**ON THE STUDY OF THE WAVE EQUATION SET ON A SINGULAR CYLINDRICAL DOMAIN**

CHAOUCHI BELGACEM

In this work we give new regularity results of solution for the linear wave equation set in a nonsmooth cylindrical domain. Di§erent types of initial and boundary conditions are imposed on the boundary of the singular domain. Our study is performed in some particular anisotropic Hölder spaces.

Presenter: Chaouchi Belgacem

**A DITOPOLOGICAL FUZZY STRUCTURAL VIEW OF HUTTON SPACES**

FİLİZ YILDIZ

The notion of texture was introduced by L. M. Brown as a point-based set- ting for the study of complement-free mathematical concepts, besides crisp sets, fuzzy sets, L-valued sets and intuitionistic sets.

Following that, it was shown that the ditopological texture spaces do indeed provide a unified setting for the study of topologies on Hutton algebras (fuzzy lattices) on the one hand, and of bitopological and topological spaces on the other. In this talk we will be especially interested in the generalization of the notion of Hutton texture to include the non-complemented case and the notion of Hutton space to Hutton dispace by not postulating an order-reversing involution and replacing the topology with a ditopology. Thus, many of the point-free concepts defined in the category of ditopological texture spaces will go over to the category whose objects are Hutton dispaces via some equivalence functors.

Presenter: Filiz Yıldız

**NEIMARK-SACKER BIFURCATION ANALYSIS IN A DISCRETE BACTERIA POPULATION MODEL**

GÜVEN KAYA AND ŞENOL KARTAL

In this paper, a differential equation with piecewise constant arguments model that describes a population density of a bacteria species in a microcosm is considered. From the discretization process of a differential equation with piecewise constant arguments, we obtain two dimensional discrete dynamical system. By using the center manifold theorem and bifurcation theory, it is shown that the discrete dy- namical system undergoes Neimark-Sacker bifurcation. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for the discrete model.

Presenter: Güven Kaya

**AN IMPROVED HARDY-SOBOLEV INEQUALITY WITH SINGULAR WEIGHT AT THE BOUNDARY**

B. ABDELLAOUI, K. BIROUD, J. DAVILA, AND F. MAHMOUDI

Let Ω ⊂ RN be a bounded regular domain of RN and 1 < p < ∞. The paper is divided in two main parts. In the first part we prove the following improved Hardy Inequality for convex domains. (FORMULAS). The optimality of the exponent of the logarithmic term is also proved.

Presenter: Biroud Kheireddine

**ON RELIABILITY BOUNDS OF CONSECUTIVE k-OUT-OF-n:F SYSTEMS**

A. DEMİRALP, M.S. ŞIK

In this paper, we study reliability bounds of consecutive k-out-of-n:F systems.This system consists of n linearly or circularly ordered components {1,2,…,n}. The system is failed if at least k consecutive components fail and sometimes it is hard to determine exact reliability for such coherent system. So, several methods have been developed to determine the useful bounds of reliability. Thus, we compute the reliability bounds of the linear and circular consecutive k-out-of-n:F systems and the obtained results are given comparatively with graphs and tables.

Presenter: Ahmet Demiralp

**COMPONENT IMPORTANCE MEASURES: A NUMERICAL STUDY**

A. DEMİRALP, M. Ş. ŞIK, AND M. GÜNGÖR

System reliability is one of the most important topics in system design. In systems, some components are more important than the other components. So, various methods have been developed to measure the importance of components. In this study, some importance measures are investigated in the literature. and then this importance measures of component of coherent systems are computed with Monte- Carlo simulations. Finally, the obtained results of these methods are compared with the help of various graphs and tables.

Presenter: Ahmet Demiralp

**A SYNTHESIZED AHP-SPEARMAN MODEL FOR MENSURATION THE SEGREGATION OF PREFERENCES FOR PUBLIC TRANSPORT SYSTEM ENHANCEMENT**

SARBAST MOSLEM, SZABOLCS DULEBA

Latterly, a superior utilization of public transport can be a remedy to mitigate the traffic especially in big cities, thereby, to environmental, economic and public health problems. However, the alternatives for reclamation are myriad and in spite of this consensus of necessity, reclamation decisions are often censured by the public. Predominantly, a significant difference can be detected between planners’ and passengers’ notion about amelioration matter. The aim of this paper is to enumerate public demand for public bus transport improvement, by analyzing public bus transport supply quality criteria between planners and public in Mersin City, Turkey. As a methodology, a combined Analytic Hierarchy Process (AHP) and Spearman correlation technique have been applied in order to illuminate the chasms between planners and public.

Presenter: Sarbast Moslem

**IMPROVED HYBRID VECTOR SIMILARITY MEASURES AND THEIR APPLICATIONS ON TRAPEZOIDAL FUZZY MULTI NUMBERS**

MEMET ŞAHİN AND FATİH S. YILMAZ

In this study, we put forward some similarity measures for trapezoidal fuzzy multi numbers (tfmn) such as; hybrid vector similarity measure and weighted hybrid vector similarity measure. also we investigate the propositions of the similarity measures. Moreover, a multi-criteria decision-making method for TFMN is improved based on these given similarity measures. then, a practical example is shown to approve the feasibility of the new method. As a result, we compare the proposed method with the existing methods in order to show the effectiveness and efficiency of the developed method in this study.

Presenter: FatIh Süleyman Yılmaz

**IMPROVED JACCARD AND COSINE SIMILARITY MEASURES AND THEIR APPLICATIONS ON TRAPEZOIDAL FUZZY MULTI NUMBERS**

MEMET ŞAHİN, FATİH S. YILMAZ

In thIs study, we put forward some sImIlarIty measures for TrapezoIdal Fuzzy MultI Numbers (TFMN) such as; Jaccard sImIlarIty measure, weIghted Jaccard sImIlarIty measure, CosIne sImIlarIty measure, weIghted cosIne sImIlarIty measure. Also we InvestIgate the proposItIons of the sImIlarIty measures. Moreover, a multI-crIterIa decIsIon-makIng method for TFMN Is Improved based on these gIven sImIlarIty measures. Then, a practIcal example Is shown to approve the feasIbIlIty of the new method. As a result, we compare the proposed method wIth the exIstIng methods In order to show the effectIveness and effIcIency of the developed method In thIs study.

Presenter: Fatih Süleyman Yılmaz

**FROM YEAR TO YEAR RANKING OF SCHOOL SUCCESS WITH MULTI CRITERIA DECISION MAKING**

FERİDE TUĞRUL, BEYHAN YILMAZ, AND MEHMET ÇİTİL

In thIs study; success rankIng of schools has been researched In multI crIterIa decI- sIon makIng. The aIm of thIs study Is to proposed an applIcatIon of multI crIterIa decIsIon makIng In IntuItIonIstIc fuzzy sets. Also from year to year rankIng of school success has been determIned wIth multI crIterIa decIsIon makIng. Annual change of success of each school has been InvestIgated. For thIs paper have been bene_t-ted from sImIlarIty measure for IntuItIonIstIc fuzzy sets In multI crIterIa decIsIon makIng problem. By usIng thIs applIcatIon, It Is obtaIned very bene_cIal results In educatIon, decIsIon makIng and preference.

Presenter: Feride Tuğrul

**EXAMINATION OF THE RELATIONSHIP BETWEEN MATHEMATICS DEPARTMENT STUDENTS’ MATHEMATICS ANXIETY LEVELS AND THEIR ACADEMIC SELF-EFFICACY LEVELS**

MEHMET ÇİTİL, FERİDE TUĞRUL, SIDDIK DOĞRULUK, AND YALÇIN MUTLUAY

ThIs research concentrates on the relatIonshIp between mathematIcs anxIety levels of students who receIve mathematIcs educatIon at the Department of MathematIcs, Faculty of ScIence and Letters and theIr academIc self-e_cacy. The research has a relatIonal survey model. The populatIon of the study constItutes the students who receIve maths educatIon at the Department of MathematIcs, Faculty of ScIence and Letters at a state unIversIty located wIthIn the provInce of Kahramanmara_s durIng the sprIng semester of 2017 2018 academIc year. The research sample consIsts of 154 students who were selected by sImple random samplIng method. The study has deployed three data collectIon tools: The “Personal InformatIon Form” developed by the researchers, “MathematIcs AnxIety Scale” developed by BaI et al.(2009) and adapted to TurkIsh by Ak_cak_n, Cebesoy and _Inel (2015), and the AcademIc Self- e_cacy Scale” adapted by EkIcI (2012). The Personal InformatIon Form Includes questIons related to gender, class level, grade poInt average, department preference order, reasons for the preference of the department and job preference after graduatIon. BeIng a 5-poInt LIkert type scale, the MathematIcs AnxIety Scale contaIns 2 sub-scales and 14 Items. The Internal consIstency coe_cIent Cronbachs alpha relIabIlIty coe_cIent has been found to be 0:91 for the overall scale. Cronbach alpha values of the sub-scales are as follows: negatIve factors a = 0:90, posItIve factors a = 0:84. Cronbachs a assessIng the consIstency of the tool on responses from the valIdatIon sample for the total Item Is 0:83 In the present study. The relIabIlIty co-e_cIents are 0:79 for the posItIve subscale and 0:82 for the negatIve subscale. The AcademIc Self-e_cacy Scale Is a _ve-poInt LIkert-scale composed of 3 factors and 33 Items. Cronbachs alpha relIabIlIty coe_cIent of the scale has been determIned to be 0:86 for the overall scale. Cronbachs correlatIons of the factors were 0:88 for SocIal sItuatIons, 0:82 for CognItIve operatIons and 0:90 for TechnIcal skIlls. The Cronbach alpha values for the present study are as such: 0:92 for the overall scale, socIal sItuatIons a = 0:81, cognItIve operatIons a = 0:88 and technIcal skIlls a = 0:74. DescrIptIve statIstIcs, Independent samples t-test, one way analysIs of varIance (ANOVA), LDS sIgnI_cance test and Pearson product-moment correlatIon were used durIng the data analysIs. Research results have IndIcated that math anxIety levels of the students sIgnI_cantly dI_er across gender, class level, grade poInt average and job preference after graduatIon. However, no sIgnI_cant dI_erence has been IdentI_ed across department preference order and reasons for the preference of the department. A closer look at students academIc self-e_cacy IndIcates a statIstIcally sIgnI_cant dI_erence across gender, grade poInt average, reasons for the preference of the department and job preference after graduatIon. Students academIc self-e_cacy does not sIgnI_cantly vary In terms of class level and department preference order. The results have hIghlIghted that the students are neutral concernIng mathematIcs anxIety levels. It has also been determIned that they have partIally hIgher level of academIc self-e_cacy. BesIdes, a low level, negatIve andstatIstIcally sIgnI_cant relatIon has been found between students mathematIcs anxIety levels and theIr academIc self-e_cacy. In thIs regard, academIc self-e_cacy ofthe students Is expected to decrease provIded that theIr mathematIcs anxIety levels Increase. Based upon the research _ndIngs, varIous semInars and motIvatIonal actIvItIes may be organIzed for students wIth the aIm of reducIng theIr math anxIety levels and IncreasIng academIc self-e_cacy.

Presenter: Yalçın Mutluay

**COMPARABLE GRAPHS OF SUBMODULES**

ALİ ÖZTÜRK AND TAHİRE OZEN

Let R be an associative ring with identity and M be a right R-module. We define the comparable graph c(M) of M with all non-trivial submodules of M as vertices and two distinct vertices A;B are adjacent if and only if A < B or B < A. In this paper, we investigate the connectivity, completeness, girth, domination number, cut edges and bipartite of c(M). Moreover, we give connections between the graph-theoretic properties of c(M) and algebraic properties of M.

Presenter: Ali Öztürk

NYSTROM METHOD FOR THE NUMERICAL SOLUTION OF INTUITIONISTIC FUZZY DIFFERENTIAL EQUATIONS

BOUCHRA BEN AMMA, SAID MELLIANI AND LALLA SAADIA CHADLI

In this paper we present a numerical algorithm for solving intuitionistic fuzzy differential equations. We discuss in detail a numerical method based on Nyström method. The accuracy and efficiency of the proposed method is illustrated by solving an intuitionistic fuzzy initial value problem.

Presenter: Bouchra Ben Amma

**FUZZY BITOPOLOGICAL SPACES GENERATED BY FUZZY RELATION**

GÜZİDE ŞENEL

The concept of fuzzy topological space generated by a fuzzy relation is studied in. In 2013, bitopological spaces generated by binary relations is studied. In this work, I introduce fuzzy bitopological spaces generated by fuzzy relation as an extension of [4]. In case of a fuzzy bitopological space generated by a fuzzy relation. I have studied separation axioms T0 and T1.

Presenter: Güzide Şenel

**A NOTE ON SEPARATION AXIOMS IN DIFRAMES **

ESRA KORKMAZ AND RIZA ERTÜRK

Frame (locale) theory is an important research area, which translates the topo-logical concepts into the point-free language. It has many applications in topos theory, logic, non-commutative rings, and even in theoretical computer science. Diframes, on the other hand, were de_ned as a point-free generalizations of ditopo-logical texture spaces. In this work, we briey introduce the concept of diframe, and then de_ne the separation axioms in diframes. Presenter: Esra Korkmaz

Presenter: Esra Korkmaz

**THE RELATIONSHIP BETWEEN THE CATEGORIES OF ORDERED SETS, TOPOLOGICAL SPACES, METRIC SPACES AND APPROACH SPACES**

GÜZİDE ŞENEL

A common extension of topological spaces and metric spaces is named as approach spaces in 1989. If a topological space generate an approach space it is named topological one, otherwise, it is named a metric one. In this study, I search the relationship between approach spaces and metric spaces is comparable to that between topological spaces and ordered sets.

Presenter: Güzide Şenel

**MATHEMATICAL FUZZY MODEL TO STUDY THE EFFECT OF FISH CONSUMPTION ON CORONARY HEART DISEASE MORTALITY IN MOROCCO**

S.MELLIANI, O. CASTILLO, A. EL ALLAOUI, AND L. S. CHADLI

Abstract. The association between _sh consumption and Coronary Heart Disease (CHD) due to n – 3 polyunsaturated fatty acids, especially fatty, fish consumption may be responsible for protecting against death from CHD. The main contribution of the paper is to give an idea about the distribution of the number of people without CHD risk, with CHD risk, and the biomass of the _sh population in Moroccan coasts over the next six years from a fuzzy math-ematical model by dint of the uncertainty of data obtained by the statistics that can not be representative of a hundred percent of the entire population, all that to have the connection between the three previous factors. The math- ematical model is based on a fuzzy di_erential equations system. We use the concept of generalized di_erentiability and obtain graphical solutions for the problem under consideration and analyze the results obtained graphically.

Presenter: A. El Allaoui

**A NEW MULTI-STEP APPROACH BASED ON TOP ORDER METHODS (TOMS) FOR THE NUMERICAL INTEGRATION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS**

YOHANNA SANI AWARI , GEOFREY MICAH KUMLENG

This paper presents an entirely new approach to obtaining self-starting Top Order Methods (TOMs) which we shall called Extended Top Order Methods (ETOMs). ETOMs were obtained through hermite polynomial used as basis function. Stability analysis of the new approach shows a uniform order six method for k=3, they also possess very good absolute stability regions which made them highly suitable for the numerical integration of stiff ordinary differential equations. Implementation of the method in block form eliminates the need for starters and hence, generating simultaneously approximate solutions yi, i=1,2,..,6 on the go. To further observe the effect of the new approach, it was implemented on four numerical initial value problems of stiff ordinary differential equations occurring in real life and was shown to compete favorably with the work of existing scientists.

Presenter: Yohanna Sani Awari

**COUNTERFLOW WAVES IN A COMBUSTION MODEL**

FATİH ÖZBAĞ

We study combustion waves that occur when air is injected into a porous medium containing initially some solid fuel. We proved the existence of traveling waves for a system of three partial differential equations that give temperature, oxygen and fuel balance laws. In [1], the existence of various combustion waves was proved by using phase plane analysis under the assumption that the combustion wave velocity is positive. In [2] oxygen and heat are both transported at the same velocity and the existence of counterflow waves was proved. In this work, we assume that oxygen is transported faster than temperature, which is physically more realistic and we consider the negative combustion wave speed and prove the existence of counterflow combustion waves. We also identify all possible generic wave sequences that solve boundary value problems.

Presenter: Fatih Özbağ

**MINIMAL MODEL AS ADAMS COCOMPLETION**

SNIGDHA BHARATI CHOUDHURY AND A. BEHERA

Deleanu, Frei and Hilton, not only considered the idea of Adams, that is the Adams completion, in a more general framework, where it is possible to work with an arbitrary category and an arbitrary set of morphisms of the category, but also introduced the dual notion, Adams cocompletion. The concept of Adams com-pletion (cocompletion) is described very nicely through category of fractions using calculus of left (right) fractions. It may be noted that many algebraic and geometrical constructions in Algebra, Analysis, Topology, Algebraic Topology, Di_erential Topology, Di_erentiable Manifolds etc., can be viewed as Adams completions or co-completions of objects in suitable categories, with respect to carefully chosen sets of morphisms. In 1960, Sullivan proposed the concept of rational homotopy theory; this study depends only on the rational homotopy type of a space or the rational homotopy class of a map. In rational homotopy theory Sullivan introduced the idea of minimal model. This article is devoted to show how the minimal model of a 1-connected or simply connected di_erential graded algebra is characterized in terms of Adams cocompletion.

Presenter: Snigdha Bharati Choudhury

**F(root(m),2)-CONTINUED FRACTIONS & BEST-APPROXIMATIONS BY THEIR CONVERGENTS**

SEEMA KUSHWAHA

The Farey graph and certain subgraphs of the Farey graph are available in the literature. Also, there are continued fractions arising from these graphs, namely, semi-regular continued fractions, F1;2-continued fractions, F1;3-continued fractions, etc. Here, we de_ne a family of graphs, namely Fp m;2. Suppose m is a square free positive integer and …

Presenter: Seema Kushwaha

**EXISTENCE OF MINIMAL AND MAXIMAL SOLUTIONS FOR SECOND DIFFERENTIEL EQUATION WITH BOUNDARY CONDITIONS IN TIME-SCALES **

MOHAMMED DERHAB AND MOHAMMED NEHARI

The purpose of this work is the construction of minimal and maximal solutions for a class of second order quasilinear elliptic equation subject to nonlocal boundary conditions. More speci_cally, we consider the following nonlinear boundary value problem …

Presenter: Nehari Mohamed

**ON SCHUR’S AND BAER’S THEOREM FOR LIE SUPERALGEBRAS**

SAUDAMINI NAYAK

In 1904, I. Schur proved that for a group G if G/Z(G) is of _nite order than so is its commutator subgroup. Further a Lie algebra analogue to the result given by Moneyhun is, if L’ is finite dimensional Lie algebra than its derived subalgebra L0 is finite dimensional. Stitzinger and Turner have gave a strong Lie algebra version of Hegarty’s result which is some variation of the mentationed famous result due to Schur. Further Niroomand obtained converse of Schur’s thorem. Here we intend to give a Lie superalgebra analogue of the result of Stitzinger and Turner and as well as we extend the result of Niroomand as a converse of Schur’s result for Lie superalgebras. Further we give Lie superalgebra analogue of Baer’s theorem and its converse.

Presenter: Saudamini Nayak

**INTUITIONISTIC FUZZY UNIVERSAL ALGEBRAS WITH TRIANGULAR NORMS**

SINEM TARSUSLU(YILMAZ) AND GÖKHAN ÇUVALCIOĞLU

The new concept of an intuitionistic fuzzy universal algebra is introduced using t-norms and t-conorms. Some basic properties are proved. Intuitionistic fuzzy congruence relations with respect to t-norms and t-conorms on (T; S)-intuitionistic fuzzy universal algebra are examined.

Presenter: Sinem Tarsuslu (Yılmaz)

**SOLVABILITY OF A QUADRATIC INTEGRAL EQUATION OF FREDHOLM TYPE VIA A MODIFIED ARGUMENT **

MERVE TEMIZER ERSOY AND HASAN FURKAN

In this study, we demonstrate the existence of solutions of a quadratic integral equation of Fredholm type with a modi_ed argument. Our solutions are placed in the spaces of functions satisfying the Holder condition and this is a part of the originality of the paper. For our study, we use a recent result about the relative compactness in Holder spaces and the classical Schauder _xed point theorem.

Presenter: Merve Temizer Ersoy

**A NOTE ON TOPOLOGICAL PROPERTIES IN SEQUENCE SPACES**

MERVE TEMIZER ERSOY, HASAN FURKAN, AND BiLAL ALTAY

In this work, we study some new spaces to obtain new type duality of a sequence space _ related to the some sequence spaces. Beforehand, we obtain some new distinguished subspaces of a FK space. Furthermore, we give some structural theorems and inclusions for these distinguished subspaces. These theorems are important to two decades the duality of a sequence space in summability theory and topological sequence spaces theory. We give properties of some special sequence space, which play an important role in the rest of the study, and also in developing duality properties.

Presenter: Merve Temizer Ersoy

**MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC SINGULAR EQUATIONS WITH CRITICAL EXPONENT**

ATIKA MATALLAH

This work deals with the existence and multiplicity of solutions to the following problem …

Presenter: Atika Matallah

**BIPOLAR SOFT TOPOLOGICAL SPACES**

TAHA YASİN ÖZTÜRK, ÇİĞDEM GÜNDÜZ ARAS

In this present study, some properties of bipolar soft closed sets are introduced and the concept of closure, interior, basis and subspaces which are the building blocks of classical topology are defined on bipolar soft topological spaces. In addition, examples have been presented so that the subject can be better understood.

Presenter: Taha Yasin Öztürk

**SOFT MAPPINGS ON SOFT GENERALIZED TOPOLOGICAL SPACES**

TAHA YASİN ÖZTÜRK, ÇİĞDEM GÜNDÜZ ARAS

In the present paper, we introduce g-open soft mapping, g-closed soft mapping, g-pseudoopen soft mapping, g-quotient soft mapping on soft generalized topological spaces. Furthermore, we discuss some characterizations and some applications of them.

Presenter: Taha Yasin Öztürk

**ON SOME DISTANCE-BASED TOPOLOGICAL INDICES OF TOTAL GRAPH OF Zn**

N. FEYZA YALÇIN

In recent years, many research articles have been published on graphs over rings, especially commutative rings. Anderson and Badawi introduced the total graph of a commutative ring. Topological indices of graphs are graph invariants that are mostly related to connectivity, degree and distance. Several topological indices of total graph of Zn are computed. In this study, we consider the total graph of Zn for n is even and n ¹2^alpha . We compute the Schultz, Gutman, eccentric connectivity and edge eccentric connectivity indices of the total graph of Zn.

Presenter: N. Feyza Yalçın

**Q TENSOR ON SASAKIAN MANIFOLDS**

HÜLYA BAĞDATLI YILMAZ

The object of present work is to study Sasakian manifolds satisfying certain conditions on Q tensor whose trace is the well-known Z tensor.

Presenter: Hülya Bağdatlı Yılmaz

**INTUITIONISTIC (T,S)-L FUZZY RINGS**

ÜMİT DENİZ

This study is built on the definition of intuitionistic L-fuzzy rings and ideals. Many researchers have used the definition of K. Atanassov’s intuitionistic fuzzy setsto move the definitions in classical algebra to intuitionistic fuzzy algebra. WhenK. Atannassov gave the definition of intuitionistic fuzzy sets he used the closed interval [0,1]. Then K. Meena and K.V. Thomas replaced the closed interval [0,1] with L-lattice. In that study they used ^ -infimum and max -supremum operations to give the intuitionistic L-fuzzy rings and intuitionistic L-fuzzy ideals. In this study we replace ^ -infimum with triangular norms and we replace max -supremum with triangular conorms and give the definition of intuitionistic (T,C)-L fuzzy rings and ideals. By using this definitions we move some definition and theorems in classical algebra to intuitionistic fuzzy algebra.

Presenter: Ümit Deniz

**FIXED POINTS THEOREM FOR WEAK COMPATIBLE MULTI-VALUED MAPPINGS IN Gp-METRIC SPACES **

SEHER SULTAN SEPET AND CAFER AYDN

Recently, Nadler [1], introduced the notion of multi-valued contraction mapping and proved well known Banach contraction principle. Aydi at al., [2] proved the Banach type _xed point results for set valued mapping in complete metric spaces (see [3, 4] and references therein). Zand and Nezhad [5], introduced a new generalized metric spaces Gp which as a both generalization of the partial metric space and G metric spaces. We present an extension of the notion of f-weak compatibility of Pathak [6]on metric space in generalization of partial metric space.

Presenter: Seher Sultan Sepet

**A FIXED POINT THEOREM FOR theta-CONTRACTIVITY IN Gp-METRIC SPACES**

SEHER SULTAN SEPET AND CAFER AYDIN

Recently, Jleli and Samet [1] introduced a new type of contractive mappings. Jleli and Samet called it as *theta*-contraction and proved a _xed point theorem for mappings of this type for which the Banach contraction principle and some other known contractive conditions in the literature can be obtained as special cases. Zand and Nezhad [2], introduced a new generalized metric spaces Gp which as a both generalization of the partial metric space and G metric spaces. Some of these works may be noted in [3, 4, 5]. We present an extension of the notion of *theta*-contraction of Jleli and Samet [1] in generalization of partial metric space.

Presenter: Seher Sultan Sepet

**DEVELOPABLE SURFACES AND TIMELIKE CLAD HELICES IN MINKOWSKI 3-SPACE**

S. KAYA, O. ATEŞ, İ.GÖK AND Y. YAYLI

Developable surfaces are ruled surfaces and have vanishing Gaussian curvature on the regular part. In this paper we consider geodesics on the tangent developable surface associated to a space curve. We will give the relationship between the space curve and geodesic curve of tangent developable surface. Then we will show that the principal normal Darboux developable surface of the curve is a *gamma*-conical surface if and only if is a time like clad helix.

Presenter: Seher Kaya

**FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)****–****STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS**

SEDA KILINÇ , ABDULLAH AKKURT, AND HÜSEYIN YILDIRIM

In this study; Hadamard and Fejer Hadamard inequalities for (h -m)-strongly convex functions via generalizeed fractional integral operators involving the generalized Mittag-Leffer function are established. In particular several knows results are mentioned.

Presenter: Seda Kılınç

**ON FUZZY phi-PRIME IDEALS**

ZAMANI NASER

Let R be a commutative ring with identity. Let FI(R) be the set of all fuzzy ideals of R and *phi* : FI(R) –> FI(R)U{0R} be a function. We introduce the concept of fuzzy *phi*-prime ideals. Some relationships between fuzzy *phi*-prime ideals and prime ideals of R will be investigated. We find conditions under which fuzzy *phi*-primness gives primness and vice versa. Also, the behaviour of this concept in rings product will be studied.

Presenter: Naser Zamani

**MISCONCEPTIONS AND ERROR ANALYSIS OF 10TH GRADE STUDENTS ON ANALYTICAL GEOMETRY**

A. ÖZKAN AND E. M. ÖZKAN

The purpose of this research is to determine the relationship between the misconceptions of errors and concepts about analytical geometry, the attitudes of students towards analytic geometry, and the misconceptions of analytical geometry in order to overcome the object misconceptions. In the first stage, an open-ended exam was applied to 2552 tenth-grade students studying at 19 high schools under stanbul Provincial Directorate of National Education and 299 students from two high schools were tested in the second stage and 10 students were interviewed in the last stage in the academic year of 2016-2017. Errors and misconceptions of the students in the questions covering the analytic geometry were examined. At the end, it was concluded that knowledge levels, errors and misconceptions of students in the analytic geometry should be identified to use proper instructional strategies. It is necessary to design diferent activities to improve the levels of students who cannot comprehend the analytic geometry on the level of their classrooms. This will ensure that the whole classroom achieves the same comprehension level. A decrease in errors and misconceptions will be observed and misconceptions will be identified more easily.

Presenter: Ayten Özkan

**SOLUTIONS FOR ELLIPTIC SINGULAR EQUATIONS WITH CRITICAL HARDY-SOBOLEV EXPONENT**

ATIKA MATALLAH

This work deals with the existence and multiplicity of solutions to the following problem … EQ ..

Where … eq …Here denotes space obtained as the completion of the space ( with the standard norm … EQ ..

Problem is related to the following well known Caffarelli-Kohn-Nirenberg inequality there is a positive constant such that … EQ …

If we take in relation (1.1) we obtain the following Hardy inequality type: … EQ …

In the space we employ the following norm for … EQ …

Presenter: Atika Matallah

**A WORK ON SET-INDEXER OF REGULAR DIAGRAM OF KNOTS**

TUĞÇE KUNDURACI, TAMER UĞUR and CEREN SULTAN ELMALI

A knot is defined by an embedding of a circle S1 to 3-dimension Euclidean space R3 or S3. Regular diagram of a knot is obtained from knot by pojecting to R2. In this study, a set-indexer is associated with the regular diagram of knots using the set-indexer definition of Acharya.

Presenter: Tuğçe Kunduracı

**ON THE FINE SPECTRUM OF THE UPPER TRIANGULAR BAND MATRIX OVER THE HAHN SEQUENCE SPACE**

NUH DURNA

In this study, we will calculate the point spectrum, the continuous spectrum, and the residual spectrum of the upper triangular band matrix over the Hahn sequence space. Hahn introduced in [1] the Hahn space h of all sequence x = (xk) …

Presenter: Nuh Durna

**A CERTAIN CLASS OF SURFACES ON PRODUCT TIME SCALES WITH INTERPRETATIONS FROM ECONOMICS**

E. YILMAZ, M. EVREN AYDIN, AND T. GULSEN

In this study, we consider a graph surface associated to Cobb-Douglas production function in economics on product time scales. We classify this surface based on the atness and minimality properties for several product time scales. Then, we interpret the obtained results from the perspective of production theory in economics. Therefore, we extend the known results in Euclidean geometry by considering time scale calculus.

Presenter: Emrah Yılmaz

**SOME RESULTS ABOUT SUBMAXIMAL SPACES, WEAKLY SUBMAXIMAL SPACES AND FAN-GOTTESMAN COMPACTIFICATION**

CEREN SULTAN ELMALI, TAMER UĞUR

A compactification of a topological space is a compact space that contains as a dense subspace. It is known that different compactification methods are applied to different spaces such as Alexandroff compactification, Stone-Cech compactification and Wallman compactification, Fan-Gottesman compactification. We studied with Fan-Gottesman compactification. In this paper, we characterize that Fan-Gottesman compactification of regular space is weakly submaximal. Also, we investigate a necessary and sufficient condition on regular spaces to obtaintheir Fan-Gottesman compactification D-spaces.

Presenter: Ceren Sultan Elmalı

**H-GROUP STRUCTURE ON INTUITIONISTIC FUZZY TOPOLOGICAL SPACE**

SIBEL DEMIRALP AND GÜLNUR HAÇAT

The fuzzy set teory was first introduced by Zadeh in [7]. A fuzzy set over X is a function _A : X –>[0; 1] ; where mA(x) describes the membership of x to the set A C X: Atanassov [1] defined the concept of the intuitionistic fuzzy set as a generalization of the fuzzy set. An intuitionistic fuzzy set is characterized by two fuzzy sets (mA;n A) ; where mA(x) and nA(x) describe the membership and non-membership of x to the set A C X; respectively. Afterwards, concepts of algebraic topology have been extended to intuitionistic fuzzy topological spaces. Homotopy theory is one of the main areas of algebraic topology. Intuitionistic fuzzy homotopy theory was described by Çitil and Çuvalcıoğlu in [2]. Padmapriya [6] defined the intuitionistic fuzzy topological group. In this talk, we study some properties of the pointed intuitionistic fuzzy topological spaces. Then intuitionistic fuzzy loop spaces are investigated. Finally, it is shown that an intuitionistic fuzzy loop space is an H-group.

Presenter: Gülnur Haçat

**K-DEFORMATION RETRACT OF A DIGITAL H-SPACE**

SIBEL DEMIRALP AND GÜLNUR HAÇAT

The purpose of digital topolgy is to study the topological properties of discrete objects, such as compactness, connectedness. The concept of digital topology was .rst de.ned in [8]. Afterwards many researchers studied the digital versions of some concepts of algebraic topology. Digital homotopy and digital fundamental group are de.ned in [7]. Digital H-space is de.ned in [4]. In this talk, we investigate some properties of digital H-spaces and digital H-groups. We prove that a k-deformation retract of an abelian digital H-group is itself a digital H-group. Also we show that there is a functor from the homotopy category of digital H-groups and digital H-homomorphisms to the category of groups and homomorphisms. Thus we provide a transition between digital topolgy and classical topology.

Presenter: Gülnur Haçat

**I-STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES DEFINED BY WEIGHT FUNCTIONS IN A LOCALLY SOLID RIESZ SPACE**

ŞÜKRAN KONCA, ERGIN GENÇ AND MEHMET KÜÇÜKASLAN

Abstract. In this work, our aim is to introduce the concepts of I-statistical convergence and I-lacunary statistical convergence of double sequences defined by weight functions in a locally solid Riesz space, based on the notion of the ideal of subsets of N x N. We also examine some inclusion relations of these concepts.

Presenter: Şükran Konca

**CURVATURE TENSOR OF SCREEN SEMI-INVARYANT HALF-LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN PRODUCT MANIFOLD WITH QUARTER-SYMMETRIC CONNECTION**

OGUZHAN BAHADIR

In this paper, we study curvature tensor half-lightlike submanifolds of a semi-Riemannian product manifold. We introduce a classes half-lightlike submanifolds of called screen semi-invariant half-lightlike submanifolds. We de_ned some special distribution of screen semi-invariant half-lightlike submanifold. We get Curvature tensor and Ricci tensor with respect quarter-symmetric non-metric connection.

Presenter: Oğuzhan Bahadır

**IMPROVEMENT OF SHUM AND WEI PROXY SIGNATURE USING RSA ALGORITHM**

S. EZZIRI AND O. KHADIR

A proxy signature scheme allows a selected person, the proxy signer, to sign documents on behalf of the original signer. It is a useful tool in many areas. For example, a manager of a company can delegate his signing rights to a proxy agent when he go for a trip. In 2003, Shum and Wei suggested a proxy signature method which is developed to safeguard the proxy signer’s identity using an alias. But the insecurity of the scheme was noticed by Sun and Hsieh. To avoid the mentioned attack, in this paper we propose an improvement of Shum and Wei proxy signature using RSA algorithm, and we study its security and complexity.

Presenter: Ezziri Salma

**A WORK ON SET-INDEXER OF REGULAR DIAGRAM OF KNOTS**

TUĞÇE KUNDURACI, TAMER UĞUR AND CEREN SULTAN ELMALI

A knot is defined by an embedding of a circle to 3-dimension Euclidean space (or ). Regular diagram of a knot is obtained from knot by pojecting to . In this study, a set-indexer is associated with the regular diagram of knots using the set-indexer definition of Acharya.

Presenter: Tuğçe Kunduracı

**NUMERICAL SOLUTION FOR THE FRACTIONAL ORDER LINEAR DIFFERENTIAL EQUATIONS USING HERMITE COLLOCATION METHOD**

AYŞEGÜL KAPLAN AND MULLA VELİ ABLAY

In this paper, the fractional order linear di_erential equations are solved by using the Hermite Collocation Method (HCM). To illustrate the accuracy of the method, two fractional order linear di_erential equations with variable and constant coefficients are studied. Obtained results are compared with some earlier works. It is seen that the method is very eficient and reliable due to obtained numerical results are satisfactorily.

Presenter: Mulla Veli Ablay

**A NOTE ON MAHARAM OPERATORS**

Ö. GÖK AND F. ÖZTÜRK ÇELİKER

In this work, we are interested in the Maharam operators on the Banach f-modules over the Archimedian f-algebras. We investigated the properties of Maharam operators on dual Banach f-modules.

Presenter: Fatma Öztürk Çeliker

**INEXTENSIBLE FLOWS OF CURVES ACCORDING TO SABBAN FRAME IN GALILEAN SPACE G3**

HÜLYA GÜN BOZOK

In this paper inextensible ows of curves in 3-dimensional Galilean space is researched. Firstly Sabban frame is defined in 3-dimensional Galilean space, then necessary and suficient conditions for inextensible ows of curves with Sabban frame in 3-dimensional Galilean space are given. Also inextensible curve flow are expressed as a partial differential equation involving geodesic curvature according to this frame.

Presenter: Hülya Gün Bozok

**INTEGRAL EQUATIONS FOR THE STURM-LIOUVILLE FUZZY PROBLEM WITH THE EIGENVALUE PARAMETER IN THE BOUNDARY CONDITION**

HÜLYA GÜLTEKİN ÇİTİL

In this paper is studied the Sturm-Liouville fuzzy problem with the eigenvalue parameter in the boundary condition. The eigenvalues and the eigenfunctions of the worked problem is examined and integral equations of the problem are found. In this study, Hukuhara differentiability is used.

Presenter: Hülya Gültekin Çitil

**A BILINEAR DISCRETIZATION OF THE MOTION OF A RIGID BODY IN AN IDEAL FLUID**

MURAT TURHAN

The Clebsch system is one of the few classical examples of rigid bodies in an ideal uid whose equations of motion are known to be integrable and given by the following system: … eq … (1)where H Î C¥(R6;R) is a quadratic polynomial in x and p. Applying bilinear method and using the gauge invariance and the time reversibility of the equations, we get gauge-invariant bilinear difference equations. Finally, we derive the explicit discrete system by considering bilinear transformation method and present sufficient number of the discrete conserved quantities for integrability. Bilinear discreteziaton leads to the discovery of four independent integrals, namely conserved quantities, of motion of the discrete-time system, which turn out to be much more complicated than the integrals of the continuous-time system.

Presenter: Murat Turhan

**ON THE ANALYZE OF THE SPECTRUM OF A STURM-LIOUVILLE PROBLEM (poster)**

OYA BAYKAL ÜNAL

After the Gelfand and Levitans colloborated work for the investigation of spectrum for the problems with di_erential operator of second order, it is observed that the importance of spectrum and trace of the self-adjoint operator L in Hilbert space H. Concerning these developments, we study the analyse of the spectrum of the boundary value problem S-L of second order in L2(H : [0; 1]) where H is a separable Hilbert space.

Presenter: Oya Baykal Ünal

**A NOTE ON DECOMPOSABILITY THEOREMS**

Ö .GÖK AND P. ALBAYRAK

In this work, we investigate the invariant closed ideals in a Banach lattice and also study the compressionally decomposability.

Presenter: Pınar Albayrak

**(k; n)-CLOSED SUBMODULE OF A MODULE OVER A COMMUTATIVE RING**

ECE YETKİN CELİKEL

In this paper the concepts of semi n-absorbing and (k,n)-closed submodules of modules over commutative rings are introduced and their basic properties are investigated. Also some characterizations in some special modules are obtained.

Presenter: Ece Yetkin Çelikel

**A CHARACTERIZATION FOR GENERIC SEMI-INVARIANT PRODUCT OF SASAKIAN MANIFOLD**

HALİL İBRAHIM YOLDAŞ, ŞEMSI EKEN MERIC AND EROL YAŞAR

In this paper, we deal with generic semi-invariant product of a Sasakian manifold admitting concurrent vector _eld. Here, we give a characterization about Ricci soliton in generic semi-invariant product. Also, we show the necessary conditions for a Ricci soliton on the invariant distribution D to be a gradient Ricci soliton.

Presenter: Halil İbrahim Yoldaş

**STATISTICAL CONVERGENCE OF PARANORMED FUNCTIONS ON TIME SCALES**

T. GÜLŞEN, E. YILMAZ, H. KOYUNBAKAN AND Y. ALTIN

In this study, we define paranormed statistical convergence and lambda- paranormed statistical convergence on an arbitrary time scale. Furthermore, we study on strongly lambda_p Cesaro summabilty on paranormed time scale. Finally, some inclusion theorems are proved.

Presenter: Emrah Yılmaz

**SIMPSON TYPE INTEGRAL INEQUALITIES FOR R-CONVEX FUNCTION**

MUSTAFA KARAGÖZLÜ AND MERVE AVCI ARDIÇ

In this paper, we established new integral inequalities of Simpson type for -convex functions via two integral identities.

Presenter: Mustafa Karagözlü

**GRADED CLASSICAL 2-ABSORBING SUBMODULES**

KHALDOUN AL-ZOUBI

The scope of this presentation is devoted to the theory of graded modules over graded commutative rings. In particular, we are dealing with graded classical 2-

absorbing submodules of graded modules over graded commutative rings. The notion of graded 2-absorbing ideals as a generalization of graded prime ideals was introduced and studied in [2, 8]. The notion of graded 2-absorbing ideals was extended to graded 2-absorbing submodules in [1]. The notion of graded classical prime submodules as a generalization of graded prime submodules was introduced in [7] and studied in [6]. Recently, In [3], the authors introduced and studied the concept of graded classical 2-absorbing submodules as a generalization of graded classical prime submodules. In this talk, some special topics in graded modules like graded classical prime submodules, graded classical 2-absorbing submodules will be presented. Some accepted results in [3] will also highlighted.

Presenter: Khaldoun Al-Zoubi

**ANALYSIS OF INBOUND AIR TRAFFIC AT IGI AIRPORT USING STOCHASTIC MODELING**

DARSHAN GOLGHATE

In the Air Traffic Management (ATM) context it is natural to couple a PSRA(Pre- Scheduled Random Arrivals) arrival process with a deterministic service process with expected service rate . The queue of this model is then a well-defined, continuous- time stochastic process. Associated to this process we can consider the embedded chain, i.e., the length of the queue at the service epochs. The actual stream of arrivals (ATA) rises from the action of random delays and thinning on a deterministic schedule (ETA). We calculate being the rate of arrival and the traffic load as .We then run simulations to check which case matches our database. For the Heathrow Airport best case was the stationary output of a queuing model with PSRA-like arrivals and a service time modeled as a triangular random variable, with mean 1/ and mode 0.8/ .Through further analysis I will be able to obtain the logic diagram with right number of servers and reduced number of entry through PSRA Stream.

Presenter: Darshan Golghate

**ON THE SIGMA INDEX OF MONOGENIC SEMIGROUP GRAPHS**

NIHAT AKGÜNEŞ AND YAŞAR NACAROĞLU

Das, Akgüneş and Cevik considered the monogenic semi group SM with zero having {0, x, x^2, … ,x^n }. Also they de_ned (undirected) graph sigma(SM) associated with SM whose vertices are the non-zero elements x, x^2, … ,x^n and any two di_erent vertices xi and xj are adjacent if i+j > n (for 1£ i; j £ n). Additionally lot of researcher studied over that important algebraic graph. In this paper we calculated sigma index of any monogenic semigroup graphs sigma(SM).

Presenter: Nihat Akgüneş

**A CHARACTERIZATION OF h-STRONGLY POROUS SUBSETS OF R**

M. ALTINOK AND M. KÜÇÜKASLAN

In this study, we define a new h-nu-strong porosity at 0 with respect to ~ = fngn2N, n 2 R for all n 2 N, for subsets of real numbers. Then we give a characterization for h-strongly porous subsets of real numbers by using this new h-nu-strongly porosity.

Presenter: Maya Altınok

**A STUDY OF CAUSTIC CURVES **

F. ATEŞ AND N. EKMEKCI

The curve is considered as a mirror and a point as a light source on the Euclidean sphere S2. The light rays, emitted from a point light source, reected by this mirror curve form a curve called as spherical orthotomic curve. This curve has an envelop and this envelope is called caustic curve of the given mirror curve. In this study, we give a mathematical formula of these curves and examine the singularities of these curves by using the Sabban frame apparatus. At the end of this study, we give visual examples of these curves on S2 by using the Mathematica program.

Presenter: Fatma Ateş

**WC* PARTNER CURVES IN THE EUCLIDEAN 3****-SPACE**

AYKUT HAS AND BEYHAN YILMAZ

In this study firstly, fT;N;Bg Frenet frame and fN;C;Wg alternative frame have been introduced. Later, a new type of special curve couple have defined called WC*-partner curves and characterizations have given for these curves according to alternative moving frame.

Presenter: Aykut Has

**ON FILTER-TYPE SOFT SETS**

MUSTAFA BURÇ KANDEMİR

In this paper, we have established filter-type soft sets and studied its basic structural properties. Besides, we give a decision-making method using filter-type soft sets in a decision-making process in any topological universe.

Presenter: Mustafa Burç Kandemir

**GENERALIZED METRIC SPACES AND FIXED POINT THEOREMS **

İBRAHİM KARAHAN AND İRFAN IŞIK

The present study aims to deal with famous fixed point theorems on generalized metric spaces. In this study we give definitions of some generalized metric spaces such as b-metric, rectangular, rectangular b-metric, b_v{s} and so on and state some fixed point theorems proved on these spaces. Also, we introduce new generalized metric spaces and generalize some famous fixed point theorems to our generalized metric spaces.

Presenter: İbrahim Karahan

**DOUBLE DEFERRED f-STATISTICAL CONVERGENCE OF ORDER ****a**

Ş SEZGEK AND İ. DAĞADUR

In this study, we define the concept of double deferred f-density of order a that is a generalization of f-density, where f is an unbounded modulus. We examine some similarities and differences between the concept of double deferred f-density of order a and the well-known notions. Also, we define the double deferred f-statistical convergence of order a for any double sequence and double deferred Cesaro summability with respect to modulus of order a. Moreover, we have investigated the relationship between the two concepts and give some characterizations.

Presenter: Şeyda Sezgek

**ON THE NUMBER OF NEGATIVE EIGENVALUES OF A DIFFERENTIAL OPERATOR**

S.KARAYEL

In this work we _nd some asymptotic formulas for the number of eigenvalues smaller than -e (e > 0) of a self-adjoint operator L which is formed by differential expression … EQ .. and with the boundary condition y(0) = 0 e–>0

Presenter: Serpil Karayel

**CUBICITY OF LINEAR COMBINATIONS OF TWO COMMUTING CUBIC MATRICES**

E.KİŞİ AND H. ÖZDEMİR

Let A1 and A2 be commuting cubic matrices and let c1 and c2 be non-zero complex numbers. Necessary and su_cient conditions for the cubicity of the linear combinations of the form A = c1A1 + c2A2 are obtained. The results obtained could be view as a generalization of the results given for the linear combinations of tripotent matrices and an expanding of the results given for the linear combinations of quadratic matrices.

Presenter: Emre Kişi

**A NOTE ON SPHERICAL PRODUCT SURFACE WITH POINTWISE 1-TYPE GAUSS MAP IN GALILEAN 3-SPACE G3**

İ. KİŞİ AND G. ÖZTÜRK

In this study, we focus on spherical product surface in Galilean 3-space G3: We determine spherical product surface which has harmonic Gauss map. Also, we give a characterization of these surfaces having _rst kind pointwise 1-type Gauss map in G3.

Presenter: İlim Kişi

**FOCAL SURFACE OF A TUBULAR SURFACE WITH BISHOP FRAME IN E3**

İ. KİŞİ, S. BÜYÜKKÜTÜK AND G. ÖZTÜRK

In this study, we focus on focal surface of a tubular surface in Euclidean 3-space E3. We characterized these surfaces with Bishop frame. We get some results for these types of surfaces to become at and we show that there is no minimal focal surface of a tubular surface in E3. Further, we obtain some results about u-parameter and v-parameter curves of the focal surface M*.

Presenter: İlim Kişi

**A SECURE VARIANT OF THE DSA DIGITAL SIGNATURE**

LEILA ZAHHAFI AND OMAR KHADIR

In this paper we present a cryptographic topic. It’s a new variant of the DSA signature protocol. We have improved the verification equation of the signature to make it more eficient. The security and complexity of our method are analyzed.

Presenter: Leila Zahhafi

**GENERALIZATION OF SOFT SETS IN FUZZY SETTINGS**

G. ŞENEL

In 1999, D.Molodtsov defined soft sets and established the fundamental results of the new theory [5], to solve complicated problems and various types of uncertainties. A soft set is an approximate description of an object precisely consisting of two parts, namely predicate and approximate value set. In this paper, the notion of soft set is generalized in fuzzy setting, and introduced several operators for L-soft set theory like the complement of an L-soft set, L-order and L-equivalence relation which are continuation of [2]

Presenter: Güzide Şenel

**ROUGH OPERATORS ON Lx DEFINED BY A SOFT SET**

G. ŞENEL

In [1], they defined the notion of a soft set in L-set theory, introduced several operators for L-soft set theory, and investigated the rough operators on the set of all L-soft sets induced by the rough operators on L*. As a continuation, in the paper, rough operators on L* is studied and discussed their properties.

Presenter: Güzide Şenel

**SIMPSON TYPE INTEGRAL INEQUALITIES FOR r-CONVEX FUNCTION**

MUSTAFA KARAGÖZLÜ AND MERVE AVCI ARDIÇ

In this paper, we established new integral inequalities of Simpson type for r-convex functions via two integral identities.

Presenter: Mustafa Karagözlü

**BINOMIAL TRANSFORMS OF THE MORGAN-VOYCE SEQUENCES **

YASEMİN TAŞYURDU

In this study, we apply binomial, k-binomial transforms to the Morgan-Voyce sequences. Also, the Binet formula, generating function of these transforms are presented and proved. Moreover, we investigate some interesting properties between the obtained new sequences and the classical Morgan-Voyce sequences. We introduce on infinite triangle consist of the elements of Morgan-Voyce sequences and their binomial, k-binomial transforms.

Presenter: Yasemin Taşyurdu

**THE INTERPRETATION OF STUDENTS ON NEW HIGHER EDUCATION ENTRANCE EXAM **

ALİ KILIÇ

In general, higher education entrance exams are the ones in which candidates are scored and ranked according to the true answers given to questions within a certain time. Therefore, these exams are the ones that focus on “sorting” students. The higher education entrance examination system has been changed at various times in our country; and the latest change was made in the system in the 2017-2018 Academic Year. Each change brings changes in the format and question types together with it. While many different forms of learning and intelligence are mentioned in our world in our age, these systems cause that students are called as “successful” or “not successful” at a rate of their true answers given to questions within a certain time period. This study was performed with the aim of determining how the last change was perceived by students in their own minds and what kind of effects they had on the studying for the exam processes with their and their families’ interpretations and perceptions in terms of the relevant aspects and with the help of their own observations.

The study was designed in the Qualitative Research Design; and when the sampling was determined, the school types were taken into consideration as much as possible. The study was conducted on a voluntary basis; and the students from each school type were interviewed with face-to-face technique. The study aimed to determine what they had lived either positively or negatively in this process. The study also aimed to guide and contribute to the literature by receiving the observations of students and their families.

Presenter: Ali Kılıç

**ON THE SIGMA INDEX OF THE CORONA PRODUCTS OF MONOGENIC SEMIGROUP GRAPHS**

YAŞAR NACAROĞLU AND NİHAT AKGÜNEŞ

In [1], Das et.al. considered the monogenic semi group SM with zero having {0, x, x^2, … , x^n}. Also they de_ned undirected graph sigma(SM) associated with SM whose vertices are the non-zero elements, x, x^2, … , x^n and any two different vertices xi and xj are adjacent if i + j > n (for 1 £ i; j £ n). In this paper we present sigma index of corona products of any two monogenic semigroup graphs sigma(S1 M ) and sigma(S2M ).

Presenter: Yaşar Nacaroğlu

**DETERMİNANTS AND PERMANENTS OF HESSENBERG MATRİCES WİTH (S, T)-JACOBSTHAL AND (S, T)-JACOBSTHAL LUCAS SEQUENCES**

YASEMİN TAŞYURDU

In this study, we consider Hessenberg matrices with applications to (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequences. We define some Hessenberg matrices and obtain determinants and permanents of these Hessenberg matrices that give terms of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequences. Also, we investigate the relationships between these sequences, and permanents and determinants of these matrices.

Presenter: Yasemin Taşyurdu

**SOLVING HYBRID-VEHICLE ROUTING PROBLEM USING SIMULATED ANNEALING **

M. ALREFAEI AND N. ALSUMAIRAT

In this paper, we consider the Hybrid-Vehicle Routing Problem (H-VRP), where a vehicle departs a depot and needs to visit each customer among n customers, once and only once. It is assumed that the vehicle uses both fuel and electricity and there are fuel and electricity stations where the vehicle can refuel and recharge during its rout. The time spent in each trip should not exceed a predetermined time. To avoid local minimality trap, we propose an algorithm that uses the simulated annealing (SA) algorithm for solving the H{VRP. The proposed algorithm starts by an initial solution, then it proceeds by SA to find an optimal or a near optimal solution. Instead of restarting the algorithm as in Yu et al. [1], the proposed method uses a constant temperature as suggested by Alrefaei and Andradottir [2], so the algorithm can navigate the state space freely and and keeps the best solution so far as the optimal solution. The proposed algorithm is tested on a generic example using several values of the temperatures parameter.

Presenter: Mahmoud Alrefaei

**EXISTENCE OF THE FIXED POINTS OF SELF MAPPINGS DEFINED IN PRODUCT OF UNIFORMLY CONVEX BANACH SPACE**

NURCAN BİLGİLİ GÜNGÖR

In this paper, the set of self mappings defined in the product of set which is a nonempty closed convex subset of a uniformly convex Banach space are presented. Also the definition of the asymptotically nonexpansiveness of this type of self mappings is given. And the existence of fixed point is proved by giving necessary conditions.

Presenter: Nurcan Bilgili Güngör

**APPLICATION OF IMPLICIT RELATIONS TO FIXED POINT THEOREMS IN COMPLETE SOFT QUASI METRIC SPACE **

NURCAN BİLGİLİ GÜNGÖR

The concept of soft quasi-metric space, according to soft element and some of its properties are given very recently by Bilgili Gungor [1](In review ). And an implicit contraction mapping via soft real numbers inspired from the article of Popa and Patriciu [5] is defined by Bilgili Gungor [2](In review ). In this paper some examples of implicit contraction mappings via soft real numbers are given and then fixed point theorems are proved by using these implicit relations.

Presenter: Nurcan Bilgili Güngör

**REDUCTION OF NAVIER-STOKES EQUATION TO A LINEAR EQUATION **

WALEED S. KHEDR

In this article, we provide two theorems on pointwise coincidence between solutions of Navier-Stokes equation and solutions of standard linear second order parabolic equations with the same data. We show that the convection, the pressure, and the external forces (if applied) are governed by some sort of balance independent of the equation that governs the solution itself. In light of the well establishment of the theory of existence, regularity and uniqueness of linear second order parabolic equations, this result represents an important step to fully understand the qualitative properties of the solutions to Navier-Stokes equation.

Presenter: Waleed S. Khedr

**SUCCESS AND SELF-EFFICACY IN NUMBER SENSE OF THE MIDDLE SCHOOL STUDENTS**

SALİHA HİLAL YARAR, HASAN ES AND NEJLA GÜREFE

The number sense is a feeling of being able to make logical estimates about various usages of numbers, recognize arithmetic errors, select the most efficient way for the calculation and notice number patterns (Hope, 1989). In this study, it was aimed to determine the achievement and self-efficacy in the number sense of the middle school students. The participants consisted of 106 students who were studying in 5th, 6th, 7th and 8th grades of a public school in Ankara. The data were collected by using ” Scale of Self-Efficacy Towards Number Sense” and “Number Sense Achievement Test” scales. In addition, interviews were actualized with students who were unsured whether they used the sense of number in answering questions in the number sense test. The answers and solutions given to the questions by the students were analyzed using qualitative and quantitative analysis methods. Whether there is a significant difference between the number sense success and self-efficacy in the number sense of the students in terms of gender and grade level variables was examined using unpaired sample t test and the one-way ANOVA test. However, to detect whether there is a relationship between self-efficacy in number sense and number sense success was made Pearson correlation test.

Presenter: Saliha Hilal Yarar

**THE DEGREE OF APPROXIMATION BY GENERALIZED ZYGMUND SUMS IN THE CLASSES C ****¥****j**

S. YASEMiN GöLBOL AND U. DEĞER

In this studying we consider the approximation to functions from the classes of j -integrals by generalized Zygmund sums in the uniform metric. That is, the value … EQ …is investigated under the some conditions, where C¥j is a special class of continuous functions, … EQ …are generalized Zygmund sums with respect to the Fourier series of f and j(k) are the values of a certain function jÎF at integer points. Here F is the set of all continuous functions j(u) monotonically increasing to infinity on [1,¥).

Presenter: S. Yasemin Gölbol