WESTERN MICHIGAN UNIVERSITY ANALYSIS SEMINAR
  FALL 2007

Wednesday at  11 a.m. - 11:50 a.m.
Alavi Commons Room, Everett Tower


Comments, questions?  Contact   Yuri Ledyaev ,  phone (269)  387-4557
 

SEMINAR'S ARCHIVE: Spring 2007Fall 2006Spring 2006 , Spring 2005


Date
Speaker, Title and Abstract
November 28
Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University


Hyperbolic Conservation Laws and Entropy Conditions

Hyperbolic Conservation Laws are nonlinear partial differential equations (PDE) which play a central role in the nonlinear PDE's theory and have numerous important applications in science and technology.

In this final talk we  derive estimates which imply uniqueness of weak solution  satisfying Kruzhkov's  entropy condition.
November 14

Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University

Hyperbolic Conservation Laws and Entropy Conditions

Hyperbolic Conservation Laws are nonlinear partial differential equations (PDE) which play a central role in the nonlinear PDE's theory and have numerous important applications in science and technology.

In the second talk we discuss a Kruzhkov's entropy condition and derive estimates which imply uniqueness of weak solution  satisfying such entropy condition.

November 7
 Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University

 Hyperbolic Conservation Laws and Entropy Conditions

Hyperbolic Conservation Laws are nonlinear partial differential equations (PDE) which play a central role in the nonlinear PDE's theory and have numerous important applications in science and technology.

In this talk we provide an introduction in the basic theory of Hyperbolic Conservation Laws including elements of the classical theory due to Kruzhkov (Kruzhkov's entropy condition).

October 31

Dr. Jim Zhu
Department of Mathematics
Western Michigan University

Markowitz portfolio, capital asset pricing model and convex analysis

My recent reading on the financial literature reveals a surprising fact: many Nobel Price laurated financial economists secretly study convex analysis. As evidence I will present two examples in this talk: Markowitz portfolio and the capital asset pricing model both crucially relying on convex duality theory.

Disclaimer: the views expressed in this talk may subject to the bias of many years of obssession with convex analysis and may not be objective.
October 24
Dr. Jay Treiman
Department of Mathematics
Western Michigan University


Update on the Calculus II Skills Test

The department has been giving calculus II students a skills test on first semester calculus problems for several years. In the fall of 2006 the exam was switched to a uniform computer generated exam. This fall a trial, in one section, was run of a completely on-line version of the exam. This spring semester the switch will be made to running only the on-line version of the exam.
This talk will go over the makeup of the exam and demonstrate what the students actually see. There will then be a demonstration of the instructors role in the on-line exams. Teachers will be responsible for adding and removing students from their class as well as downloading their students' test scores.
October 17 Dr. Clifton E. Ealy
Department of Mathematics
Western Michigan University


Loewy Decomposition of Linear Differential Equations

In this talk, I will review the results leading to "the Loewy  decomposition of linear differential equations" and consider  few examples.
October 10
Dr.  D. Steven  Mackey
Department of Mathematics
Western Michigan University

 A New Schur-like Form for Matrices under Unitary Congruence
(
continuation of October 3 talk)
October 3
Dr.  D. Steven  Mackey
Department of Mathematics
Western Michigan University

 A New Schur-like Form for Matrices under Unitary Congruence

Abstract

September 26
 Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University

Commutators of flows and fields (after  Mauhart and Michor)



This is the last talk  in this series in  which we discussed a proof of a global approximate-controllability result for infinite-dimensional control systems. This proof is based on  a generalization (due to M.Mauhart and P.Michor) of a classical formula  expressing  Lie brackets of vector fields in terms of appropriate commutators of flows  for Banach spaces. In this talk we discuss a derivation of the Mauhart-Michor result.
September 19
 Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University

Commutators of flows and fields (after  Mauhart and Michor)



This is a continuation of the previous talk under the same title  in which we discussed a proof of a global approximate-controllability result for infinite-dimensional control systems. This proof is based on  a generalization (due to M.Mauhart and P.Michor) of a classical formula  expressing  Lie brackets of vector fields in terms of appropriate commutators of flows  for Banach spaces. In this talk we discuss a derivation of the Mauhart-Michor result.

September 12
 Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University

Commutators of flows and fields (after  Mauhart and Michor)



We discuss  a generalization (due to M.Mauhart and P.Michor) of a classical formula  expressing  Lie brackets of vector fields in terms of appropriate commutators of flows  for Banach spaces. In the case of finite-dimensional spaces such results have found important applications in geometric control theory. We start with a brief survey of relevant controllability results.



Last modified :November 7 2007

indow.onunload; window.onunload = SymOnUnload; } SymRealOnLoad = window.onload; window.onload = SymOnLoad; //+->