I. Kadın Matematik¸ciler Derne˘gi C ¸ alı¸stayı

02-04 Mayıs 2014

¨ ˙ US ¨ U, ¨ KOCAELI˙ GEBZE YUKSEK TEKNOLOJI˙ ENSTIT

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˙ cindekiler I¸ Davetli Konu¸smacılar Emel Bilgin . . . . . . Gonca Ayık . . . . . . G¨ ulnihal Meral . . . . Hatice Boylan . . . . . Meral Tosun . . . . . . M¨ uge Kanuni . . . . . M¨ unevver Tezer . . . . ¨ Oznur Ya¸sar Diner . . Selma Altınok Bhupal Sevin G¨ umg¨ um . . . . ¨ Sibel Ozkan . . . . . . Emine S¸ule Yazıcı . .

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Poster Sunumları Arife Aysun Karaaslan . . . Ay¸se Beler . . . . . . . . . Ayten Ko¸c . . . . . . . . . Bahar Korkmaz . . . . . . . Burcu G¨ ulmez Tem¨ ur . . . . Didem S¨ urgevil . . . . . . . Ece Yetkin . . . . . . . . . . Emel Aslankarayi˘git U˘gurlu Esra Dalan Yıldırım . . . . Ezgi Erdo˘gan . . . . . . . . Figen Kangalgil . . . . . . G¨ ul¸sen Ulucak . . . . . . . . Leyla I¸sık . . . . . . . . . . Neslihan Nesliye Pelen . . .

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¨ Nesrin Ozsoy . . . . ¨ Ozlem Ak G¨ um¨ u¸s . Semiha Emino˘glu . . Sibel Pa¸salı Atmaca . S¨ umeyye Bakım . . ¨ S¸ule Ayar Ozbal . . ¨ Ulk¨ u Dinlemez . . . Yasemin B¨ uy¨ uk¸colak Zeynep Fidan Ko¸cak

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Davetli Konu¸smacılar Emel Bilgin ¨ ˙ Galatasaray Universitesi, Istanbul [email protected]

Some invariants of surface singularities and Newton polyhedron Lojasiewicz exponent is a topological invariant for weighted homogeneous isolated singularities of complex surfaces. So far several estimates of the Lojasiewicz exponent are given for nondegenerate isolated singularities, together with exact formulas for some special cases. In this talk I will present an overview of these results. For this, I will focus on the properties of the Newton polyhedron of the singularity.Then I will give a bound for the Lojasiewicz exponent of some special singularities of surfaces with respect to the ideals in their local ring. This is a joint work with Meral Tosun and G¨ ulay Kaya.

Gonca Ayık ¨ C ¸ ukurova Universitesi, Adana [email protected]

D¨ on¨ u¸su ¨ mler Yarıgrubunda C ¸ arpanlara Ayırma ve Do˘ guray K¨ umeleri Bu konu¸smada ¨oncelikle Xn = {1, 2, . . . , n} k¨ umesi u ¨zerindeki t¨ um d¨on¨ u¸su ¨mler yarıgrubu Tn de patika-devirler (path-cycles) vasıtasıyla ¸carpanlara ayrılı¸s y¨ontemi verilecektir. Sn simetrik grup olmak u ¨zere, (2 ≤ m ≤ r ≤ n) sabit bir m ve r i¸cin sing¨ uler d¨on¨ u¸su ¨mler yarıgrubu Singn = Tn \ Sn nin (m, r)-patika-devirler tarafından do˘guruldu˘gu ispatlanmı¸stır. Ayrıca Singn nin min{|A| : hAi = STn ve A, (m, r)-patika-devirin bir k¨ umesidir } oldu˘gu g¨osterilcektir. Son olarak Singn nin ¸seklinde tanımlanan (m, r)-rankı nın n(n−1) 2 bo¸stan farklı bir A alt k¨ umesinin, Singn yi do˘guruyor olması i¸cin gerek ve yeter ko¸sullar verilecektir.

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G¨ ulnihal Meral ¨ B¨ ulent Ecevit Universitesi, Zonguldak [email protected]

˙ ˙ cin Matematiksel Modeller Kanser H¨ ucre Istilası I¸ Matematik her zaman geli¸sen bilimlerle sıkı bir ba˘g i¸cerisinde olmu¸stur. S¸u ¨phesiz biyomedikal uygulamalar ve bunlar arasında da metastasın ilk a¸saması olan kanser h¨ ucre istilası matemati˘gin en ilgi c¸ekici modern uygulamalarından biridir. Konu¸smamızda kanser h¨ ucre istilası ile ilgili matematiksel modelleri genel olarak inceledikten sonra ısı ¸sok proteinlerinin t¨ um¨or h¨ ucre g¨o¸cu ¨ndeki etki- sini inceleyen ¸cok o¨l¸cekli bir modele odakla˙ naca˘gız. Ilgili model ısı ¸sok protein dinami˘ginin etkilerini i¸ceren bir gecikmeli diferensiyel denklem ile birle¸stirilecek olan, kanser h¨ ucre yo˘gunlu˘gu, ekstrasel¨ uler matris ve matris a¸sındıcı enzim kon- santrasyonu i¸cin bir reaksiyon dif¨ uzyon denklemler sisteminden olu¸smaktadır. Ayrıca kar¸sılık gelen sistemin yerel varlık ve teklik ispatını ve istilanın beklenen davranı¸sını sergiledi˘gini g¨orece˘gimiz n¨ umerik sim¨ ulasyonları da inceleyece˘giz.

Hatice Boylan ˙ ¨ ˙ Istanbul Universitesi, Istanbul [email protected]

Representations of SL2 over maximal orders in a number field In various applications of automorphic forms it becomes crucial to know the finite dimensional representations of SL( 2, O), where O is a maximal order in a number field. There are amazingly open questions concerning these representations. But recently there has been some progress. In particular, we determined all linear characters of SL(2, O) and we applied the general theory of Weil representations of locally compact abelian groups invented by Weil to generate interesting family of representations of SL(2, O) which possibly contain all finite dimensional representations of SL(2, O) of finite image.

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Meral Tosun ¨ ˙ Galatasaray Universitesi, Istanbul [email protected]

Defining Equations, resolution Graphs and algebras This talk aims to describe the closed relation between singularities in algebraic geometry with graph theory and algebras. For this, we will first give some combinatorial properties of resolution graphs. Then we will present an algorithm to obtain the defining equations of a singularity from its resolution graph and relate this equations with some algebras.

M¨ uge Kanuni ¨ D¨ uzce Universitesi, D¨ uzce [email protected]

News from the Non-Commutative Ring Theory Research: Interdisciplinary study groups are in action... We will give a survey of the last 10 years of research done in a particular example of non-commutative rings flourishing from the fact that free modules over some noncommutative rings can have two bases with different cardinality. This would not have happened in vector spaces... :) Surprisingly enough not only non-commutative ring theorists, but also C*-algebraists gather together to advance the work done. The interplay between the topics stimulate interest and many proof techniques and tools are used from symbolic dynamics, ergodic theory, homology, K-theory and functional analysis. Open problem pages are put up and research schools are organized throughout the world. Over 100 papers have been published on this structure, so called Leavitt path algebras, which is constructed on a directed graph.

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M¨ unevver Tezer ¨ Ankara ODTU, [email protected]

Recent Developments and Applications of Numerical Analysis Modern numerical analysis does not seek exact answers because exact answers are often impossible to obtain or impractical in terms of computation. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors. Areas of numerical analysis vary from highly theoretical mathematical studies (developing numerical methods based on mathematical theories) to computer science issues (computer hardware and software) on the implementation of specific algorithms. Numerical analysis finds applications in engineering, physical sciences, social sciences, medicine and business. The numerical solution of mathematical models of these physical or social problems involves some combination of themes or mathematical problems to be solved approximately. These are numerical solution of systems of linear equations, numerical solution of systems of nonlinear equations, numerical solution of differential and integral equations, numerical solutions of eigenvalue or singular value problems, approximation of functions, evaluating integrals, interpolation, extrapolation, regression and optimization. Common concerns in numerical analysis are the studies of error bound and stability of computed approximate solution of the mathematical problem, and also the efficiency of the numerical algorithm used. This study gives, shortly the need for numerical computation first. The principle areas of numerical analysis for developing numerical methods in solving mathematical problems are summarized and recent important engineering and biomedical applications are presented.

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¨ Oznur Ya¸sar Diner ¨ ˙ Kadir Has Universitesi, Istanbul [email protected]

Kuratowski Type Theorems for Graphs with Fixed Edge Search Number Kuratowski’s theorem, from 1930, tells that a graph is planar whenever it does not contain a subdivision of neither the complete graph K5 nor the complete bipartite graph K3,3 . Later at 1936, Wegner showed that planar graphs forbid these two graphs as minors. These have led to general discussions on embeddings of graphs on surfaces and the possibility of bounding the number of graphs which must be forbidden as minors. One of the major results of the seminal Graph-Minor Project by Robertson and Seymour is that there are only a finite number of minor minimal graphs that must be forbidden for graphs invariants that are inherited by minors when the invariant has a fixed value. In this talk we characterize the forbidden minors for some graph families with a fixed edge search number.

Selma Altınok Bhupal ¨ Hacettepe Universitesi, Ankara [email protected]

Some problems in the theory of piecewise polynomial functions For a d-dimensional polyhedral complex ∆ embedded in Rn , we define C r (∆) to be the set of polynomials on ∆ that are continuously differentiable of order r. The elements of C r (∆) are also known as C r -splines. Such functions have been widely used in many areas, such as numerical approximations, finite element method for solving partial differential equations, computational geometry, computer-aided design and so on. In this respect, we want to talk about fundamental problems in spline theory.

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Sevin G¨ umg¨ um ˙ ¨ ˙ Izmir Ekonomi Universitesi, Izmir [email protected]

Numerical Simulation of Micropolar and Nano fluid flow in cavities by DRBEM This study presents the numerical investigation of unsteady mixed and natural convection in square cavities considering the effects of micro and nano fluids. The governing equations given in terms of stream function, vorticity, temperature and microrotation are solved by the Dual Boundary Element Method (DRBEM). The time derivative is approximated by an im- plicit Finite Difference Scheme (FDM) which enables to use considerably large time step. DRBEM discretizes only the boundary of the region and the resulting matrices contain integrals of logarithmic function or its nor- mal derivative. The convection terms and the unknown vorticity boundary conditions are approximated with the help of DRBEM coordinate matrix. Numerical solutions are obtained for several values of problem variables. Results are presented in terms of streamlines, isotherms, vorticity and mi- crorotation contours as well as the temperature and u-velocity variations at the mid-plane of the cavity.

¨ Sibel Ozkan Gebze Y¨ uksek Teknoloji Enstit¨ us¨ u, Kocaeli [email protected]

The Hamilton - Waterloo Problem with Uniform Cycle Sizes Decomposing graphs into edge-disjoint cycles is may be the most studied graph decomposition problem. If we add the condition that the cycles must be resolved into parallel classes, then this problem becomes a 2-factorization problem where each 2-factor is a parallel class of cycle(s). r A {Cm , Cns }-decomposition of the complete graph on v vertices, Kv , asks for a 2factorization of Kv , where r of the 2-factors consists of m-cycles, and s of the 2-factors consists of n-cycles. (For even v, it is a decomposition of Kv − F , where F is a 1-factor.) This is a case of the Hamilton-Waterloo Problem(the HWP) with uniform cycle sizes m and n. The HWP is an extension of the well-known Oberwolfach problem which asks for isomorphic 2-factors. Main focus of this talk will be on the HWP with uniform cycle sizes; some new results on the various lengths of cycles will be presented. 9

Emine S ¸ ule Yazıcı ¨ ˙ Ko¸c Universitesi, Istanbul [email protected]

A polynomial embedding of pairs of orthogonal partial latin squares Let N represent a set of n distinct elements. A non-empty subset P of N × N × N is said to be a partial latin square, of order n, if for all (x1 , x2 , x3 ), (y1 , y2 , y3 ) ∈ P and for all distinct i, j, k ∈ {1, 2, 3}, xi = yi and xj = yj implies xk = yk . If |P | = n2 , then we say that P is a latin square, of order n. Two partial latin squares P and Q, of the same order are said to be orthogonal if they have the same non-empty cells and for all r1 , c1 , r2 , c2 , x, y ∈ N {(r1 , c1 , x), (r2 , c2 , x)} ⊆ P implies {(r1 , c1 , y), (r2 , c2 , y)} 6⊆ Q. In 1960 Evans proved that a partial latin square of order n can always be embedded in some latin square of order t for every t ≥ 2n. In the same paper Evans raised the question as to whether a pair of finite partial latin squares which are orthogonal can be embedded in a pair of finite orthogonal latin squares. We show that a pair of orthogonal partial latin squares of order t can be embedded in a pair of orthogonal latin squares of order at most 16t4 and all orders greater than or equal to 48t4 . This is the first polynomial embedding result of its kind.

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Poster Sunumları Arife Aysun Karaaslan ¨ ˙ I¸sık Universitesi, Istanbul

˙ cin Giri¸s Zamanları Feigenbaum D¨ on¨ u¸su ¨ m¨ u I¸ Dinamik sistemler bilim dalı, kararlı sistemlerin zamana ba˘glılı˘gını tanımlayan bir bilim dalıdır. Bu ¸calı¸smamızda, dinamik sistemlerin bir par¸cası olan Feigenbaum d¨on¨ u¸su ¨m¨ u incelenmi¸stir. Ranklarda olu¸san aralıkların dı¸sında, Feigenbaum d¨on¨ u¸su ¨m¨ un¨ un sabit noktasının ¸cok yakınında bir nokta aldı˘gımızda; bu noktanın ranklarda bulunan t¨ um aralıklara ge¸ci¸s rotasyonu ara¸stırılmı¸stır.

Ay¸se Beler ¨ ˙ Dokuz Eyl¨ ul Universitesi, Izmir

Iterated Defect Correction with B-splines for Non-Linear Boundary Value Problems In this study, we consider the numerical solution to strongly nonlinear Boundary value problem. The application and the convergence behaviour of the iterated defect correction with B-spline polynomials are given by numerical results.

Ayten Ko¸c ˙ ¨ ˙ Istanbul K¨ ult¨ ur Universitesi, Istanbul

The Module Category of Leavitt and Cohn-Leavitt Path Algebras Leavitt and Cohn-Leavitt path algebras of a directed graph G are generated by the vertices and the arrows of G with relations (also determined by G) analogous to those of Cuntz-Krieger C∗-algebras. We study their representations, in particular we determine all finite dimensional representations. When G is finite, we give an effective algorithm to determine the existence of a finite dimensional representation.

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Bahar Korkmaz ¨ Eski¸sehir Anadolu Universitesi, Eski¸sehir

Q-Bernstein Polynomial on [a, b] Long after the introduction of q-Bersntein polynomials on [0, 1] by Phillips Ann. Num. Math. (1997), the paper by Simenov, Zafiris and Goldman Jat(2012) extended the q-Bernstein basis polynomials over arbitrary inerval. The main purpose of the latter work was to develop q-blossoming and subdivision techniques to generate q-Bezier curves. Based on this recent work we define one parameter family of q-Bernstein polynomials Bn(f ; [a; b]; q; x). It reduces the classical Bernstein polynomials when q = 1. We discuss convergence properties and find the degree of approximation by modulus of continuity for Bn(f ; [a; b]; q; x). Furthermore it is shown that if f is symmetric on the interval [−a; a], the corresponding q-Bernstein polynomials satisfy the property Bn(f ; [a; b]; q; x) = Bn(f ; [a; b]; 1/q; x).

Burcu G¨ ulmez Tem¨ ur ¨ Atılım Universitesi, Ankara

Fibre Products of Kummer Covers with Many Points ¨ This is a joint work with Ferruh Ozbudak. In this work, we study the general fibre products of Kummer covers over finite fields with many rational points. We will present examples of such curves over some finite fields.

Didem S¨ urgevil ¨ ˙ Ege Universitesi, Izmir

˙ ¨ G¨ u¸ cl¨ u Ranklanmi¸s Ikili Gruboidlerin T¨ urevleri Uzerine Bu ¸calı¸smada, g¨ u¸cl¨ u ranklanmı¸s ikili gruboidlerin t¨ urevleri tanımlanıp,¨ornekler ve bunlara ili¸skin ¨ozellikler verilmi¸stir.Ayrıca g¨ u¸cl¨ u ranklanmı¸s altsistemi tanımı verilip,ilgili t¨ urev altında de˘gi¸smez oldu˘gu g¨osterilmi¸stir.

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Ece Yetkin ¨ ˙ Marmara Universitesi, Istanbul

Generalizations of Primary Ideals in Commutative Rings In this study, we introduce the concept of 2-absorbing primary ideal of a commutative ring R which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary √ √ ideal of R if whenever a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I. Some results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are presented.

Emel Aslankarayi˘ git U˘ gurlu ¨ ˙ Marmara Universitesi, Istanbul

Nakayama Lemma for Multiplication Lattice Module In this study,we determine multiplicative lattice module with principal element. Also we define multiplication element in lattice and lattice module. Then we obtain a new characterization of multiplication lattice module. Consequently, we prove Nakayama Lemma for multiplication lattice module: Theorem (Nakayama Lemma): Let M be a non-zero multiplication P G-lattice L- module. Let a ∈ L such that for all maximal element q ∈ L, a ≤ q. Then a1M < 1M .

Esra Dalan Yıldırım ¨ ˙ Ya¸sar Universitesi, Izmir

Soft Grills and Soft Topological Spaces In 1999, Molodtsov introduced soft set theory accepted as a new mathematical approach to uncertainty. Afterwards, many researchers applied this theory to various problems in real life. Then, Shabir and Naz, having defined soft topological space concept, open a new direction for researchers. In this study, we introduced soft grill on soft set theory using the grill concept given by Choquet. We constructed soft topology τG by means of this definition. Also, we defined soft operator ΓG and investigated its basic properties.

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Ezgi Erdo˘ gan ¨ ˙ Marmara Universitesi, Istanbul

Bazı Dizi Uzaylarındaki Spektral Analiz Bu ¸calı¸smada, matris c¸arpımı ile elde edilmi¸s yeni bir W matris operat¨or¨ un¨ un bazı dizi uzaylarındaki spektral analizi ¸calı¸sılmı¸s ve spektrum k¨ umesi noktasal spektrum, s¨ urekli spektrum ve artık spektrum olarak sınıflandırılmı¸stır.

Figen Kangalgil ¨ Cumhuriyet Universitesi, Sivas

Travelling Wave Solutions of The Schamel-Korteweg-De Vries and The Schamel Equations The main aim of this paper is to demonstrate the reliability and efficiency of the extended (G/G) -expansion method. Hence, the method has been applied in order to obtain travelling wave solutions for the Schamel- Korteweg-de Vries (s- KdV) equation and the Schamel equation. The travelling wave solutios are exressed by the hyperbolic and the trigonometric functions.

G¨ ul¸sen Ulucak Gebze Y¨ uksek Teknoloji Enstit¨ us¨ u, Kocaeli

The Zariski Topology on L-module M In this study, we defined a base for the Zariski topology on σ(L) which is the set of all prime elements of a multiplicative lattice L and we investigate irreducible closed subset of σ(L). We prove thatσ(L) is a T0 -space, and max(L) = σ(L) with max(L) = {p ∈ σ(L)| p is maximal element} iff σ(L) is a T1 -space iff σ(L) is an R0 -space. Then we introduce a topology called the Zariski topology on σ(M ) which is the set of all prime elements of L-module M .

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Leyla I¸sık ¨ ˙ Sabancı Universitesi, Istanbul

On The Minimum Distance of Cycle Codes Estimation of the minimum distance of cyclic codes is a classical problem in coding theory. Using the trace representation of cyclic codes and Hilbert’s 90 Theorem, Wolfmann found a general estimate for the minimum distance of cyclic codes in terms of the number of the rational points on certain Artin-Schreier curves. In this talk, we present a variety of conditions, under which the Wolfmann bound can be improved by the use of permutation polynomials. This is a joint work with Cem G¨ uneri and Alev Topuzo˘glu.

Neslihan Nesliye Pelen ¨ Orta Do˘gu Teknik Universitesi, Ankara

Constantin’s Inequality for Nabla and Diamond-Alpha Derivatives Calculus for Dynamic Equations on Time Scales which offers a unification of discrete and continuous systems is a recently developed theory. Our main aim is to investigate Constantin’s Inequality on Time Scales that is an important tool used in determining some properties of various dynamic equations such as global existence,uniqueness and stability. In this talk, Constantin’s Inequality is investigated in particular for nabla and the diamond-alpha derivatives.

¨ Nesrin Ozsoy ¨ Adnan Menderes Universitesi, Aydın

Deyim ve Atas¨ ozlerimizde Kadınlarımız Anamız, avradımız, bacımız; kadınlarımız! Evinin kadını, c¸ocukların anası, i¸s kadını, bilim kadını olan kadınlarımız. . Deyimlerimizde, atas¨ozlerimizde kadının yeri, saygınlı˘gı, kadından beklenenler kısaca ne g¨ uzel anlatılmı¸stır. Genellikle ger¸cek anlamından az ¸cok ayrı bir anlamı olan, ilgi ¸cekici bir anlatımı bulunan, ifadeyi daha zengin kılan, iki veya daha fazla kelimeden meydana gelen, kalıpla¸smı¸s s¨oz topluluklarına ”deyim denir. (http://deyimler.bilgicik.com/deyim_ne_demektir.htm . 27 Nisan 2012 da bakıldı.) Uzun uzun anlatmak yerine kadının de˘geri ne g¨ uzel anlatılmı¸stır deyimlerimizde. 15

Cennet anaların aya˘gı altındadır, Ba¸sımızın tacı, evimizin dire˘gidir. A˘glarsa anam a˘glar gerisi yalan a˘glar. Kadına toplumun y¨ ukledi˘gi g¨orevlerde ¸s¨oyledir: Kadın dedi˘gin hamur yo˘gurur, c¸ocuk do˘gurur. Kadının karnından sıpayı, sırtından sopayı eksik etmeyeceksin. Kadın dedi˘gin koluna taktınmı yakı¸sacak, duvara vurunca yapı¸sacak. Kadın eksik etektir. Sa¸cı uzun aklı kısadır. Avradı eri saklar, peyniri deri. Erke˘gin okumu¸su kadı, kadının okumu¸su cadı olur. Erkek getirmeyi, kadın yetirmeyi bilmeli. Kadın aynı zamanda kurnaz ve akıllıdır. Kadının fendi erke˘gi yendi atas¨oz¨ un¨ u ¸cok duyarız. Avrat ev yapar avrat ev yıkar. Poster ¸calı¸smamızda deyim ve atas¨ozlerinde kadının yerini karikak¨ urlerle destekleyip sunmaya ¸calı¸saca˘gız.

¨ Ozlem Ak G¨ um¨ u¸s ¨ Adıyaman Universitesi, Adıyaman

Stability Analysis in Host Parasitoid Interaction We have investigated in this paper equilibrium points of host-parasitoid model. Also, the local stability of the equilibrium points is analyzed. The results are supported with numerical simulations.

Semiha Emino˘ glu ¨ ˙ Ege Universitesi, Izmir

¨ us¨ ¨ Minimum Tepe Ort¨ u Problemi Uzerine ¨ us¨ ¨ Minimum Tepe Ort¨ u Problemi Uzerine Bilgisayar bilimlerinde graflar yaygın bir veri yapısı modelidir. Bu c¸alı¸smada minimum tepe o¨rt¨ us¨ u problemi graflar u ¨zerinde modellenmi¸stir.Minimum Tepe o¨rt¨ us¨ u problemi ,polinomzamanda ¸c¨oz¨ ulemeyen bir problem olup NP-Tam sınıftandır.Minimum tepe o¨rt¨ us¨ u probleminin di˘ger Np-Tam prob¨ lemlerle ili¸skisi incelenmi¸stir.Ozellikle tepe o¨rt¨ u sayısı ve ba˘gımsızlık sayısı arasındaki ili¸ski u ¨zerinde durulmu¸stur.Ba˘gımsızlık sayısı i¸cin elde edilen sonu¸clar tepe ¨ort¨ u sayısı i¸cin de kullanılmı¸stır.Grafların kartezyen c¸arpımı ile olu¸san grafların ba˘gımsızlık sayısı sonu¸clarından hareketle , ikili a˘ga¸cların kartezyen ¸carpımı sonucu olu¸san grafların tepe o¨rt¨ u sayısı incelenmi¸stir.Bu grafların tepe ¨ort¨ u sayısını bulmak i¸cin greedy algoritması kullanılmı¸s ve greedy algoritmasının optimal sonucu garanti etmemesine ra˘gmen bu graflarda algoritmanın optimal sonuca ula¸stı˘gı g¨ozlenmi¸stir. Problemin ¸c¨oz¨ um¨ u i¸cin ilgili algoritmalar incelenmi¸s, ula¸sılan sonu¸clar irdelenmi¸stir. 16

Sibel Pa¸salı Atmaca ¨ Mu˘gla Sıtkı Ko¸cman Universitesi, Mu˘gla

Grid Discretization of Parametric Polyhedral Surfaces Polyhedral surfaces are piecewise linear approximation of smooth surfaces. Commonly they involve triangle mesh elements. However, most of studies have shown that mimetic discretization methods are more reliable with physical domain based problems and long time simulations. In this study we purpose a new method to find a non-uniform grid structure on a parametric polyhedral surface to construct mimetic methods. Also we demonstrate the metric tensor of a polyhedral surfaces respect to non-uniform grids.

S¨ umeyye Bakım ¨ Sel¸cuk Universitesi, Konya

Fibonacci Dizisi ve Altın Oranın M¨ uzikte Kullanımının ˙ Incelenmesi ˙ Orta¸ca˘g’ın en o¨nemli Italyan matematik¸cilerinden biri olan Leonardo Fibonacci (11701250) o¨zg¨ un bir teori geli¸stirmi¸stir. Fibonacci Dizisi veya Sayıları olarak anılan teorideki sayıların ve bunlara ba˘glı olarak olu¸san Altın Oran’ın do˘gal bilimler ve m¨ uzikte kullanıldı˘gına dair d¨ unyada bir¸cok ¸calı¸sma yapılmı¸stır. Fibonacci Dizisi ve Altın Oran’ın m¨ uzikteki varlı˘gına dair ¸calı¸smalar, Avrupa sanat m¨ uzi˘gi bestecilerinin eserlerinde bu sayıların kullanıldı˘gının kanıtlanmaya ¸calı¸sılması ¸seklindedir. Ancak bu ¸calı¸smaları yapanların ¸co˘gunlukla Fibonacci Dizisi ve Altın Oran’ın m¨ uzikteki varlı˘gını ba¸stan kabul ettikleri, do˘grudan bu sayıları bulmaya y¨oneldikleri ancak bu sayıların m¨ uzik kuramıyla o¨rt¨ u¸su ¨p ¨ort¨ u¸smedi˘gine bakmadıkları ve incelenen bestecilerin bu sayıları bilin¸cli olarak kullanıp kullanmadıklarını sorgulamadıkları g¨or¨ ulm¨ u¸st¨ ur. Bu durumlar Fibonacci Dizisi ve Altın Oran’ın m¨ uzikteki varlı˘gına ili¸skin bir problem ortaya ¸cıkarmı¸s, ilgili sayıların uluslararası m¨ uzik kuramına uymadı˘gı, dolayısıyla yapılan ¸calı¸smalarda hatalar oldu˘gu tespit edilmi¸stir. Bu ¸calı¸smada, Avrupa sanat m¨ uzi˘gi eserlerinde Fibonacci Dizisi ve Altın Oran’ın varlı˘gını ¸ce¸sitli y¨ontemlerle ifade eden kaynakların incelenmesi ve do˘grulu˘gunun tartı¸sılması ama¸clanmaktadır.

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¨ S ¸ ule Ayar Ozbal ¨ ˙ Ya¸sar Universitesi, Izmir

On Multipliers of Incline Algebras In this paper, we defined ∗ and + multipliers on an incline algebra and studied their properties on an incline algebra. We also investigate the properties of multipliers on an integral incline.

¨ u Dinlemez Ulk¨ ¨ Gazi Universitesi, Ankara

Global and Blow-up Solutions for A Nonlinear Hyperbolic Equations with Initial-Boundary Conditions In this paper, we consider an initial -boundary value problem to a nonlinear string equations with linear daming term. It is proved that under suitable conditions that the solution is global in time and the solution with a negative initial energy blows up in ¨ Onite time.

Yasemin B¨ uy¨ uk¸colak Gebze Y¨ uksek Teknoloji Enstit¨ us¨ u, Kocaeli

Canonical Induction for Trivial Sourse Rings A Mackey functor is an algebraic structure having operations which behave like the induction, restriction and conjugation mappings in representation theory. Such operations appear in a variety of diverse contexts such as G-algebras, Burnside rings, group cohomology, the algebraic K-theory of group rings and algebraic number theory. It is their widespread occurrence which motivates the study of such operations in abstract. We discuss the canonical induction formula for some special Mackey functors by following the construction of Boltje. For a Mackey functor M and a restriction subfunctor A ⊆ M , there is a surjective a map linG : A+ (G) → M (G)

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which is called the linearization homomorphism. Boltje constructed a map canG : M (G) → A+ (G) such that the composition canG linG is identity map on M . Making use of a natural correspondence between the Mackey algebra and the finite algebra spanned by the three kinds of basic bisets, namely the conjugation, restriction and induction, we investigate the canonical induction formula in terms of the theory of bisets. We concern with the trivial source rings and the canonical induction formula for them. The main aim is to get an explicit formula for the canonical induction of regular bimodules in the trivial source; Main Theorem: For a regular bimodule FG, we have X canG (FG) = [U, λU ]G U ≤G; U :p0 -group

P P where λU = |U | U ≤U 0 ≤G;U,U 0 :p0 -group |U10 | µ(U, U 0 )resU,U 0 ( ϕ∈Uˆ0 (F) ϕ). The reason of investigating the regular bimodules is that they are a step towards canonical induction on blocks. However unfortunately no general results are obtained about canonical induction of blocks yet.

Zeynep Fidan Ko¸cak ¨ Mu˘gla Sıtkı Ko¸cman Universitesi, Mu˘gla

Matematik E˘ gitiminde Annenin Rol¨ u Matematik, bilimde oldu˘gu kadar g¨ unl¨ uk ya¸sayı¸sımızdaki problemlerin ¸co¨z¨ ulmesinde kullandı˘gımız o¨nemli ara¸clardan biridir. Bu ifadedeki “problem” kelimesi sadece sayısal problemleri de˘gil, genel olarak “sorun” kelimesi ile adlandırdı˘gımız problemleri de kapsar (1). Bu ¨onem g¨oz o¨n¨ une alındı˘gında matemati˘gin hayatımızın her alanında etkili oldu˘gu a¸cık¸ca g¨or¨ ul¨ ur. Matematik o¨˘grenciler tarafından karma¸sık, olduk¸ca zor bir ders olarak nitelendirilir. Bu konuda ailelerin matemati˘ge kar¸sı tutumları o¨nemli bir etkendir. C ¸u ¨nk¨ u ¸cocuk ilk e˘gitimini aileden alır ve bu bilincin temelini olu¸sturacak ki¸si annedir. Bu ara¸stırmanın amacı matematik e˘gitiminde ¨og˘renme kalitesini arttırma adına ¸cocu˘gun gelecekte matematik ile ilgili sorunlarla kar¸sıla¸smaması i¸cin anne etkisinin varlı˘gını kanıtla¨ maktır. Ara¸stırma bilgi edinmeye y¨onelik Mu˘gla Sıtkı Ko¸cman Universitesi’nde tesad¨ ufen belirlenen o¨g˘renciler tarafından ger¸cekle¸stirilmi¸stir. 2013-2014 yılında bir anket aracılı˘gı ile 100 o¨˘grenciden veri toplanmı¸stır. Ankette matematik e˘gitiminde ailenin e˘gitim d¨ uzeyinin, ¸cevrenin, ya¸sam standartlarının ¸cocuk u ¨zerinde etkili olup olmadı˘gına ili¸skin sorulara yer verilmi¸stir. Verilerin analizinde SPSS 20 paket programı kullanılmı¸stır. 19

Program

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