Here are the titles and abstracts of the seminars which were held in 2010:
2010-12-21 Seminar
Piotr Kasprzak
Application of the 202424.png)
cone to theory of multifunctions
We will discuss extension property for multifunctions. The Radström-Hörmander embedding theorem, which states that the cone consisting of all non-empty, closed, bounded and convex subset of a normed space 
can be isometrically and algebraically embedded as a convex cone in a Banach space, plays a key role in the proofs of the presented results. The talk is based on the paper Applications of the Radström-Hörmander Embedding Theorem to Multifunctions, Bull. Acad. Pol. Sci. Math. 53 (3) (2005), 259-271 by Anna Kucia.
2010-12-07 Seminar
On some properties of the MRH cone
We will establish necessary and sufficient conditions under which the MRH cone is a lattice. We will also discuss the so-called translation property.
2010-11-30 Seminar
The 2010-11-30 Seminar has been cancelled.
2010-11-23 Seminar
Jerzy Grzybowski
On extremal subsets
(Continuation of the 2010-10-26 and 2010-11-09 seminars.)
2010-10-26 Seminar
Jerzy Grzybowski
On extremal subsets
We will show a formula for an extremal subset of a given set. An application to uniqueness of metric segments in the cone of convex sets with the Hausdorff metric will also be presented.
2010-10-19 Seminar
Daria Bugajewska
On superposition operators in spaces of functions of bounded variations with applications to non-linear integral equations
(Continuation of the 2010-10-05 and 2010-10-12 seminars.)
2010-10-12 Seminar
Daria Bugajewska
On superposition operators in spaces of functions of bounded variations with applications to non-linear integral equations
(Continuation of the 2010-10-05 Seminar)
2010-10-05 Seminar
On superposition operators in spaces of functions of bounded variations with applications to non-linear integral equations
In this talk we are going to present some sufficient conditions under which the classical superposition operator maps the space of functions of bounded variation into itself. We will consider the variation in the sense of Jordan, Young and also so-called generalized 
-variation.
As applications of those results we are going to present some theorems on the existence and uniqueness of solutions to the non-linear Hammerstein as well as Volterra-Hammerstein integral equations. We will consider solutions to these equations (local as well as global) belonging to the space of functions of bounded variation in the above mentioned meanings.
2010-06-22 Seminar
Xiao-Xiong Gan
(Mathematics Department, Morgan State University, Baltimore, USA)
Just-In-Time Transportation Problem and Its Algorithm
Just-In-Time (JIT) philosophy or management was originally introduced by Toyota Automobiles. JIT management considers that the storage is a waste and hence eliminating storage equals eliminating the waste.
This presentation introduces the JIT-Transportation problem, which requires that all demanded good be shipped to their destination on schedule, at the zero or minimal destination-storage cost. The JIT-Transportation problem is a special goal programming problem with discrete constraints. We provide a mathematical model for such transport problem and introduce the JIT solution, the deviation solution, the JIT deviation, etc. By introducing the 20202424.png)
-problem we establish the equivalence between the optimal solution of -problem and the optimal solutions of JIT-Transportation problem, and then provide an algorithm for the JIT-Transportation problems. This algorithm is proven mathematically and is also illustrated by an example.
The lecture will be held in English
2010-06-11 Seminar
Piotr Kasprzak
Mappings of higher order and applications to nonlinear equations
(Continuation of the 2010-06-04 Seminar)
2010-06-09 Seminar
Daria Bugajewska
BV solutions to nonlinear integral equations
(Continuation of the 2010-06-02 Seminar)
2010-06-08 Seminar
Jerzy Grzybowski
Minimal pairs of bounded closed convex sets as minimal representation of elements of the Minkowski-Rådström-Hörmander spaces
The theory of minimal pairs of bounded closed convex sets was treated extensively in the monograph Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets by D. Pallaschke and R. Urbański. During the seminar we will summarize the known results and present new ones. Illustrative examples will be given as well.
Marcin Borkowski
On Henstock-Kurzweil integral over unbounded intervals
(Continuation of the 2010-06-01 Seminar)
2010-06-04 Seminar
Piotr Kasprzak
Mappings of higher order and applications to nonlinear equations
2010-06-02 Seminar
Daria Bugajewska
BV solutions to nonlinear integral equations
2010-06-01 Seminar
Marcin Borkowski
On Henstock-Kurzweil integral over unbounded intervals
2010-05-25 Seminar
Ryszard Urbański
Application of shadowing of sets to exhausters
We will define the concept of shadowing of sets and show some of its properties. Furthermore, we will apply shadowing of sets to prove the minimality criterion for exhausters.
2010-05-11 Seminar
Didem Tozkan
Department of Mathematics, Faculty of Science, Anadolu University, Eskişehir, Turkey
Minimal pairs of compact convex subsets in topological spaces
We will show some properties of minimal pairs of compact convex sets in topological vector spaces. Furthermore, we will iscuss the sufficient conditions for the minimality of a pair of compact convex sets from the geometric point of view.
2010-04-27 Seminar
Ryszard Urbański
Minkowski difference in semigroups
2010-04-20 Seminar
Jerzy Grzybowski
On the embedding of the cone of convex sets in the MRH cone
(Continuation of the 2010-04-13, 2010-03-23 and 2010-03-16 seminars)
2010-04-13 Seminar
Jerzy Grzybowski
On the embedding of the cone of convex sets in the MRH cone
(Continuation of the 2010-03-16 and 2010-03-23 seminars)
2010-03-23 Seminar
Ryszard Urbański
On the embedding of the cone of convex sets in the MRH cone
(Continuation of the 2010-03-16 Seminar)
2010-03-16 Seminar
Ryszard Urbański
On the embedding of the cone of convex sets in the MRH cone
(Continuation of the 2010-03-09 Seminar)
2010-03-09 Seminar
Ryszard Urbański
On the embedding of the cone of convex sets in the MRH cone
We will show that there exists an embedding of a cone 202424.png)
, which consists of nonempty, convex and closed subset of a real Hausdorff topological vector space, into the generalized MRH cone.
2010-03-02 Seminar
dr Wojciech Kowalewski
On Navier-Stokes equations
(Continuation of the 2010-02-16 Seminar)
2010-02-16 Seminar
dr Wojciech Kowalewski
On Navier-Stokes equations
We will begin with the fundamentals of the theory of numerical solutions to differential equations. After that, we will derive the Navier-Stokes equations and discuss some problems connected with solving them numerically.
2010-01-05 Seminar
Paweł Suplicki
Algorithm for the computation of the Minkowski difference
During the seminar we will present the algorithm for the computation of the Minkowski difference of two (not necessarily convex) polygons due to Světlana Tomiczková from University of West Bohemia.