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TRANSCRIPT
İZMİR MATEMATİK GÜNLERİ - II 12-13 Eylül 2019 http://img.deu.edu.tr
İzmir Matematik Günleri, lisansüstü öğrencilerin ve genç araştırmacıların çalışmalarını, fikirlerini ve tecrübelerini paylaşacakları, araştırma ve mentor ağları kurabilecekleri bir platformdur.
Çalıştayın sabah oturumlarında davetli konuşmacılar kendi çalışma alanlarını tanıtan kolokyum konuşmaları vereceklerdir. Öğleden sonra oturumları ise lisansüstü öğrencilerin ve genç araştırmacıların konuşmalarına ayrılmıştır.
DAVETLİ KONUŞMACILAR
Yusuf Civan (SDÜ) Konstantinos Kalimeris (Cambridge) Müge Kanuni Er (Düzce Ü.) Haydar Göral (DEÜ)
DÜZENLEME KOMİTESİ
Münevver Pınar Eroğlu (DEÜ) Asl ı Güçlükan İ lhan (DEÜ) Sabri Kaan Gürbüzer (DEÜ) Celal Cem Sarıoğlu (DEÜ)
İLETİŞİM
i [email protected] http://img.deu.edu.tr/
BİLİMSEL DANIŞMA KOMİTESİ
Refai l Al izade (Yaşar Ü.) Engin Büyükaşık ( İYTE) Didem Coşkan (DEÜ) Selçuk Demir (DEÜ) Emine Mısır l ı (Ege Ü.) Oktay Pashaev ( İYTE) Bayram Şahin (Ege Ü.) Serap Topal (Ege Ü.) Ergün Yalçın (Bi lkent Ü.) Ahmet Yantır (Yaşar Ü.)
Abstract Book
Izmir Mathematics Days IISeptember 12-13, 2019
Buca, Izmir, Turkey
img.deu.edu.tr
Organized by
Dokuz Eylul UniversityIzmir, Turkey
Contents
1 Preface ii
2 Program iii
3 Colloquium Talks 1Yusuf Civan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Haydar Goral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Konstantinos Kalimeris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Muge Kanuni Er . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Contributed Talks 6Cagatay Altuntas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Sinem Benli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Zehra Cayic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Didem Cil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Esma Dirican . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Elona Fetahu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Ezgi Gurbuz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Ulviye Busra Guven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Ece Hazal Korkmaz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Hikmet Burak Ozcan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Busra Ozsavas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Hakan Sanal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Ege Tamcı . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Tugba Yazan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Neslihan Yıldırım . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Filiz Yıldız . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 Participants and Committees 23Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Committees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
i
Preface
One of two aims of Izmir Mathematics Days is to provide a platform for graduate students to sharetheir works, ideas and experiences and to build research and mentoring networks. The other one isto encourage undergraduate math majors to pursue a career in Mathematics.
In the morning sessions, four colloquium talks will be given by the invited speakers to introducetheir research of interests. The afternoon sessions are devoted to graduate students and youngresearchers. All students are welcome to apply. There will also be an informative panel of facultymembers describing the graduate program at DEU.
All abstracts must be submitted in English. The talk can be either in English or in Turkish butthis must be clearly stated in the submission process. The workshop will be organized by DokuzEylul University in September 12-13, 2019.
Scientific and Organizing Committees.
ii
Program
IMG II-2019 Workshop Program
Thursday 12.09.2019Time Colloquium Talks C Blok - Conference Room09:15–09:30 Opening09:30–10:35 Yusuf Civan Chair: Aslı Guclukan Ilhan10:35–10:55 Tea Break10:55–12:00 Konstantinos Kalimeris Chair: Aslı Guclukan Ilhan12:00–13:30 Lunch
Contributed TalksTime Session 1 Chair: Halil Oruc B-253 Session 2 B-25613:30–14:00 Elona Fetahu Esma Dirican Chair: Yusuf Civan14:00–14:30 Ece Hazal Korkmaz Didem Cil Chair: Yusuf Civan14:30–14:45 Tea Break14:45–15:15 Zehra Cayic Ulviye Busra Guven Chair: Muge Kanuni Er15:15–15:45 Ege Tamcı Sinem Benli Chair: Muge Kanuni Er15:45–16:15 Busra Ozsavas
Friday 13.09.2019Time Colloquium Talks C Blok - Conference Room09:30–10:35 Muge Kanuni Er Chair: Engin Mermut10:35–10:55 Tea Break10:55–12:00 Haydar Goral Chair: Engin Mermut12:00–13:30 Lunch
Contributed TalksTime Session 1 B-253 Session 2 B-25613:30–14:00 Cagatay Altuntas Chair: Murat Altunbulak Filiz Yıldız Chair: Aslı Guclukan Ilhan14:00–14:30 Hikmet Burak Ozcan Chair: Murat Altunbulak14:30–14:45 Tea Break14:45–15:15 Ezgi Gurbuz Chair: Haydar Goral Tugba Yazan Chair: Ilhan Karakılıc15:15–15:45 Hakan Sanal Chair: Haydar Goral Neslihan Yıldırım Chair: Ilhan Karakılıc16:00–17:30 PANEL: Burcu Silindir Yantır, Selcuk Demir, Noyan Er, Halil Oruc, Ahmet Yantır
iii
Colloquium Talks
1
A short tour in combinatorics
Yusuf CivanSuleyman Demirel University, Department of Mathematics, Isparta, Turkey
This is an invitatory talk to a short trip through the jungle of combinatorics, one of the fascinatingfields of modern mathematics. If time permits, we plan to visit various sites in the jungle, includ-ing those from combinatorial number theory to discrete geometry, graph theory to combinatorialcommutative algebra, etc. Lastly, after showing our respect to the founder king ”Paul Erdos” of thejungle, we review the current status of some of his favorite open problems.
2
Arithmetic Progressions
Haydar GoralDokuz Eylul University, Department of Mathematics, Izmir, Turkey
A sequence whose consecutive terms have the same difference is called an arithmetic progression.For example, even integers form an infinite arithmetic progression. An arithmetic progressioncan also be finite. For instance, 5, 9, 13, 17 is an arithmetic progression of length 4. Findinglong arithmetic progressions in certain subsets of integers is at the centre of mathematics in the lastcentury. In his seminal work, Szemeredi (1975) proved that ifA is a subset of positive integers withpositive upper density, then A contains arbitrarily long arithmetic progressions. With this result,Szemeredi proved the long standing conjecture of Erdos and Turan. Another recent remarkableresult was obtained by Green and Tao in 2005: The set of prime numbers contains arbitrarily longarithmetic progressions. In this talk, we will survey these results and some ideas behind them.
3
Water waves - Two asymptotic approaches
Konstantinos KalimerisUniversity of Cambridge, Department of Mathematics, United Kingdom
Asymptotic methods have a long and illustrious history in a plethora of categories both in pureand applied mathematics. The theoretical tools of asymptotic analysis provide the appropriatebackground for the development of methods for studying problems originated from the real world;furthermore, these methods find several applications in hysical problems.
In this talk we emphasise their application to partial differential equations which model certainproblems of fluid dynamics. First, we use techniques from asymptotic analysis and perturbationtheory to obtain approximate analytical and numerical solutions of a non-linear boundary valueproblem which comes from the Euler’s equations for fluids and describes two dimensional waterwaves travelling at constant speed. Second, we derive a non-local formulation for a more gen-eral modelling of water waves, including waves with moving boundaries which are related withthe study of tsunamis; we present analytical and computational results that the above techniquesproduce for particular cases of this problem.
4
Mad Vet...
Muge Kanuni ErDuzce University, Department of Mathematics, Duzce, Turkey
How does a recreational problem ”Mad Vet” links to interesting and interdisciplinary mathematicalresearch ”Leavitt path algebras” in algebra and ”Graph C*-algebras” in analysis.
We will give a survey of the last 15 years of research done in a particular example of non-commutative rings flourishing from the fact that free modules over some non-commutative ringscan have two bases with different cardinality. Surprisingly enough not only non-commutative ringtheorists, but also C*-algebraists gather together to advance the work done. The interplay betweenthe topics stimulate interest and many proof techniques and tools are used from symbolic dynamics,ergodic theory, homology, K-theory and functional analysis. Many papers have been published onthis structure, so called Leavitt path algebras, which is constructed on a directed graph.
5
Contributed Talks
6
ON THE ρ-ADIC VALUATION OF HARMONIC NUMBERS
Cagatay AltuntasIstanbul Technical University, Istanbul, Turkey
For any positive integer n, the nth harmonic number Hn is defined as∑n
k=11k
. Let Jp be the set ofpositive integers n such that the numerator of Hn is divisible by p. In this talk, some properties ofthe set Jp will be covered.
References[1] A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), no. 3, 249-257.
[2] C. Sanna, On the p-adic valuation of harmonic numbers, J. Number Theory 166 (2016) 41-46.
7
Almost perfect prime local rings are CJ -rings
Sinem BenliIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey.
[email protected] : Engin Mermut
Renault defined a ring R to be a right C-ring if for every right R-module M and for every essentialproper submodule N of M , the quotient module M/N has a simple submodule. The concept ofCJ -rings, which is a generalization for C-rings, is defined by Generalov as follows: A ring R issaid to be a right CJ -ring if for any proper J -dense right ideal I of R, there exists an elementr ∈ R such that (I : r)r is a maximal right ideal where J is a set of right ideals of R. On the otherhand, almost perfect domains, that is, the commutative domains whose every proper quotient isperfect, have been introduced by Bazzoni and Salce in the investigation of strongly flat covers overa commutative domain. This notion has been generalized to noncommutative setting by Facchiniand Parolin. In this talk, we shall discuss the relations between these classes of rings. In particular,for a prime ring R, we show that R is almost perfect if and only if R is h-local and R is a leftCJ -ring.
References[1] Generalov, A. I. (1978). On weak and w-high purity in the category of modules. Mathematics of the USSR-Sbornik,
34, 345-356.
[2] Salce, L. (2011). Almost perfect domains and their modules. Commutative Algebra, Noetherian and non-Noetherian Perspectives, 363-386, Springer, New York.
[3] Facchini, A. & Parolin, C. (2011). Rings whose proper factors are right perfect. Colloquim Mathematicum, 122(2),191-202.
[4] Benli, S. (2015). Almost perfect rings. M.Sc. Thesis, Dokuz Eylul University, Izmir.
8
Time-evolution of squeezed coherent states of a generalized quantumparametric oscillator
Zehra CayicIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey
[email protected]: Sirin A. Buyukasık
Time-evolution of squeezed coherent states of a generalized quantum parametric oscillator is foundexplicitly using the unitary displacement and squeeze operators and the exact evolution operatorobtained by the Wei-Norman algebraic approach. Properties of these states are analyzed accordingto the complex parameter of the squeeze operator and the time-variable parameters of the gener-alized quadratic Hamiltonian. An exactly solvable model is constructed to illustrate explicitly thesqueezing and displacement properties of the wave packets.
References[1] Buyukasık S. A. and Cayic Z., Time-evolution of squeezed coherent states of a generalized quantum parametric
oscillator, J. Math. Phys., 60, 062104 (2019).
9
On Small Covers Over A Product Of Simplices
Didem CilDokuz Eylul University, Department of Mathematics, Izmir, Turkey
[email protected] : Aslı Guclukan Ilhan
In [1], Davis and Januskiewicz introduce small covers as manifolds with locally standard Zn2 -action
whose orbit space is a simple convex polytope. Two small covers M1 and M2 are DJ-equivalentif there is a weakly Zn
2 -equivariant homeomorphism f : M1 → M2 covering the identity on P.They also show that DJ-equivalence classes of small covers can be classified by their characteristicfunctions.
After giving a necessary background on small covers, we consider the case where P is a productof simplices and we give formulas for the number of DJ-equivalence classes and Zn
2 -equivarianthomeomorphism classes of small covers over P. These formulas are obtained in [2] and [3], respec-tively. However, there is no known formula for the number of weakly Zn
2 -equivariant homeomor-phism classes. We also calculate the number of weakly Zn
2 -equivariant homeomorphism classes ofsmall covers for some particular cases.
This work is supported by the Scientific and Technological Research Council of Turkey, GrantNo: TBAG-118F310.
References[1] M.W. Davis, T. Januszkiewicz, Convex Polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 1991, 62,
417451.
[2] S. Choi, The number of small covers over cubes, Algebr. Geom. Topol. 2008, 8, 2391-2399.
[3] M. Altunbulak, A. Guclukan Ylhan, On small covers over a product of simplices, Turk. J. Math. 2018, 42, 1528-1535.
10
Connected Sum of Orientable Surfaces and Reidemeister Torsion
Esma DiricanIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey
[email protected] : Yasar Sozen
The topological invariant Reidemeister torsion was first introduced by K. Reidemeister in his studyon 3−dimensional lens spaces [2], where he used this invariant to give piecewise linear classifica-tion of lens spaces. In 1935 W. Franz extended the notion of Reidmeister torsion in order to classifyhigher dimensional lens spaces [1]. Later, various properties and applications of Reidemeister tor-sion on manifolds and knot theory have been explored by [3], [7], [4] and [6]. Let Σg,n be anorientable surface with genus g ≥ 2 bordered by n ≥ 1 curves homeomorphic to circle. In thistalk, we focus on obtaining a formula to compute Reidemeister torsion of one-holed-torus Σ1,1 byusing the notion of symplectic chain complex and homological algebra techniques. Then, applyingthis result and considering Σg,n as a connected sum Σ1,0# · · ·#Σ1,0#Σ1,n, we establish a formulato compute Reidemeister torsion of Σg,n in terms of Reidemeister torsion of Σ1,1 and Reidemeistertorsion of Σ1,n, n ≥ 2 for homologies with untwisted coefficients (R,C).
This work is supported by Tubitak Grant 114F516.
References[1] W. Franz, Uber die torsion einer uberdeckung, J. Reine Angew. Math. 173 (1935), 245–254.
[2] K. Reidemeister, Homotopieringe und linsenraume, Hamburger Abhandl. 11 (1935), 102–109.
[3] J. Milnor, Whitehead torsion, Bull. Amer. Soc. 72 (1966), 358–426.
[4] J. Porti, Torsion de Reidemeister pour les varietes hyperboliques, AMS Chelsea Publishing, 1997.
[5] Y. Sozen, Symplectic chain complex and Reidemeister torsion of compact manifolds, Math. Scand. 111 (2012),65-91.
[6] V. Turaev, Torsions of 3-manifolds, Geometry & Topology Monographs, Verlag: Birkhuser, 2002.
[7] E. Witten, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), 153–209.
11
The collapse of a vertical cylindrical cavity of circular cross sectionsextending from the free surface and having less depth than a surrounding
fluid of finite depth
Elona FetahuIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey
[email protected] : Oguz Yılmaz
The gravity-driven potential flow due to the collapse of a vertical cylindrical cavity of circular crosssections surrounded by a liquid region is examined. The cavity starts from the free surface havingless depth than a fluid, which is initially at rest. When the cylinder is suddenly removed, the gravitydriven flow starts and the resulting flow is potential and three dimensional. The leading order outersolution is derived by applying asymptotic analysis using a small parameter that represents the shortduration of the stage. Fourier series method is used in solving the linear problem. On the limitingcase, the problem reduces to the 2-D dam break flow of two immiscible fluids by Yılmaz, Korobkinand Iafrati (2013). Singularity at the bottom circle of the cavity is observed, which is of the sametype as in the paper aforementioned. The methods applied in these computations are expected tobe useful in the analysis of gravity-driven flow free surface shapes.
References[1] O. Yılmaz, A. Korobkin and A. Iafrati, The initial stage of dam-break flow of two immiscible fluids. Linear analysis
of global flow, Applied Ocean Research, 42 (2013), 60-69.
12
Unique Decomposition Into Ideals
Ezgi GurbuzIzmir Institute of Technology, Mathematics, Izmir, Turkey
The ring R is said to have the unique decomposition into ideals (UDI) property if, for any R-module that decomposes into a finite direct sum of indecomposable ideals, this decomposition isunique apart from the order and isomorphism class of the indecomposable ideals. In other words,for any indecomposable ideals I1, . . . , In, J1, . . . , Jm of R, if I1 ⊕ . . . ⊕ In ∼= J1 ⊕ . . . ⊕ Jm,then n = m and, after reindexing, Ii ∼= Ji for each index i. In this talk, R is assumed to be acommutative Noetherian, non-Artinian, indecomposable ring and our aim is to show that R has theUDI property if and only if R has at most one non-principal maximal ideal and R has the UDIproperty locally at every maximal ideal [1].
References[1] Omairi, A., h-local Rings, PhD thesis, 2019.
13
Normalizers in Homogeneous Symmetric Groups
Ulviye Busra GuvenIzmir University of Economics, Izmir, [email protected]
For any infinite prime sequence ξ = (p1, p2, . . .), let ni = p1p2 . . . pi. Then for every pi ∈ ξconsider the embeddings dpi from the symmetric group Sni−1
to Sniwhere for any α ∈ Sni−1
if
α =(
1 2 ··· ni−1
j1 j2 ··· jni−1
), then
dpi(α) =(
1 2 ··· ni−1
j1 j2 ··· jni−1| ni−1+1 ··· 2ni−1
ni−1+j1 ··· ni−1+jni−1| ······ |
(pi−1)ni−1+1 ··· (pi−1)ni−1+ni−1
(pi−1)ni−1+j1 ··· (pi−1)ni−1+jni−1
)dpi’s are called strictly diagonal embeddings. For any ξ, the direct limit groups S(ξ) =
∞⋃i=1
Sni
constructed by using the strictly diagonal embeddings above is called homogeneous symmetricgroups. The construction and the classification of these groups are due to Kroshko-Suschansky,see [2].
In this talk first I will construct the direct limit group S(ξ) =∞⋃i=1
Sniand I will discuss the
normalizers of some special subgroups which are done in [1].
References[1] Guven U.B, Kuzucuoglu M., Normalizers of finite subgroups in homogeneous symmetric groups and automor-
phisms, Comm. Algebra, DOI No. 10.1080/00927872.2019.1612423, published online.
[2] Kroshko N. V., Sushchansky V. I., Direct Limits of symmetric and alternating groups with strictly diagonal em-beddings,Arch. Math. 71 (1998), 173-182.
14
Wave Radiation from a Truncated Cylinder of Arbitrary Cross Sections
Ece Hazal KorkmazIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey
[email protected] : Oguz Yılmaz
In this talk, we define the wave radiation from a truncated cylinder of arbitrary cross sections infinite-depth water. The fluid domain is divided into two regions: an interior region below thecylinder and an exterior region outside of the cylinder. Velocity potentials satisfy the Laplaceequation, free surface and boundary conditions in each region. The problem is formulated in polarcoordinate system (r, θ, z). In the early 1980s, wave radiation by a truncated circular cylinderin finite-depth waters was presented by Yeung [1]. The cross section of the vertical cylinder isdescribed by the equation r = R[1 + εf(θ)]. Then, asymptotic series of velocity potentials are usedto find an approximate solution of the problem. Similarly, asymptotic methods used for the problemof wave diffraction from a bottom-mounted cylinder of arbitrary cross section by Disibuyuk et al.[2]
This is a joint work with Oguz Yılmaz.
References[1] Ronald W.Yeung. Added mass and damping of a vertical cylinder in finite-depth waters, Applied Ocean Research
Volume 3, Issue 3, July 1981.
[2] N. B. Disibuyuk; A. A. Korobkin; and O. Yılmaz. Linear Wave Interaction with a Vertical Cylinder of ArbitraryCross Section: An Asymptotic Approach, Journal of Waterway, Port, Coastal, and Ocean Engineering / Volume143 Issue 5 - September 2017.
15
Prime Ideal Theorem on Number Fields
Hikmet Burak OzcanDokuz Eylul University, Department of Mathematics, Izmir, Turkey
[email protected] : Haydar Goral
In 1896, de la Vallee Poussin and Hadamard independently gave an asymptotic formula for theprime counting function π(n), which counts the number of primes less than some integer n. In theliterature this is known as Prime Number Theorem. In this talk, firstly we will introduce the notionof number fields and we will mention the ring of integers for a given number field. Then, we willtalk about the Prime Ideal Theorem, which is the number field generalization of the prime numbertheorem. It was proved by Edmund Landau in 1903. This theorem provides an asymptotic formulafor the prime ideal counting function πK(n), which counts the number of prime ideals in the ringof integers of K with norm at most n.
References[1] Frazer Jarvis, Algebraic Number Theory, Springer, 2014.
[2] Hugh L. Montgomery, Robert C. Vaughan, Multiplicative Number Theory I. Classical Theory, Cambridge Univer-sity Press, 2006.
[3] Pierre Samuel, Algebraic Theory of Numbers, Dover Publications, 1970.
16
Oscillation of Partial Difference Equations with Variable Coefficients
Busra OzsavasDokuz Eylul University, Department of Mathematics, Izmir, Turkey
[email protected] : Basak Karpuz
In this talk, we will review the results on the oscillation of ordinary difference equations
u(m+ 1)− u(m) +r∑
k=1
pk(m)u(m− τk) = 0, m ≥ 0, (4.1)
and partial difference equations
u(m+ 1, n) + u(m,n+ 1)− u(m,n) +r∑
k=1
pk(m,n)u(m− τk, n− σk) = 0, m, n ≥ 0.
Later, we will provide improve some results for the oscillation of partial difference equations.
References[1] L. H. Erbe and B. G. Zhang. Oscillation of discrete analogues of delay equations. Differential Integral Equations,
2(3):300–309, 1989.
[2] I. Gyori and G. Ladas. OLinearized oscillations for equations with piecewise constant arguments. DifferentialIntegral Equations, 2(2):123–131, 1989.
[3] I. Gyori and G. Ladas. Oscillation Theory of Delay Differential Equations. Oxford University Press, New York,1991.
[4] G. Ladas, Ch. G. Philos, and Y. G. Sficas. Necessary and sufficient conditions for the oscillation of differenceequations. Libertas Math., 9:121–125, 1989.
[5] G. Ladas, Ch. G. Philos, and Y. G. Sficas. Sharp conditions for the oscillation of delay difference equations. J.Appl. Math. Simulation, 2(2):101–111, 1989.
[6] E. C. Partheniadis. Stability and oscillation of neutral delay differential equations with piecewise constant argu-ment. Differential Integral Equations, 1(4):459–472, 1988.
[7] Q. G. Tang and Y. B. Deng. Oscillation of difference equations with several delays. Hunan Daxue Xuebao,25(2):1–3, 1998.
[8] J. S. Yu, B. G. Zhang, and Z. C. Wang. Oscillation of delay difference equations. Appl. Anal., 53(1-2):117–124,1994.
[9] B. G. Zhang and S. T. Liu. Necessary and sufficient conditions for oscillations of partial difference equations.Dynam. Contin. Discrete Impuls. Systems, 3(1):89–96, 1997.
[10] B. G. Zhang and S. T. Liu. On the oscillation of two partial difference equations. J. Math. Anal. Appl., 206(2):480–492, 1997.
[11] B. G. Zhang and Y. Zhou. Qualitative Analysis of Delay Partial Difference Equations. Hindawi PublishingCorporation, New York, 2007.
17
On Isoartinian and Isonoetherian Modules
Hakan SanalDokuz Eylul University, Department of Mathematics, Izmir, Turkey
[email protected] : Salahattin Ozdemir
Facchini and Nazemian generalize the idea of artinian and noetherian modules by considering theirchain conditions up to isomorphism. Let R be a ring and M be a right R-module. M is calledisoartinian if, for every descending chain M ≥M1 ≥M2 ≥ ... of submodules of M , there exist anindex n ≥ 1 such that Mn is isomorphic to Mi for every i ≥ n. Dually , M is called isonoetherian,if, for every ascending chain M1 ≤ M2 ≤ ... of submodules of M , there exist an index n ≥ 1such that Mn is isomorphic to Mi for every i ≥ n. Similarly an isosimple module is defined as anon-zero module whose all non-zero submodules are isomorphic to it.
In this talk, we are interested in these three classes of modules.
References[1] Facchini A. and Nazemian Z. Modules with chain conditions up to isomorphism. J. Algebra 453 (2016):578-601.
[2] Facchini A. and Nazemian Z. Artinian dimension and isoradical of modules. J. Algebra 484 (2017):66-87.
[3] Prakash, Surya, and Avanish Kumar Chaturvedi. Iso-Noetherian rings and modules, Communications in Algebra47.2 (2019): 676-683.
18
Stability Analysis of Random Nonlinear Systems
Ege TamcıIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey
In recent studies, in single machine infinite bus power systems, the stochastic excitations have beenmodeled as alpha-stable Levy and Gaussian Type processes. through the simulations of the corre-sponding stochastic differential equations, the impulsiveness and/or asymmetry in the distributionsof the load fluctuations can cause the instability of the rotor angle. In order to rescue the unstability,Levy type fluctuations were used to improve the stability of rotor angle in the sense of probabilityand this result was considered as the benefit of noise was obtained as a numerical consecuences.We want to give the theoretical meaning to these consequences.
19
Semigroup Theory and Some Applications
Tugba YazanIzmir Institute of Technology, Department of Mathematics, Izmir, Turkey
[email protected] : Ahmet Batal
In this talk, we consider the evolution equation (Cauchy problem) which is the basis for our study.We show how various linear PDE’s can be transformed into the Cauchy problem form. Solving theCauchy problem is equivalent to find a family of evolution operators T(t) which sends the initialstate of the system to the solution state at a later time t. It turns out that this family of operatorsT(t) must satisfy some properties which we call semigroup properties. We give some fundamentaldefinitions, properties related to semigroup theory and useful theorems such as Hille-Yosida andLumer Phillips theorems which help us to generate a contraction semigroup for a given Cauchyproblem. Finally we apply these theorems to the Heat equation as an example.
References[1] A.Pazy, Semigroups of Linear Operators and Partial Differential Equations, New York, 1992.
[2] Dirk Hundertmark, Martin Meyries and Roland Schnaubelt, Operator Semigroup and Dispersive Equations, 2012-2013, https://isem.math.kit.edu
[3] Klaus-Jochen Engel and Rainer Nagel,One-Parameter Semigroups for Linear Evolution Equations, 1999.
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Kinematic Aspects Of Underwater Swimming Frogs
Neslihan YıldırımDokuz Eylul University, Graduate School of Natural and Applied Sciences,
Department of Mathematics, Izmir, [email protected]
Co-author : Ilhan Karakılıc
Under liquid swimming for the robots is extremely interesting. In this context one can think ofdeep sea beds, oil deposits, acid tanks, etc. The next generation of robots will be based on animalsrather than humans.The papers published by Gal & Blake [1,2] are keys to the studies for frog swimming. In thesestudies, experiments done by frogs (Hymenochicus Boettgeri), establish the relation between trustand drag depending on the water density, wetted surface area, drag coefficient and velocity. Thehydrodynamic mechanism of frog swimming and the hind limb kinematics (in the experimen-tal observations of Xenopus Leavis) are given in [3]. There is a comparation of the swimmingkinematics and hydrodinamics between the purely aquatic (X. leavis and H. boettgeri) and semi-aquatic/terrestrial(R. pipiens and B. americanus) in [4].The relationship between the kinematics and performance of frogs make them worthy for underwa-ter swimming. Their underwater motion is trust-drag based. By using the hydrodynamic equationsof experimantal results of frogs’ underwater swimming, we obtain the speed and the distance forsuch a motion.
References[1] Gal,J.M,Blake, R.W.1988 Biomechanics of Frog Swimming I. J. Exp. Biol. 138, pp. 399-411.
[2] Gal, J.M., Blake, R.W. 1988. Biomechanics of Frog Swimming II. J. Exp. Biol. 138, pp. 413-429.
[3] Richards, C.T. 2008. The Kinematic Determinations of Anuran Swimming Performance: An Inverse and ForwardDynamics Approach. Jour. Exp. Biol. 211, pp. 3181-3194. DOI: 10.1242/jeb.019844.
[4] Richards, C.T. 2009. Kinematics and Hydrodynamics Analsis of Swimming Anurans Reveals Striking InterspecificDifferences in the Mechanism for Producting Thrust. Jour. Exp. Biol. 213, pp. 621-634. DOI: 10.1242/jeb.032631.
[5] Videler, J.J. 1993. Fish Swimming. 2nd edition. Vol. 1.Chapman and Hall, 260 pages.
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Remarks On Antisymmetric T0-Quasi-Metric Spaces
Filiz YıldızHacettepe University, Department of Mathematics, Ankara, Turkey
[email protected] : Hans-Peter A. Kunzi
Following the studies about symmetric connectedness theory for T0-quasi-metric spaces, in the con-text of asymmetric topology, we define antisymmetric T0-quasi-metric spaces as a kind of oppositeto the notion of a metric space.
Subsequently some useful results about antisymmetric spaces are emphasized by investigatingsome natural relations between the theories of symmetrically connected T0-quasi-metric spaces andantisymmetric spaces.
References[1] H.-P. A. Kunzi, An introduction to quasi-uniform spaces, in: Beyond Topology, eds. F. Mynard and E. Pearl,
Contemp. Math., Amer. Math. Soc. 486 (2009), pp. 239–304.
[2] F. Yıldız and H.-P. A. Kunzi, Symmetric connectedness in T0-quasi-metric spaces, Bulletin of the Belgian Mathe-matical Society Simon Stevin, in press, 2019.
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Participants and Committees
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Participants of Izmir Mathematics Days II
1. Ahmet Yantır Yasar University ahmet.yantir[at]yasar.edu.tr2. Ali Sevimlican Dokuz Eylul University ali.sevimlican[at]deu.edu.tr3. Alper Ulker Agrı Ibrahim Cecen University aulker[at]agri.edu.tr4. Aslı Guclukan Ilhan Dokuz Eylul University asli.ilhan[at]deu.edu.tr5. Asya Isbil Bogazici University asyaisbill[at]gmail.com6. Ayca Ileri Dokuz Eylul University aycileri[at]gmail.com7. Aylin Bozacı Izmir Institute of Technology bozaciiayliin[at]gmail.com8. Ayse Beler Dokuz Eylul University ayse beler[at]hotmail.com9. Azem Berivan Adıbelli Izmir Institute of Technology azemadibelli[at]hotmail.com10. Bahar Cakırgoz Dokuz Eylul University bahar.cakirgoz[at]gmail.com11. Basak Karpuz Dokuz Eylul University basak.karpuz[at]deu.edu.tr12. Berkay Cambaz Pamukkale University13. Birsu Kaplan Pamukkale University birsukaplan99[at]hotmail.com14. Burak Turfan Dokuz Eylul University burakturfan7[at]gmail.com15. Burcu Silindir Yantır Dokuz Eylul University burcu.silindir[at]deu.edu.tr16. Busra Ozsavas Dokuz Eylul University busraozsavas[at]gmail.com17. Celal Cem Sagıroglu Dokuz Eylul University celalcem.sarioglu[at]deu.edu.tr18. Cihan Sahilliogulları Izmir Institute of Technology cihansahilliogullari[at]iyte.edu.tr19. Cagatay Altuntas Istanbul Technic University cagataysw[at]gmail.com20. Derya Bayrıl Aykut Dokuz Eylul University derya.bayril[at]deu.edu.tr21. Derya Cokgur Izmir Institute of Technology derya.cokgur[at]icloud.com22. Didem Coskan Dokuz Eylul University didem.coskan[at]deu.edu.tr23. Didem Cil Dokuz Eylul University didemcil.22[at]gmail.com24. Dilara Altay Dokuz Eylul University dilaraltay9[at]gmail.com25. Ece Hazal Korkmaz Izmir Institute of Technology ecekorkmaz[at]iyte.edu.tr26. Ege Tamcı Izmir Institute of Technology egetamci[at]iyte.edu.tr27. Elif Ozge Tufekci Dokuz Eylul University eo.tufekci[at]gmail.com28. Elif Sarı Dokuz Eylul University sarielif66[at]gmail.com29. Elona Fetahu Izmir Institute of Technology fetahuelona[at]gmail.com30. Engin Buyukasık Izmir Institute of Technology enginbuyukasik[at]iyte.edu.tr31. Engin Mermut Dokuz Eylul University engin.mermut[at]deu.edu.tr32. Eren Canan Dokuz Eylul University erenncanan[at]gmail.com33. Ersel Tahir Dokuz Eylul University ersel197[at]hotmail.com34. Esma Dirican Izmir Institute of Technology esmadirican[at]iyte.edu.tr35. Esra Altıntas Ege University esraaltntas[at]gmail.com36. Esra Coskun Afyon Kocatepe University esracskn29[at]gmail.com37. Ezgi Gurbuz Izmir Institute of Technology ezgigurbuz[at]iyte.edu.tr38. Ezgi Tutar Izmir Institute of Technology ezgitutaar[at]gmail.com39. Fatma Zehra Alpaslan Ege University fatmazehraalpaslan250[at]gmail.com40. Filiz Yıldız Hacettepe University yfiliz[at]hacettepe.edu.tr41. Gizem Su Ozkul Ege University gizem.su95[at]outlook.com42. Gonca Demirkol Dokuz Eylul University gonca.demirkol95[at]gmail.com43. Gulsah Yuksel Dokuz Eylul University gulsahyuksel96[at]gmail.com44. Gulter Budakcı Dokuz Eylul University gulter.budakci[at]deu.edu.tr45. Gurcihan Zaman Dokuz Eylul University gurcihan zaman[at]hotmail.com
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46. Hakan Sanal Dokuz Eylul University sanal.hakan35[at]gmail.com47. Halil Oruc Dokuz Eylul University halil.oruc[at]deu.edu.tr48. Haydar Goral Dokuz Eylul University haydar.goral[at]deu.edu.tr49. Hikmet Burak Ozcan Izmir Institute of Technology hikmetburakozcan[at]gmail.com50. Isınsu Celebioglu Izmir Institute of Technology isinsucelebioglu[at]gmail.com51. Ihsan Ergulen Dokuz Eylul University ihsanrgln7[at]gmail.com52. Ilhan Karakılıc Dokuz Eylul University ilhan.karakilic[at]deu.edu.tr53. Kemal Cem Yılmaz Izmir Institute of Technology cemyilmaz[at]iyte.edu.tr54. Konstantinos Kalimeris Cambridge University k.kalimeris[at]damtp.cam.ac.uk55. Melda Duman Dokuz Eylul University melda.duman[at]deu.edu.tr56. Melek Sofyalıoglu Ankara Hacı Bayram Veli University melek.sofyalioglu[at]hbv.edu.tr57. Meltem Adıyaman Dokuz Eylul University meltem.evrenosoglu[at]deu.edu.tr58. Meltem Altunkaynak Dokuz Eylul University meltem.topcuoglu[at]deu.edu.tr59. Meltem Gullusac Dokuz Eylul University meltem.gullusac[at]deu.edu.tr60. Metin Turgay Selcuk University metin.turgay[at]selcuk.edu.tr61. Murat Altunbulak Dokuz Eylul University murat.altunbulak[at]deu.edu.tr62. Mustafa Kutay Kutlu Dokuz Eylul University kutlu mkkutlu58[at]gmail.com63. Muge Diril Izmir Institute of Technology mugediril[at]gmail.com64. Muge Kanuni Er Duzce University mugekanuni[at]duzce.edu.tr65. Munevver Pınar Eroglu Dokuz Eylul University mpinar.eroglu[at]deu.edu.tr66. Nermin Alp Izmir Institute of Technology nerminylc[at]gmail.com67. Neslihan Yıldırım Dokuz Eylul University nesslihanyildirim[at]gmail.com68. Neslisah Imamoglu Karabas Izmir Institute of Technology neslisahimamoglu[at]iyte.edu.tr69. Noyan Fevzi Er Dokuz Eylul University noyan.er[at]deu.edu.tr70. Sabri Kaan Gurbuzer Dokuz Eylul University kaan.gurbuzer[at]deu.edu.tr71. Salahattin Ozdemir Dokuz Eylul University salahattin.ozdemir[at]deu.edu.tr72. Sedef Karakılıc Dokuz Eylul University sedef.erim[at]deu.edu.tr73. Sedef Taskın Dokuz Eylul University sedeftaskin92[at]hotmail.com74. Selcuk Demir Dokuz Eylul University selcuk.demir[at]deu.edu.tr75. Selin Simsek Canakkale Onsekiz Mart University seliinsimseek[at]gmail.com76. Sena As Dokuz Eylul University senaa8021[at]icloud.com77. Setenay Akduman Izmir Demokrasi University setenay.akduman[at]idu.edu.tr78. Sinem Benli Izmir Institute of Technology sinembenlii[at]gmail.com79. Sirin Atılgan Buyukasık Izmir Institute of Technology sirinatilgan[at]iyte.edu.tr80. Sirin Yılmaz Ege University sirinyilmaz123[at]gmail.com81. Sule Kılıcaslan Dokuz Eylul University kilicaslan.sule95[at]gmail.com82. Tayfur Barıskan Dokuz Eylul University tayfur bariskan[at]hotmail.com83. Tugba Yazan Izmir Institute of Technology tugbayazan[at]iyte.edu.tr84. Ulviye Busra Guven Izmir Ekonomi University busracinarguven[at]hotmail.com85. Yusuf Civan Suleyman Demirel University yusufcivan[at]sdu.edu.tr86. Zehra Cayic Izmir Institute of Technology zehracayic[at]iyte.edu.tr87. Zehra Tuncer Dokuz Eylul University zehratuncer48[at]gmail.com88. Zubeyir Turkoglu Dokuz Eylul University zubeyir.turkoglu[at]deu.edu.tr
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Committees of Izmir Mathematics Days II
Scientific Committee
1. Refail Alizade (Yasar University)2. Engin Buyukasık (Izmir Institute of Technology)3. Didem Coskan (Dokuz Eylul University)4. Selcuk Demir (Dokuz Eylul University)5. Emine Mısırlı (Ege University)6. Oktay Pashaev (Izmir Institute of Technology)7. Bayram Sahin (Ege University)8. Serap Topal (Ege University)9. Ergun Yalcın (Bilkent University)
10. Ahmet Yantır (Yasar University)
Organizing Committee
1. Munevver Pınar Eroglu (Dokuz Eylul University)2. Aslı Guclukan Ilhan (Dokuz Eylul University)3. Sabri Kaan Gurbuzer (Dokuz Eylul University)4. Celal Cem Sarıoglu (Dokuz Eylul University)
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