M. Pınar Eroğlu

Hydroelastic waves propagating in ice-covered channel

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Prof. Dr. Tatyana Khabakhpasheva, School of Mathematics, University of East Anglia, Norwich/United Kingdom

Date: May 24, 2024, Friday

Time: 14:00 am

Place: B255, Faculty of Science, Dokuz Eylül University

Abstract: Characteristics of linear hydroelastic waves propagating in an ice channel are investigated. The channel is of rectangular cross section with finite depth and of infinite extent. Liquid in the channel is inviscid and incompressible. The liquid flow caused by the ice deflection is potential. The ice is modeled by a thin elastic plate. The coupled hydroelastic problem is reduced to the problem of the wave profiles across the channel. The wave profiles are sought as series of normal dry modes of the plate, coefficients of which are to be determined. Dispersion relations of these hydroelastic waves, their critical speeds, and corresponding strain and stress distributions in the plate are determined. Several special cases in which boundary conditions, ice thickness distributions across the channel width, and ice plate compression were changed were investigated and compared with each other.

Coupled/decoupled linear/nonlinear responses of ice cover to external loads

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Prof. Dr. Alexander Korobkin, School of Mathematics, University of East Anglia, Norwich/United Kingdom

Date: May 24, 2024, Friday

Time: 13:00 am

Place: B255, Faculty of Science, Dokuz Eylül University

Abstract: Modelling response of an elastic floating plate to a body moving under the plate is discussed. The original problem is nonlinear and coupled with the plate deflection being dependent on the hydrodynamic pressure, which in turn depends on the plate deflection. It is shown that the problem can be treated as decoupled for some conditions of the body motion, which significantly simplifies the analysis. Within the decoupled model, the body motion and the hydrodynamic pressure along the plate/water interface are calculated without account for the plate deflection. Then this pressure is applied to the equations of the plate dynamics without account for the fluid response to the plate deflection. It is known that only rather small strains are allowed in ice plates, which limits the deflections of the ice and importance of the nonlinear effects. It is shown that nonlinear effects in problems of hydroelastic response of floating ice sheets can be approximately neglected in many practical situations.

On the Edge Cover Polynomial Properties of Certain Graph Families

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Prof. Dr. Feryal Alayont, Mathematics at Grand Valley State University

Date: May 16, 2024, Thursday

Time: 11:00 am

Place: B257, Faculty of Science, Dokuz Eylül University

Abstract: An edge cover of a simple graph is a subset of the edges so that each vertex is incident with at least one edge in the subset. The edge cover polynomial of a graph is the generating polynomial of the number of edge covers of the graph. Specifically, the edge cover polynomial is defined as where is the number of edge covers with edges. The edge cover polynomials of path and cycle graphs are known to have real roots, and hence have log-concave and unimodal coefficients. In this talk, we will describe how to construct other graph families whose edge cover polynomials have real roots and some whose polynomials have non-real roots, but still have log- concave and unimodal coefficients. This is joint work with Evan Henning and Can Selek.

Feryal Alayont is a Professor of Mathematics at Grand Valley State University. She received her B.S. in mathematics from Bilkent University, Turkey, and her Ph.D. in mathematics from the University of Minnesota. She was a teaching postdoctoral fellow at the University of Arizona from 2003 to 2006. Since 2006, she has been at Grand Valley State University in the Department of Mathematics, where she also served as the Mathematics Advising and Engagement Coordinator from 2016-2022. She is an active undergraduate research mentor and has mentored more than 75 students at GVSU. Her research interests include enumerative combinatorics, graph theory, ethics in mathematics, and the scholarship of teaching of mathematics.

Matematiksel Bilginin Doğası

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Prof. Dr. Beno KURYEL, İzmir Ekonomi Üniversitesi (Ege Üniv. Kimya Mühendisliği, Emekli) Tarih: Daha sonra ilan edilecek. Zaman: Daha sonra ilan edilecek. Yer: Deü Fen Fakültesi B255 nolu derslik

Özet: Matematik, tarih boyunca felsefi düşüncenin ve araştırmalarının zengin kaynaklarından birisi olmuştur. Karşılıklı bir etkileşim bütünlüğünde felsefe de matematiksel bilginin üretimine, kavramsal zenginlik kazanmasına, yöntemsel tasarımların oluşmasına kaynaklık etmiştir. Ancak son yıllarda teknolojinin belirleyici kültür şemsiyesinde matematik, teknik ve pragmatik bir araçsallığa indirgenmiştir. Bu durum hem matematik öğrenimini hem de matematiksel teori ve pratiği dar bir kalıp içine hapsetmektedir. Matematiksel bilginin doğasını incelemek ve öğretim süreçleri ile bütünleştirmek bu araçsallığın eleştirisi için atılacak önemli adımlardan birisidir. Bu çalışma, konunun farklı boyutlar içinde bilgikuramsal bir çözümlemesini ve yeni felsefi açılımların geliştirilmesini hedeflemektedir.

Quantitative unique continuation or “If we don’t know everything, how much do we actually know”?

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Matthias Täufer, Analysis group, FernUniversität in Hagen, Germany Date: 1th March 2024, Friday Time: 13:00 Place: DEU, Faculty of Science, Department of Mathematics, Room B255

Abstract: Unique continuation is a basic property of many partial differential equations stating that solutions vanishing on subsets must be identically zero. In many cases one would like to have a quantitative version of that, meaning that one can bound the norm of solutions by their norm on subsets. In this talk, we review some history of quantitative unique continuation and present several results on quantitative unique continuation in unbounded domains. Based on joint works with Ivica Nakic (Zagreb), Martin Tautenhahn (Leipzig), Sedef Özcan (Dokuz Eylül), Paul Pfeiffer (Hagen), Albrecht Seelmann (Dortmund) and Ivan Veselic (Dortmund).

Computing eigenvalues of the discrete p-Laplacian via graph surgery

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Matthias Hofmann, Texas A&M University Date: 16th February 2024, Friday Time: 13:00 Place: DEU, Faculty of Science, Department of Mathematics, Room B255

Abstract: We discuss the dependence of the eigenvalues and eigenfunctions for the discrete signed p-Laplacian under perturbation by a cut parameter. In particular, we prove a formula for the derivative of the eigenvalues and show that the eigenvalues of the discrete signed p-Laplacian on the original graph can be characterized via extremal points of the perturbed system. In this context, we elaborate on how graph surgery can be used in order to compute eigenvalues of the discrete (signed) p-Laplacian by looking at some examples. The derivation formula is reminiscent of the formula for linear eigenvalue problems given by the Hellmann-Feynman theorem and our results extend previous results for the linear case p=2 attained by [Berkolaiko, Anal. PDE 6 (2013), no. 5, 12131233].

ATA FORECASTING METHOD AS A BENCHMARK

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Prof. Dr. Güçkan YAPAR, Department of Statistics, Faculty of Science, DEU, İzmir Date: December 13, 2023, Wednesday Time: 15:00 Place: Classroom B256, Department of Mathematics, Faculty of Science, DEU, İzmir.

Abstract: ATA forecasting method is a new method which is proposed as an alternative to basic forecasting method exponential smoothing (ES) and ARIMA. Although Ata method is structurally similar to the ES method but it is completely different in content. Ata method is simple, fast and more accurate than its alternatives. Ata method has taken its place in the literature by proving its success with its forecasting performance in M-competition data sets.

On rings whose cyclic modules have cyclic injective hulls

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Prof. Dr. Christian Lomp, Department of Mathematics, University of Porto in Porto, Portugal. Date: 19th of April 2023, Wednesday. Time: 11:00. Place: Online/Microsoft Teams- Meeting ID: 351 128 968 15 Passcode: Gy4n4B

Abstract: In 1964, Barbara Osofsky proved in her PhD thesis that a ring whose cyclic modules are injective is semisimple Artinian. William Cadwell in his PhD thesis from 1966 studied when injective hulls of cyclic modules are cyclic and termed them hypercyclic rings. He characterised left perfect left hypercyclic rings as well as commutative local hypercyclic rings. In this talk we will revise the literature on rings whose cyclic modules have cyclic injective hulls and present some more recent results, obtained jointly with Mohamed Yousif and Yiqiang Zhou.