The seminar of the OCTD takes place at **8:30** in room **B3-38**, in the Faculty building at **ul. Umultowska 87** in **Poznań**.

Since 2010, also on Tuesdays at 10:00 a **seminar in nonlinear analysis**, conducted by prof. UAM dr hab. Dariusz Bugajewski, is also held.

Here are the titles and abstracts of the seminars:

Jerzy Grzybowski**Application of MRH spaces to crystal growth description**

Paweł Suplicki**Using Octave application to display 2D and 3D graphics**

Jerzy Grzybowski**Generalized Demyanov's Difference of Convex Sets**

Paweł Suplicki**Convex hull finding algorithm**

Ryszard Urbański**Infinite exhausters of convex sets**

Jerzy Grzybowski**Generalization of Demyanov's difference**

Paweł Suplicki**Convex hull finding algorithm**

prof. UZ dr hab. Krzysztof Przesławski

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra

**Self-dual convex bodies**

The seminar is going to take place at **11:00** in B3-38.

prof. UZ dr hab. Krzysztof Przesławski

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra

**On the decomposability of the set of positive-semidefinite normalized matrices**

Professor David Yost

(University of Ballarat, Australia)

**Norm one projections in Banach spaces**

On all of the familiar Banach spaces, it is very easy to write down a formula which defines a norm one (linear) projection. This is not true for arbitrary Banach spaces. The following rough trichotomy indicates the range of behaviour.

- Most finite dimensional Banach spaces admit no norm one projections at all (except those with rank one). Such examples may be smooth, strictly convex, or polyhedral.
- Some separable Banach spaces admit no continuous projections at all (except those with finite rank or co-rank).
- Many non-separable Banach spaces admit many nontrivial norm one projections, even under every equivalent norm.

The seminar is going to take place at **10:00** in **B3-38**.

Xiao-Xiong Gan

(Mathematics Department, Morgan State University, Baltimore, USA)

**Formal Power Series and the Boundary Convergence of Power Series**

The behaviour of power series on boundary of convergence domain has been an interesting topic since power series was introduced. For example,

converges on but diverges at , and diverges at both and . The composition of formal power series has been an important part of the *formal power series theory*. We introduce some relationship between these two subjects and provide a condition for convergence of a power series at every point in its interval of convergence, including endpoints or boundary points.

Xiao-Xiong Gan

(Mathematics Department, Morgan State University, Baltimore, USA)

**Composition and Generalized Composition of Formal Power Series**

Given two formal power series

and

the composition has been a very interesting topic for many years, where is called the nonunit. If with , such a composition is called the generalized composition if it exists. We introduce the history of these two compositions and some results of them. Both of them are applied widely although the generalized composition is much younger than the regular one.

**The seminar will take place at 9:00**.

The joint seminar of the Optimization and Control Theory Department and the Department of Theory of Function Spaces will take place at **13:30** in room **A1-33**.

Mahide Kucuk

Department of Mathematics, Faculty of Science, Anadolu University, Eskişehir, Turkey

**Construction and Some Properties of a Total Ordering Cone and Scalarization and Vectorization Using This Cone**

Yalcin Kucuk

Department of Mathematics, Faculty of Science, Anadolu University, Eskişehir, Turkey

**Weak Conjugacy of Scalar and Set Valued Maps and WeakConjugate Duality of Non-convex Scalar and Vector Optimization Problems**

Timothy Myers

(Department of Mathematics, Howard University, Washington, D.C., USA)

**Some Applications of the Sequence: 1, 5, 22, 93, 386,... to Dyck Paths and Ordered Trees.**

The integer sequence starting: 1, 5, 22, 93, 386,... occurs in a variety of situations involving Dyck paths, grand Dyck paths, and ordered trees. We will discuss some new and some known connections, and in particular explore the enumeration of vertices in ordered trees by height using generating functions and the equation.

**The seminar has been cancelled.**

prof. UZ dr hab. Krzysztof Przesławski

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra

**Sets of constant width**

During the seminar we will recall the definition of a set of constant width. Furthermore, we will provide some properties of the above-mentioned sets. All the presented results will be illustrated by examples.

**The seminar is taking place at 11:30 in room A2-22**.

Jakub Bielawski**Embedding theorem for fuzzy sets.**

During the seminar we introduce and study new fuzzy algebraic operations: -sum and scalar -multiplication deﬁned by

and

where are fuzzy subsets and . This allows us to investigate a new deﬁnition of fuzzy convexity.

The seminar will take place in room A2-22 at 11:30.

Jerzy Grzybowski**On finite exhausters**

**The seminar will take place in room A2-22 at 11.30**

We will introduce the notion of a shadowing set, which is a generalization of the notion of separating set to the family of more than two sets. Then we will give a criterion for an upper exhauster to be an exhauster of sublinear function as well as the criterion for minimality of finite upper exhauster.

Ryszard Urbański**On some applications of Simons' Theorem**

During the seminar we will discuss a few theorems concerning the extension of functionals. Moreover, we will indicate possible applications of the above-mentioned results to convex analysis.

Ryszard Urbański**Some remarks on the Hahn-Banach theorem**

The seminar is taking place at **11:30** in room **A2-22**.

(Continuation of the 2011-01-04 and 2011-03-22 Seminars).

dr Magdalena Łysakowska**Decomposition of into unit balls**

The seminar is taking place at **11:30**.

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra

**Finitely additive measures**

It will be demonstrated that numerous operations over convex sets induce linear or multiliear mappings on vector spaces spanned by characteristic functions of such sets. A theorem of McMullen, Pukhlikov and Khovanskii on polynomial finite measures on polyhedra will be discussed as an application.

The seminar is taking place at **11:30**.

Marcin Borkowski**On some properties of almost periodic functions**

(Continuation of the 2011-01-11, 2011-01-18 and 2011-03-01 seminars).

Jerzy Grzybowski**Geometry of convex surfaces**

The convex seminar is taking place at **11:30** in room **A2-22**.

Hubert Przybycień**On the completeness of the Minkowski-Radström-Hörmander space**

(Continuation of the 2011-02-22 Seminar).

Marcin Borkowski**On some properties of almost periodic functions**

(Continuation of the 2011-01-11 and 2011-01-18 seminars).

Hubert Przybycień**On the completeness of the Minkowski-Radström-Hörmander space**

The aim of the talk is to prove the completeness of the Minkowski-Radström-Hörmander space endowed with a certain metric.

Marcin Borkowski**On some properties of almost periodic functions**

(Continuation of the 2011-01-11 Seminar).

Marcin Borkowski**On some properties of almost periodic functions**

During the talk we will present a construction of certain uniformity on a given topological group *G*. It turns out that the class of (real or complex) uniformly continuous functions with respect to this uniformity coincides with the class of Bohr almost periodic functions on *G*. The talk is based on the paper of E. M. Alfsen and P. Holm *A note on compact representations and almost periodicity in topological groups*, Math. Scand. 10 (1962), 127-136.