I. Kadın Matematik¸ciler Derne˘gi C
¸ alı¸stayı
02-04 Mayıs 2014
¨
˙ US
¨ U,
¨ KOCAELI˙
GEBZE YUKSEK
TEKNOLOJI˙ ENSTIT
1
˙ 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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Program
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3
Davetli Konu¸smacılar
Emel Bilgin
¨
˙
Galatasaray Universitesi,
Istanbul
emel.bn@gmail.com
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
agonca@cu.edu.tr
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.
4
G¨
ulnihal Meral
¨
B¨
ulent Ecevit Universitesi,
Zonguldak
gulnihal.meral@beun.edu.tr
˙
˙ 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
hatice.boylan@gmail.com
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.
5
Meral Tosun
¨
˙
Galatasaray Universitesi,
Istanbul
mrltosun@gmail.com
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
mugekanuni@duzce.edu.tr
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.
6
M¨
unevver Tezer
¨ Ankara
ODTU,
munt@metu.edu.tr
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.
7
¨
Oznur
Ya¸sar Diner
¨
˙
Kadir Has Universitesi,
Istanbul
oznur.yasar@khas.edu.tr
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
sbhupal@hacettepe.edu.tr
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.
8
Sevin G¨
umg¨
um
˙
¨
˙
Izmir
Ekonomi Universitesi,
Izmir
sevin.gumgum@ieu.edu.tr
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
s.ozkan@gyte.edu.tr
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
eyazici@ku.edu.tr
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.
10
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.
11
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.
12
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.
13
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 .
14
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.
17
¨
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)
18
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
20
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