为紧要。

注：此段有一节，画面，音乐，对白都与《大话西游》神似，因为刘镇伟与王家卫称兄道弟交情非浅，拍片时戏防好友也是一乐，其间包括大话中最为有名的“一万年期限”便是来自《重庆森林》。刘镇伟用原班人马同时拍摄了搞笑片《东成西就》的一个原因是投资方怕《东邪西毒》亏本（事实上其票房可用凄惨来形容），另一个原因是没有人知道王家卫能什么时候收工。

大嫂遗忘 原来黄药师每年惊蛰时分的探访只是为了这个喜欢桃花的女人，原来让欧阳锋离开白驮山的是这个嫁给了他哥哥的女人，原来她不跟他走只是因为一句话，一句她想要而他没说的话，原来那坛“醉生梦死”只是她开的一个玩笑：你越想知道自己是不是忘记，反而记得更清楚。

最后的这节故事成功地让这部影片具有了一个环形的结构：人物关系以及叙述的时间，而关于遗忘我们也有了两种截然不同的看法：

人最大的烦恼，就是记性太好，如果什么都可以忘掉，以后的每一天将会是一个新的开始，你说这有多开心。

我曾经听人说过，当你不能够再拥有的时候，唯一可以做的，就是令自己不要忘记。

义利之辨

欧阳锋在大漠干的是中间人的生意，也就是帮人物色杀手，解决麻烦。他是一个生意人，因此没有钱他是不会去帮一个只有一篮子鸡蛋和一头驴的女孩报仇，那是侠士才有的义举。女孩象她那头驴一样固执地等待，坚守着对正义的期待，不愿迈过她的道德底线，出卖肉体。我们这个社会就在这样的对峙中投射到了大漠之上。

洪七直接 洪七是为了解决这个对峙而出现的，杀了太尉府刀客之后的一段话，算是对这个问题的一个直接回答：

欧阳峰：为了一个鸡蛋而失去了一只手指，值得吗？

洪七：不值得！但我觉得痛快，这才是我自己。我本来应该没事，但是我的刀没以前的快了。我以前快是因为我直接，认为是对的就去做，从来不去想什么代价。我以为自己一辈子不会变，直到那个女孩来求我，我才发现我自己完全变了，我竟然没有答应她，因为我知道你一定不会答应。那天，我很失望，我觉得我已经和你混在一起，变成了一个人，没有了自己。我不想跟你一样，因为我知道欧阳峰绝对不会为一只鸡蛋去冒险，这是我和你的分别。

他还回答了另外一个问题，这个问题曾让盲武士命丧天涯，让欧阳锋独守大漠，那就是“谁说过不准带老婆闯荡江湖，对不对！”洪七用简单的思路处理了家庭和事业的矛盾，虽然这样会很麻烦。

经典台词

你这种年青人我见不少了，懂一点武功就以为可以横行天下，其实行走江湖是一件很痛苦的事。懂了武功，你们有很多东西不能做。你不想耕田吧？又不耻去打劫，更不象抛头露面在街头卖艺，你怎么生活？武功高强也要吃饭的。

把武功换成知识，赠给所有要找工作的毕业生。

洪七：不知道过了这个沙漠，后面是什么地方。

欧阳峰：又是另一个沙漠。

每一个人都会经历这个阶段，看见一座山，就想知道山后面是什么。我很想告诉他，可能翻过去山后面，你会发觉没有什么特别，回头看会觉得这边更好。但我知道他不会相信，以他的性格，自己不试过是不会甘心。

婚姻便是如此，人生也大都如此。

我不知道她是不是真的要为弟弟报仇，还是没别的事情可做。每个人都会坚持自己的信念，在别人看来是浪费时间，她却觉得很重要。

也许我们这本杂志根本就是在浪费时间。

我以前听人说过如果刀快的话，血从伤口喷出来的时候像风声一样，很好听，想不到第一次听到的是我自己流出来的血。

配上梁朝伟，真的很酷。

欧阳峰：怎么，你们觉得十两银子这价钱太高了吗？那么你们可以去找些便宜的，那边有几个，没穿鞋子的，你给几两银子他们已经很高兴。可是一个连鞋子也没有的刀客，你们对他有信心吗？……至少在这方面，你们该相信一个穿鞋的人吧。

怪不得大家应聘时都是西装革履。

以前我认为那句话很重要，因为我相信有些事一旦说出来就一生一世，现在想想，其实说不说也没有什么分别了，因为有些事情是会变的。我一直以为自己赢了，直到有一天看着镜子，才知道自己输了，在我最美好的时间，我最喜欢的人也不在我身边。如果时间可以重新开始该多好。

花开堪折直须折，莫待无花空折枝。

于坚的诗

2005-10-02T15:27:00.000-07:00

在漫长的旅途中

便条集
１５９
老教授
在一棵柏树下
练习太极拳
姿态优美
象一只正在长出羽毛的
白鹤
他忽然摇身一变
象杂志那样打开
于坚　我告诉你一件事
我儿子
要到美国去了

文摘：中美教育

2005-10-01T15:25:00.000-07:00

原载《博览群书》从中美教育的一点比较谈起
经过了多年的发展，美国的社会制度化比较完善。然而，“凡事有一利必有一弊”，在美国比较完善的教育制度里也体现了出来。就像他们的信用记录体系一样，学生的成绩也是被系统记录的。中小学阶段后果影响不太明显，但高招和研究生院招生的时候就明显了。比如，中学阶段的平时成绩记录不好，就不容易被好的大学录取，本科成绩记录不好，平均积分点不高，就很难进入一流的研究生院。虽然他们也有像ＧＲＥ之类的考试，但是成绩在录取中占的权重不太大，平时成绩所占权重至少不会低于这些考试成绩。这是美国的学生升学录取制度。而中国则不同，一个学生高中一二年级甚至三年级平时成绩不怎么样，如果高考发挥得好，考分高，就可以升入名牌重点大学；本科成绩平平，只要研究生入学考试成绩好，同样可以被一流研究生院录取。也就是我们通常所说的“一考定终身！”虽然有人批评它，但它也有可以带给人的好处。虽然实际上一考可能不会定一个人的终身，但是那一个考试在入学录取上的作用远比美国的入学考试大得多，可以说是决定性的。这样的不同录取方法也就是不同的游戏规则，为人们提供了不同的机会。在美国平时成绩差，某一天浪子回头了，即使发奋图强入学考试时成绩好了也很难为录取委员会所青睐。而在中国，一个以前不知用功的学生，高三或者大三什么时候忽然悔悟，努力奋发，只要高招研招考试成绩棒，也可以进入优秀的学校深造发展。

又见罗大佑

2005-10-01T14:09:00.000-07:00

罗大佑开演唱会了，而且很多人，很多人地集体怀旧，一个时代过去了。１９７４年，罗大佑怀旧他的童年的时候，我才刚刚诞生。他的出现，震撼，以及那些歌，和另外一些元素一样散落在我成长的时代背景之中。我只是喜欢那些感动而已，没有去完整地辨别过这个人和这个人的作品。如同崔健。我的青年时代不可能完全回避《一无所有》这个声音，但也只限于此。一首歌影响太大，会遮盖和歪曲本人。犹如树和森林。谈到某片森林，我们会以为就是那棵最大最古老，出现在明信片上的那棵树。那棵树很好，很大，很震撼，以至人们忽略了整个森林。

一直到那个下午，因为罗大佑要开演唱会，媒体开始热炒这个传奇和偶像，我才如此清晰地注意到原来有那么多触动过我，必然也触动过很多人的歌曲，原来都是他的，都是一个森林的。

带过来了很多的mp３，罗大佑和猫王在一张盘。开始完整地听他的歌，专辑，然后才第一次听到了《乡愁四韵》，听到了《亚西亚的孤儿》。这个黑衣人的地位更加巩固。他是一个延续诗歌传统的音乐人，李白和苏轼在音乐上的传承。

不过我老了。都老了。一个清瘦的中年人，在我还不知道那个卷发黑衣墨镜，怀抱吉他的叛逆形象之前，我就接受他已老了。这样的一个中年人更适合他那些民谣似的哀愁，这样的一个形象更为深沉，更为适合怀旧。

苏东坡和他的朋友们

2005-09-17T20:53:00.000-07:00

苏东坡和他的朋友们
李亚伟

古人宽大的衣袖里
藏着纸、笔和他们的手
他们咳嗽
和七律一样整齐

他们鞠躬
有时著书立说，或者
在江上向后人推出排比句
他们随时都有打拱的可能

古人老是回忆更古的人
常常动手写历史
因为毛笔太软
而不能入木三分
他们就用衣袖捂着嘴笑自己

这些古人很少谈恋爱
娶个叫老婆的东西就行了
爱情从不发生三国鼎立的不幸事件
多数时候去看看山
看看遥远的天
坐一叶扁舟去看短暂的人生

他们这些骑着马
在古代彷徨的知识分子
偶尔也把笔扛到皇帝面前去玩
提成千韵脚的意见
有时采纳了，天下太平
多数时候成了右派的光荣先驱

这些乘坐毛笔大字兜风的学者
这些看风水的老手
提着赋去赤壁把酒
挽着比、兴在杨柳岸徘徊
喝酒或不喝酒时
都容易想到沦陷的边塞
他们慷慨悲歌

唉，这些进士们喝了酒
便开始写诗
他们的长衫也像毛笔
从人生之旅上缓缓涂过
朝廷里他们硬撑着瘦弱的身子骨做人
偶尔也当当县令
多数时候被贬到遥远的地方
写些伤感的宋词

文摘: 说说台湾民歌运动(zt from e0575)

2005-09-05T15:03:00.000-07:00

 1975年，杨弦和胡德夫在台北中山堂举行了一个小型的音乐会，作品唱的是余光中的诗，余是当时极受台湾青年推崇的诗人，此音乐会被台湾乐界视为“民谣（或民歌）运动”的起点。

 民歌早期的作品一般是歌咏山水之美、青春之情、旋律清新自然、歌词朴素无华，叶佳修、苏来、李建复、刘兰溪、邰肇玫、施碧梧、王海玲、陈明韶、邱晨、赵树海等歌手；靳铁章、毕心一、毕奂一、林建助、许翰君、陈云山、黄大城、王新莲、吴楚楚等词曲作者是当时民歌运动的主力，他们的创作吸引了台湾青年。而随着候德建、罗大佑、李泰祥的介入，民歌运动有了质的飞跃，比初期的淳朴无暇多了人文精神和社会责任。由于当时创作力量的不足，大量的歌曲是谱名家的诗作，如三毛、余光中、赖西安、罗门、席慕容、李熬、蒋勋等台湾本土作家，而随着侯、罗、李的作品的流传，民歌运动达到前所未有的高度。

 候德建当时创作主要的是为李建复的<龙的传人>，罗大佑的第一首歌是刘文正的<歌> 第一张制作专集是张艾嘉的<童年>，李泰祥的处女作是为齐豫<橄榄树>创作，但他们的最好作品还是自己的专辑，候德建的<三十以后才明白>，罗大佑是<之乎者也> ，李泰祥个人认为是<错误>最好。

 按流派来分的话，杨弦、叶佳修属早期创作及领导者，清新的格调象中国水墨，这一派歌手最多。侯德建与罗大佑相似，才气逼人，叛逆、批判，以音乐来表达思绪、思考、思索，稍后有李寿全，不过，两人早期的歌还是散发着迷人的纯真情感，如<捉泥鳅>、< 童年> 、<落叶纷纷>。相比之下，李泰祥则充满了艺术气质，他选择的歌手也和当时的民歌手有着质的不同，早期的齐豫、唐晓诗，中期的潘越云，后期的许景淳无不透着高雅的魅力，李让台湾民歌具有了文学味和艺术感悟。

 如果要追溯台湾民歌运动的渊源那应该是60年代的美国民谣运动，在鲍勃迪伦、琼贝兹的音乐引导下开始写自己的歌。李双泽、杨祖君是鼻祖，后来才有杨弦和胡德夫的中山堂的民歌音乐会。李是受杨的影响，承传了她的思考方式，充满民粹精神的作为使他成为台湾的鲍勃迪伦。李是第一个将大陆歌曲<我的祖国>介绍到台湾的音乐人。这契合了他的大中国情节，这也和台湾青年推崇当时风靡全球的学生运动相关。很不幸，李双泽唱完<破鱼网>后于次年遇难。和李相比，杨祖君是民歌手中的异类，70年代末放弃了音乐投身社会运动。而候德建做得更彻底，于83年出走大陆，算是替70年代的理想主义画下了一个象征性的句号。

 70年代的台湾民歌运动不光我们怀旧，台湾人也同样怀念那个创作年代，大时代的背景，激情和理想共存。民歌运动初期，学生的参与是主流，尔后发扬至全社会，成为70年代台湾一个重要的文化现象，影响了当时的艺术文学和社会观念，一大批台湾本土作家从被动参与到主动介入，也提升了台湾音乐的自我觉醒。70年代中期诞生的〈金韵民歌奖〉使整个民歌运动有了推广的可能，一年一届的评奖成了当时台湾乐界的一大盛事。《金韵民歌奖》也顺势发行了大量的民歌唱片，一大批作品也随着音乐的传播而光大，如邰肇玫的《如果》、邱晨的《小茉莉》、施孝荣的《拜访春天》叶佳修的《渔歌》、黄大城和钟丽丽的《让我们看云去》、王梦麟的《雨中即景》、银霞的《兰花草》等都是我们传唱已久的歌。民歌时代进入80年代后，大量的投机校园歌曲出现，一些唱片公司也纷纷加入，民歌运动开始走下坡，矫情且假意的作品多了起来，商业化也开始介入。幸好，及时出现了一批后进者，李宗盛、陈志远、翁孝良、梁弘志、郑怡等、才使民歌运动还能依旧保持一份纯真。

 叶佳修是第一届"民谣风"的歌手，"民"是随着"金韵民歌奖"而诞生的，第一届还有齐豫，她演唱的<乡间的小路>当时就给人一种豪放的旷野感，同届的"小乌鸦"是高中三人组合，他们的音乐虽然简单，但那种企图表现自己的感觉让人感受得到，那届的林诗达的东西则比较细腻，而叶佳修是属于文学性的，比较在意文字的冼练度，在乎能不能让别人产生异想，<流浪者的独白>是叶自己最满意的歌。90年代中期叶开始着力于闽南语歌曲的创作。如果说民歌是针对"唱自己的歌" 台语歌则渐渐摆脱底层而属于所有的人，这也是闽南语歌曲在90年代后期被重新唤醒的原因之一，毕竟，在新音乐的观念下，闽南语歌曲还是有着另一种美感。叶佳修的<稻草人的心情>是他个人第三张也是最后一张专集，专集名就象是叶佳修的作品带给我们的感受一样。

 台湾民歌运动虽然属于本岛范畴，但对香港也产生了一定影响。80年代初，香港也诞生了民谣运动，只不过影响不及台湾，和香港当时的流行风潮比也只是小小的波澜，区瑞强、张明敏、奚秀兰、张德兰是代表人物。其中，区擅长粤语民谣创作，也翻唱欧美民谣，张明敏纯台湾民歌翻唱，奚唱中国民歌。这股民遥风潮区别于许冠杰当时创导的粤语原创，音乐更纯朴新，也有大中国情结，暗合台湾民谣纯朴的格调，许冠杰70年代的创作和同期台湾民歌的创作有质的不同，香港的殖民地情节使许的作品带上了底层文化色彩，而台湾民歌运动则充满了强烈的学院气息和孤岛情绪。这种特点一直和民歌运动本身交叉平衡，透出了浓浓的大时代气息，刘文正就是这个交叉点。

 台湾民歌运动的中后期也不乏优秀的乐人和创作，虽然那时已有不少人因对民歌运动整个环境的失望而淡出歌坛，但还是出现了<天水乐集>这样优秀的创作团体，<天水乐集>由李建复/蔡琴/苏来/许乃胜/靳铁章和李寿全组成，她的成立是民歌风潮末期力挽狂澜的尝试，团体在演唱创作制作编曲都拥有最顶尖的人才，在80年代初期做出了具有惊人原创性的两张唱片<柴拉可汗>和<一千个春天>。严谨的制作和出色的演唱使之成为民歌时代中晚期的颠峰之作，<天水乐集>只维持了短短的三年但替日后林立的音乐工作室建立了最早的分工模式，在民歌运动和流行音乐间起到了承前启后的作用。

 民歌运动的发展一直和当时的台湾社会的变化伴随着，无论是电影的言情化，文学的乡土性，还是艺术的公众风潮都和音乐的民歌运动的创作动机相切合。这一股风潮带来的最直接的结果是台湾的知识分子的参与和介入，这无疑提升了那一个很强调"自己"的年代，跳自己的舞，写自己的文学，唱自己的歌。可是，没有人知道什么才是"自己" ，因为那时一个台湾被国际孤立的悲情时代，而强调"自己"至少可以表示自己的存在，民歌就是在如此的时代感的背景下诞生的，创作成了那时唯一的出路，于是，一些组合和团体应运而生。较著名的有邰肇玫和施碧悟、杨芳仪和徐晓荩、黄大城和钟丽莉、许淑绢和林佳蓉、王新莲和马宜中的二重唱，黄韵玲、黄珊珊、许景淳、张瑞薰的四重唱，木吉他、小乌鸦、原野、丘丘、新格等团体，它们都是民歌运动中有影响的创作和演唱团体。值得一提的是新格合唱团，这是台湾新格唱片成立的童声合唱团，演唱的民歌运动的作品以西洋的方式处理，无疑提升了当时歌曲的趣味。李泰祥后期与荷兰阿姆斯特丹管弦乐团的合作出版的民歌交响化也是具有相同的意义。而广受欢迎的二重唱作品，如杨芳仪和徐晓荩的<听泉>、<秋蝉>，黄大城和钟丽莉的<让我们看云去>、<看花>，邰肇玫和施碧悟的<如果>都是清新之作，小乌鸦的<俏姑娘>、木吉他的<散场电影>则是充满了风趣和幽默。民歌运动的后期，娃娃领衔的丘丘合唱团应该是西式乐团的台湾模型，后期还有<红蚂蚁>。民歌运动的组合和团体从运动诞生至结束一直扮演着重要的角色，为日后的台湾商业化流行音乐的多元化起着重要的作用。

 民歌三十年是从杨弦的中山堂＜乡愁四韵＞演唱会开始的，这一年＜滚石＞月刊也创刊了，民歌运动的传播渠道开始畅通。当时推广的方式很简单，办演唱会和电台宣传。陶晓清是中广台的音乐主持人　那一年为民歌而开设了＜中国现代民歌＞节目，因为之前陶一直主持西洋音乐，相对的，民歌的原创性更具有着力点和兴奋感。由于当时的台湾政府认为节目名中有＂现代＂二字暗合当时大陆正热提的＂四个现代化＂，于是陶的节目改名＂中西民歌＂，此节目一开出马上成了民歌运动推广的主力平台，因为是民歌运动的刚发芽　陶为了让听众有听不同音乐创作的机会，只要是创作新歌，节目都给发表的机会，而自己在节目里扮演的是听众和民歌手的桥梁角色。陶晓清在制作民歌音乐节目的同时还从事音乐会的策划人工作，并编辑了＜这一代的歌＞，成立了＜民风乐府＞，台湾的民歌运动从星星之火到可以燎原，电台的传播不可忽视，电视在当时的确还不能扮演重要角。

 来说说我所知道的民歌乐人去向，苏来、王海玲、李丽芬、郑怡都往广播发展；赵树海、王梦麟已是演艺圈的人；吴楚楚成了著名的＂飞碟＂唱片的老板；黄大城据说在民航；施孝荣先回到原来的学校重做体育老师，后从事音乐的活儿；杨弦定居美国，搞中医；王新莲在美国从事资讯业；邰肇玫和陈明韶都在美国；李建复是IT业精英；罗大佑、候德建等的动向大家已了解了；李泰祥90年代后期因患帕金森氏症而停止音乐创作，令人遗憾。李泰祥在2000年发行的专集《最美的遗憾》既是对李25年艺术音乐创作的回顾，也是留给了我们一个“最美的遗憾”。

Math20C Homework

2005-04-30T22:56:00.000-07:00

Homework 21 15.7 9, 11, 15, 25; Section 15.8 7, 9, 11

Homework 20 15.6 3, 7, 9, 21; Section 15.7 3, 5

Homework 19 15.5 23, 25; Section 15.6 1

Homework 18 Section 15.4 17, 21, 31; Section 15.5 1, 5

Mising HW for 14.4: 1, 3, 5, 11

Homework 17 Due Thursday Mar 9 Section 15.4 1-6, 9, 13

Homework 16 Due Thursday Mar 9 Section 15.3 1, 5, 7, 13, 21, 43, 45

Homework 15 Due Thursday Feb 23 Section 15.2 3, 5, 7, 9, 15

Homework 14 Due Thursday Feb 16Section 14.8 3, 7, 11, 19, 23

Homework 13 Due Thursday Feb 16 Section 14.7 29, 31, 37, 39, 45

Homework 12 Due Thursday Feb 16 Section 14.7 1, 5, 9, 13

Homework 11 Due Thursday Feb 9 Section 14.6 7, 9, 15, 19, 25, 27

Homework 10 Due Thursday Feb 9 Section 14.5 1, 5, 7, 11, 17

Homework 9 Due Thursday Feb 9 Section 14.2 7, 35; Section 14.3 13, 17, 27

Homework 8 Due Thursday Feb 9 Section 14.1: 13, 17, 23, 29, 43; Read Example 3(page 889), 7(page 891) and 13(page 895)

Homework 7 Due Thursday Jan 26 Section 13.3: 23, 33, 47; Section 13.4: 7, 11, 15, 33

Homework 6 Due Thursday Jan 26 Section 13.3: 3, 5, 11, 13, 29, 39

Homework 5 Due Thursday Jan 26 Section 10.1: 9, 21 Section 13.2: 1, 5, 19

Homework 4 Due Thursday Jan 26 Section 12.5: 5, 9, 13, 27, 65, 69 Section 13.1: 3, 19-24

Homework 1 Due Thursday Jan 19 Section 12.2: 3, 7, 11, 15, 29
Section 12.3: 3, 5, 7

Homework 2 Due Thursday Jan 19 Section 12.2: 17, 21, 25, 27
Section 12.3: 9, 11, 13, 19, 41, 49

Homework 3 Due Thursday Jan 19Section 12.4: 9, 15, 19, 31
Homework will be assigned on the course homework page and should be completed by the indicated due date. Homework will not be collected; your homework will be evaluated by your performance on periodic quizzes and midterm exams. You should make every effort to complete the homework assignments and seek help with problems you have not been able to solve. You can get help with the homework assignments in the Calculus Tutoring Lab (APM 2402). A Student Solutions Manual (available in the Bookstore) has complete solutions for odd-numbered problems in the text.

Math20C Quiz Exam

2005-04-30T09:47:00.000-07:00

Quiz 3 on Friday, Mar 17, covers Section 15.6, 15.7

Practice Exam for Final Exam

Final Exam: Monday March 20, 8:00 - 11:00 a.m. CENTR 119.

It is cumulative and will cover Chapter 12-15 with the following exceptions:
12.6; Spherical coordinate; Graphs of curves and surfaces; osculating circle; Hepler's laws of planetary motion; Partial differential equations; The Cobb-Douglas production function; Implicit differentiation; Lagrange multiplier with two constrains; 15.1; 15.5; Applications of triple integrals; Triple integrals in spherical coordinate; 15.9

Mid Exam 2 on Friday, Mar 3 covers Chapter 14

Practice Problems

Old Exams for Mid II

Quiz 2 on Friday, Feb 18 covers Sections 14.4-14.6

Quiz 1 on Friday, Jan 20 covers Sections 12.1-12.4

Mid Exam 1 on Friday, Feb 3 covers Chapter 12(12.1-12.5) and Chapter 13(13.1-13.4)

Old Exams for Mid I
You may bring one 8.5 by 11 inch handwritten sheet of notes with you to each midterm exam.
There will be three (3) quizzes and two (2) midterm exams given during the lecture on certain Fridays. Each quiz will consist of two or three problems taken directly from the assigned homework and you will be allowed twenty (20) minutes to complete each quiz. No notes (or books) will be allowed during the quizzes. There will be no makeup quizzes for any reason.

Math20C Calendar

2005-04-20T12:44:00.000-07:00

Winter Quarter 2006
Note: This calendar is subject to revision during the term.

Week	Monday	Wednesday	Friday
1	Jan 9 12.2, 12.3	Jan 11 12.1,12.4	Jan 13 12.5
2	Jan 16 Martin Luther King Day	Jan 18 12.5, 13.1	Jan 20 10.1, 13.2;Quiz 1
3	Jan 23 13.3	Jan 25 13.4	Jan 27 14.1
4	Jan 30 14.2	Feb 1 14.3	Feb 3 Mid Exam 1
5	Feb 6 14.4	Feb 8 14.5	Feb 10 14.6
6	Feb 13 14.7	Feb 15 14.8	Feb 17 15.1; Quiz 2
7	Feb 20 Presedent's day	Feb 22 15.2	Feb 24 15.3
8	Feb 27 15.4	Mar 1 Review	Mar 3 Mid Exam 2
9	Mar 6 15.4, 15.5	Mar 8 15.5, 15.6	Mar 10 15.6, 15.7
10	Mar 13 12.7,15.8	Mar 15 Review	Mar 17 Quiz 3, Review

Math20C Info

2005-04-19T14:06:00.000-07:00

Lecture: M W F 8:00 am -- 8:50 am in CENTR 119
Instructor: Long Chen chenlong@psu.edu
Ofice Hours: M F 2:00 pm -- 3:30 pm in APM 5848
Teaching Assistant:
Swec, Timothy APM 2325, tswec@math.ucsd.edu
Office Hours: M 11am-1pm and W 2-4pm.
Costello, Kevin APM 2301, kcostell@math.ucsd.edu
Office Hours: W 4-5pm and R 3-4pm

Discussion: Thursday 8:00 am -1:00 am

A01 R 8:00am-8:50am in WLH2112 Swec, Timothy

A02 R 9:00am-9:50am in WLH2112 Swec, Timothy

A03 R 10:00am-10:50am in WLH2112 Swec, Timothy

A04 R 11:00am-11:50am in WLH2112 Swec, Timothy

A05 R 12:00pm-12:50pm in WLH2114 Costello, Kevin

A06 R 1:00pm-1:50pm in WLH2114 Costello, Kevin

Other 20C sections

Calculus Tutoring Lab (APM 2402) Online tutoring services available.
Math20C Workshop run by UCSD's Office of Academic Support and Instructional Services OASIS.

Math20C Syllabus

2005-04-06T21:57:00.000-07:00

Calculus and Analytic Geometry for Science and Engineering

Grading: Your course grade will be based on the maximum of the following two weighted averages:
20% Quizzes, 20% Midterm I, 20% Midterm II, 40% Final Exam
20% Quizzes, 20% Best Midterm Exam, 60% Final Exam

Credit Hours: 4 (2 credits if taken after Math 10C)

Prerequisite: AP Calculus BC score of 3, 4, or 5, or Math. 20B with a grade of C– or better

Textbook: Calculus: Early Transcendentals, fifth edition, by James Stewart; published by Brooks/Cole; 2003. We shall cover parts of chapters 12, 13, 14 and 15 of the text.

Quizzes: There will be three (3) quizzes given during the lecture on certain Fridays; please see the course calendar for the dates of the quizzes. Your cumulative quiz grade will be based on the best 2 of the 3 quizzes. Each quiz will consist of two or three problems taken directly from the assigned homework and you will be allowed twenty (20) minutes to complete each quiz. No notes (or books) will be allowed during the quizzes. There will be no makeup quizzes for any reason.

Midterm Exams: There will be two (2) midterm exams. See the course calendar for the dates of the midterm exams. You may bring one 8.5 by 11 inch handwritten sheet of notes with you to each midterm exam. There will be no makeup exams.

Final Exam: The final examination will be held at the following date, time and place.
Final Exam: Monday March 20 8 - 11 a.m.

You may bring one 8.5 by 11 inch handwritten sheet of notes with you to the final examination. Bring your personal photo ID to the exam. It is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in this class if you cannot take the final examination at its scheduled time.

Homework: Homework will be assigned on the course homework page and should be completed by the indicated due date. Homework will not be collected; your homework will be evaluated by your performance on periodic quizzes and midterm exams. You should make every effort to complete the homework assignments and seek help with problems you have not been able to solve. You can get help with the homework assignments in the Calculus Tutoring Lab (APM 2402). A Student Solutions Manual (available in the Bookstore) has complete solutions for odd-numbered problems in the text.

Calculus Tutoring Lab: A tutoring lab for Calculus students will generally be open Monday through Friday, 9:00am - 8:00pm in APM 2402; please see the Calculus Tutoring page and follow the link in the Tutoring Lab section for a complete listing of dates and times when the tutoring lab is open. There will usually be at least 2 tutors and/or TAs available to help with homework, calculators, and coursework. We strongly recommend that you make use of the Calculus Tutoring Lab.

Calculators: A TI-85 or -86 calculator, or one less powerful, may be used during the class and during the midterm exams. Please do not bring a calculator with the capability of storing notes in it. The TI-89 and -92 are not allowed. You will be expected to show all relevant computational steps: No credit will be given for unsupported answers gotten directly from a calculator.

Academic Dishonesty: Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.

P7

2004-12-10T11:32:00.000-08:00

Long Chen, Ricardo H. Nochetto, and Jinchao Xu. Multilevel Methods on Bisection Grids I: $H^1$ system.

coming soon

ABSTRACT:
In this paper, optimal additive and multiplicative multilevel methods are designed and analyzed on adaptive grids obtained by newest vertex bisection. The analysis relies on a novel decomposition of newest vertex bisection which give a bridge to transfer results from uniform refined grids to local refined grids.

Long Chen 陳 龍

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