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******************** Note: Two Talks on Special Date ********************

Seminar

Department of Systems Engineering and Engineering Management,

The

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Title: Generalized convexity and separation theorems

Speaker: Kazimierz Nikodem, Professor

Date : September 19th, 2006 (Tuesday)

Time : 4:30p.m. - 5:00p.m.

Venue : Room 513

CUHK

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Abstract:

In 1937 E. F. Beckenbach generalized the notion of convex

functions. In a similar way F-convex sets are defined. Many

properties of F-convex functions and F-convex sets are similar

to those known for the classical convexity. In the talk some new

results of this type will be presented. First, the Kakutani theorem

(stating that two disjoint convex sets can be separated by

complementary convex sets) will be extended to F-convex sets.

Then some characterizations of pairs of functions that can be

separated by an F-convex function or by a function belonging to F

will be given.

(For detailed information, please see the pdf file attached).

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Biography:

Kazimierz Nikodem holds a M.Sc. degree in Mathematics,

Full Professor of

the Department of Mathematics,

His research interests can be summarized as Convex analysis,

functional equations and inequalities, set-valued functions, etc.

He has published over 50 publications in mathematical journals in

He talked on over 50 international conferences in Polana and abroad

(

Reviews and
Zentralblatt f¨¹r Mathematik.

Title: On embedding of diffeomorphisms on Banach space

in regular iteration semigroup

Speaker: Marek Cezary Zdun, Professor

mczdun@ap.krakow.pl

Date : September 19th, 2006 (Tuesday)

Time : 5:00p.m. - 5:30p.m.

Venue : Room 513

CUHK

Abstract:

Let X be a real Banach space, U (subset of X) is an open set and

F is a diffeomorphism. A family of C1 mappings

is said to be a regular iteration semigroup or semiflow of f.

An application for C1 iterative roots of f is given in this paper, that

is the functions g such that g^n=f.

(For detailed information, please see the pdf file attached).

Biography:

Marek Cezary Zdun holds a M.Sc. and a Ph. D. degree in Mathematics,

He is currently a Full Professor and Dean of Faculty of Mathematics,

Physics and Engineering in Pedagogical University.

His research interests can be summarized as Functional equations,

iteration theory, dynamical systems, real functions, functional analysis,

probability theory, calculus, linear and abstract algebra, etc.

He has published 53 papers in scientific journals, 56 talks on

international symposiums. He has been the member of Polish

Mathematical Society since 1971 and the member of American

Mathematical Society since 1983.

************************ ALL ARE WELCOME **********************

Enquiries: Mr. Peixiang Zhao or Prof. Jeffrey Xu Yu,

Department of Systems Engineering and Engineering Management

CUHK

Website: http://www.se.cuhk.edu.hk/~seg5810

Email: seg5810@se.cuhk.edu.hk

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