General Seminars of
Department of Mathematics
Department of Mathematics
General Seminars of
Department of Mathematics
Department of Mathematics
Announcements
This site is to announce General Seminars of our department in this academic year. Below is a list of speakers in reverse chronological order. Our seminars are open to anyone interested to listen and/or give a talk. If you need any assistance, please get in touch with the organizer.
- July 30, 2010
- July 29, 2010
- June 15, 2010
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Rauf Amirov (Cumhuriyet Univ.)
- Title: Inverse problems for Sturm-Liouville operators / Sturm-Liouville operatörleri için ters (inverse) problemler
- Place: M301
- Time: 16:00-17:00
- Abstract: Sunulan konuşmada regüler ve singüler Sturm-Liouville operatörlerin doğa bilimlerindeki uygulamaları ve onlar için konulabilecek ters (inverse) problemler ve çözüm tekniklerinden bahs edilecektir.
- May 7, 2010
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Elvan Ceyhan (Koç University)
- Title: A Graph Invariant of a Random Digraph Family for Testing Multivariate Spatial Interaction
- Place: M301
- Time: 15:30-16:20
- Abstract: In this talk, I will first introduce a random digraph family, which is a parametrized proximity catch digraph (PCD) based on data from two different classes in R^2. The digraph is based on neighborhoods of points from one class and the Delaunay triangulation of the points from the other class. The graph invariant I will describe is relative (arc) density of this digraph family. I will use this invariant as a statistic for testing spatial interaction between two (or more) classes of points. When scaled properly, I will show that the relative arc density is a U-statistic. So I derive the asymptotic distribution of the statistic, using the standard central limit theory of U-statistics and illustrate with an application to testing spatial patterns of segregation and association. The consistency of the test is proved, and the performance of the test statistic is assessed via Pitman's and Hodges-Lehmann asymptotic efficacies, thereby yielding the optimal proximity map parameters for the test. I will also present some other related digraph families in literature, other graph invariants used in spatial analysis, and other possible applications. I will also state the open problems in this area. Finally, I discuss extensions of the approach to higher dimensions.
- April 26, 2010
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Oktay Duman (TOBB ETU)
- Title: Recent Developments on Statistical Approximation Theory
- Place: M301
- Time: 16:30-17:30
- Abstract: The classical Korovkin theory which deals with the approximation properties of positive linear operators has been developed by Gadjiev and Orhan in 2002 by replacing the ordinary convergence with the concept of statistical convergence. This new approximation method is known as "Statistical Korovkin Theory" in the literature. In recent years, we improve this theory by using non-positive operators as well as some appropriate operators defined on the space of complex-valued analytic functions. Since we do not need the positivity condition of the approximating operators, our results present a broader context, the so-called "Statistical Approximation Theory". In this talk, we mainly discuss it and display some significant applications explaining why we study this approximation method rather than the classical one.
- April 12, 2010
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Emre Berk (Bilkent University)
- Title: An Inventory System with Stock-dependent Demands and Random Deal Offerings
- Place: M301
- Time: 16:30-17:30
- Abstract: In this talk, I will discuss a model developed for an inventory system which operates in the presence of price deals (discount offerings). The demand is assumed to be stock-dependent - a type of demand that is most suited to stocks that deteriorate with a constant rate such as industrial chemicals and pharmaceuticals. This type of demand has been found empirically in retail environments where the customers' purchase intent is strengthened with visual stock - the more we see, the more we buy in a store!
The model operating characteristics will be obtained and the structure and optimization of the objective function will be discussed. I will also provide some numerical examples illustrating potential benefits that may ensue from this model.
- March 15, 2010
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Murat Altunbulak (Dokuz Eylül University)
- Title: The Pauli Principle, Representation Theory, and Geometry of Flag Varieties
- Place: M301
- Time: 16:30-17:30
- Abstract: According to the Pauli exclusion principle, discovered in 1925, no two identical electrons may occupy the same quantum state. In terms of electron density matrix this amounts to an upper bound for its eigenvalues by 1. In 1926, it has been replaced by skew-symmetry of a multi-electron wave function. In the talk I will describe two different solutions to a problem about the impact of this replacement on the electron density matrix, which goes far beyond the original Pauli principle.
- December 14, 2009
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Ceki Franko
- Title: Reliability Optimization of Series-k-out-of-M Systems Using a Genetic Algorithm
- Place: M301
- Time: 15:30-16:30
- Abstract: Series-parallel systems are commonly used in optimal design problems. This paper presents a generalization of the series-parallel system. Since it is difficult to obtain the exact solution for series-k-out-of-M system, a heuristic method is developed for solving a multi-objective model in which system reliability and costs are considered. A mathematical model is provided by transforming the multi-objective model into single-objective model, which is a very practical and efficient approach. Also, a modified genetic algorithm is proposed in order to solve this model. Finally, the numerical example is provided and the result is illustrated.
- November 23, 2009
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Burcu Silindir Yantır
- Title: The R-matrix approach to integrable systems on regular time scales.
- Place: M301
- Time: 16:30
- Abstract: A general unification and extension framework is introduced for integrable soliton-like systems on regular time scales. The R-matrix formalism is utilized in terms of which infinite hierarchy of commuting vector fields can be constructed. The theory is illustrated by an infinite field integrable hierarchy (Kadomtsev-Petviashvili hierarchy) and by a finite-field restriction (AKNS system).
- November 9, 2009
- Poster: As a document (pdf) or as a poster (png) file.
- Speaker: Ebru Özbilge
- Title: Identification of an Unknown Coefficient Approximately via Semigroup Approach
- Place: M301
- Time: 16:30
- Abstract: This article presents a semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient a(x,t) in the parabolic equation ut(x,t) = uxx(x,t)+a(x,t)u(x,t), with Dirichlet boundary conditions u(0,t)=ψ0, u(1,t)=ψ1. It is shown that the unknown coefficient a(x,t) can be approximately determined via semigroup approach.
