Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science
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Publication Metadata only A certain class of harmonic mappings related to functions of bounded radius rotation(2018) Kahramaner, Yasemin; Yemişçi Şen, Arzu; POLATOĞLU, YAŞARLet R-k be the class of functions with bounded radius rotation and let S-H be the class of sense-preserving harmonic mappings. In the present paper we investigate a certain class of harmonic mappings related to the function of bounded radius rotation.Publication Open Access Application of the subordination principle to the multivalent harmonic mappings with shear construction method(2011-06) Yavuz Duman, Emel; Özkan, H. Esra; POLATOĞLU, YAŞARThe harmonic function in the open unit disc D = (z is an element of C vertical bar z vertical bar < 1} can be written as a sum of an analytic and an anti-analytic function. f = h(z) + g(z), where h(z) and g(z) are analytic functions in D, and are called the analytic part and co-analytic part of f, respectively. One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion), because the growth theorem and distortion theorem give the compactness of the classes of these functions. In this paper we consider both of these questions with the shear construction method. (C) 2010 Elsevier Ltd. All rights reserved.Publication Metadata only Average Vector Field Method of The Strongly Coupled Nonlinear Schrodinger Equation(2019-07) akkoyunlu, canan; 113376In this work, average vector field method (AVF) is derived for strongly coupled Schrodinger equation (SCNLS). The SCNLS equation is discretized in space by finite differences and is solved in time by structure preserving AVF method. Numerical results for different paremeter compare with the Lobatto IIIA-IIIB method.The results indicate that AVF method are effective to preserve global energy and momentum.Publication Open Access Blockchain based secure communication for Iot devices in smart sities(2019-04) Yetiş, R.; ŞAHİNGÖZ, ÖZGÜR KORAYIn smart city technologies we have witnessed advanced technological improvements in small computing devices, which can be connected to the Internet and named as Internet of Thing (IoT) devices, and cooperatively working complex systems. With this increased use of new technologies, the security problem is becoming more and more important because complex systems lead to unpredictable security vulnerabilities, which result in financial and private information losses. As a recently emerged technology, Blockchain was emerged as an alternative solution to security breaches of a different application environment. In contrast to the central structure used by most systems, it is preferred especially in the area of security by its distributed structure and the cryptographic hash algorithm it uses. Today, structures such as Smart Home, Smart City, Smart Environment and Smart Agriculture, which are created by using IoT are seen as active research areas with more security shortages. The reason for the security weakness in these areas arises from the hardware restriction on the IoT devices used. In the proposed system, an authorization system for IoT devices has been tried to be set up by using the distributed node structure of Blockchain system and blocks kept in these nodes. UDP (User Datagram Protocol), which uses a simple communication model without establishing a connection to the minimum protocol mechanism for communication of nodes in the system, was preferred. The communication between the nodes has been encrypted using encryption methods, thus creating a secure environment.Publication Open Access Convolution Properties for Salagean-Type Analytic Functions Defined by q-Dıfference Operator(2019) Çetinkaya, AsenaIn this paper, we define Salagean-type analytic functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for Salagean-type analytic functions denoted by S-q(m,lambda) [A,B].Publication Metadata only Deep learning based classification of malaria from slide images(2019) Kalkan, Soner Can; ŞAHİNGÖZ, ÖZGÜR KORAYAs one of the most life-threatening disease in the tropical and warmer-climate countries, Malaria affects not only animals but also humans who can be infected by only a single bite from a mosquito. Although this disease is wiped out in high-income countries, as a result of traveling people, it can even emerge in all part of the world. World Health Organization announced that more than 400,000 people are expected to die due to this illness. However, it is a curable and preventable disease, if early detection is possible. Traditionally, Pathologists diagnosed this disease manually by using microscope which is a time-consuming process in our computerized world, and this model depends on the experience of the Pathologists, which is a critical problem in rural areas. Therefore, in recent years detection of Malaria using computerized image analysis which is trained using some dynamic learning mechanism has gained increasing importance. In this paper, we proposed an image processing-based Malaria detection system which is trained by deep learning. We used relatively big data for increasing the accuracy of the system, and the reached accuracy showed that the proposed system has an outstanding classification rate that can be used in real-world detection.Publication Open Access Diffused label popagation based transductive classification algorithm for Wwrd sense disambiguation(2019-07) Kocaman, G.; Gerek, A.; Altınel, B.; Ganiz, M.C.; ŞİPAL, BİLGEA major natural language processing problem, word sense disambiguation is the task of identifying the correct sense of a polysemous word based on its context. In terms of machine learning, this can be considered as a supervised classification problem. A better alternative can be the use of semi-supervised classifiers since labeled data is usually scarce yet we can access large quantities of unlabeled textual data. We propose an improvement to Label Propagation which is a well-known transductive classification algorithm for word sense disambiguation. Our approach make use of a semantic diffusion kernel. We name this new algorithm as diffused label propagation algorithm (DILP). We evaluate our proposed algorithm with experiments utilizing various sizes of training sets of disambiguated corpora. With these experiments we try to answer the following questions: 1. Does our algorithm with semantic kernel formulation yield higher classification performance than the popular kernels? 2. Under which conditions does a kernel design perform better than others? 3. What kind of regularization methods result with better performance? Our experiments demonstrate that our approach can outperform baseline in terms of accuracy in several conditions.Publication Open Access Duals of Cesaro Sequence Vector Lattices, Cesaro Sums of Banach Lattices, and Their Finite Elements(Springer Basel AG, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R.In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesaro sequence spaces ces(p) for p is an element of{0}boolean OR[1,infinity) and, second, after the Cesaro sum ces(p)(X) of a sequence of Banach spaces is introduced, where p = infinity is also allowed, we characterize their duals and the finite elements in these sums if the summed up spaces are Banach lattices. This is done by means of a remarkable extension of the corresponding result for direct sums.Publication Metadata only Gelfrand-Kirillov Boyutu Sonlu Olan Leavitt Yol Cebirlerinin Yapısı ve Temsilleri(2018-09) KOÇ, AYTEN; 112205Leavitt yol cebirleri (kısaca LPA: Leavitt Patlı Algebra) 2004 yılında Ara- Moreno-Pardo ve Abrams-Arando Pino tarafından, çizge C'*-cebirlerinin (80’lerde tanımlanan) cebirsel benzerleri olarak tanımlandı ama kökleri Bili Leavitt’iıı 60’lardaki çalışmalarına dayanır. LPA’nın modül kategorisinin çizgenin ok temsillerinin bir alt kategorisine denk olmasından başlayarak temsil sınıflandırmaları yapılabilir.Konuşmanın ilk kısmında gerekli temel tanımlar verilecek ve de LPA’nın cebirsel özellikleri ile çizgenin geometrisi arasındaki ilişki vurgulanacaktır, ikinci kısımda ise (M. Özaydın ile ortak çalışma) Gelfand-Kirillov boyutu sonlu olan Leavitt yol cebirlerinin yapıları ve temsillerinden bahsedilecektir.Publication Metadata only Generalizations for certain p-valent functions(2019-08) YAVUZ, EMEL; 111202Publication Metadata only Harmonic Univalent Functions Defined by Post Quantum Calculus Operators(SCIENDO, DE GRUYTER POLAND SP Z O O, BOGUMILA ZUGA 32A STR, 01-811 WARSAW, POLAND, 2019-08)We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.Publication Metadata only Intrusion detection systems with deep learning: A systematic mapping study(2019) Ösken, Sinem; Yıldırım, Ecen Nur; BAYDOĞMUŞ, GÖZDE KARATAŞ; CUHACI, LEVENTIn this study, a systematic mapping study was conducted to systematically evaluate publications on Intrusion Detection Systems with Deep Learning. 6088 papers have been examined by using systematic mapping method to evaluate the publications related to this paper, which have been used increasingly in the Intrusion Detection Systems. The goal of our study is to determine which deep learning algorithms were used mostly in the algortihms, which criteria were taken into account for selecting the preferred deep learning algorithm, and the most searched topics of intrusion detection with deep learning algorithm model. Scientific studies published in the last 10 years have been studied in the IEEE Explorer, ACM Digital Library, Science Direct, Scopus and Wiley databases.Publication Metadata only Krivine's Function Calculus and Bochner Integration(CAMBRIDGE UNIV PRESS, EDINBURGH BLDG, SHAFTESBURY RD, CB2 8RU CAMBRIDGE, ENGLAND, 2019-09) Troitsky, VG; TÜRER, MEHMET SELÇUKWe prove that Krivine's Function Calculus is compatible with integration. Let (Omega, Sigma, mu) be a finite measure space, X a Banach lattice, x epsilon X-n, and f : R-n x Omega -> R a function such that f(., w) is continuous and positively homogeneous for every w E 12, and f (s, ") is integrable for every s E R. Put F(s) = f f (s, w) d (w) and define F(x) and f (x, w) via Krivine's Function Calculus. We prove that under certain natural assumptions F(x) = f f (x, w) d (w), where the right hand side is a Bochner integral.Publication Open Access A Note on the Laplacian Energy of the Power Graph of a Finite Cyclic Group(Sakarya Üniversitesi Fen Bilimleri Enstitüsü, 2024) VARLIOĞLU, NURŞAH MUTLU; Büyükköse, ŞerifeIn this study, the Laplacian matrix concept for the power graph of a finite cyclic group is redefined by considering the block matrix structure. Then, with the help of the eigenvalues of the Laplacian matrix in question, the concept of Laplacian energy for the power graphs of finite cyclic groups was defined and introduced into the literature. In addition, boundary studies were carried out for the Laplacian energy in question using the concepts the trace of a matrix, the Cauchy-Schwarz inequality, the relationship between the arithmetic mean and geometric mean, and determinant. Later, various results were obtained for the Laplacian energy in question for cases where the order of a cyclic group is the positive integer power of a prime.Publication Metadata only On the regularity of the monomial point of a border basis scheme(2020) Kreuzer, M.; Long, L.N.; ŞİPAL, BİLGEThe border basis scheme BO parametrizes all 0-dimensional ideals in K[x1, … , xn] , where K is an arbitrary field, which have a border basis with respect to a given order ideal of terms O. Its vanishing ideal I(BO) is generated by quadratic equations which are easy to describe, and it contains a unique monomial point, namely the point corresponding to the monomial ideal generated by the terms outside O. Based on a detailed study of the generators of I(BO) , we describe a K-basis of the cotangent space m/ m2, where m is the maximal ideal of the monomial point. Moreover, we provide an efficient algorithm to compute such a basis and use it to characterize the regularity of the monomial point. © 2020, The Managing Editors.Publication Metadata only Partitioned Average Vector Field Method for Nonlinear Schrodinger Equation(2019-07) akkoyunlu, canan; 113376In this work, partitioned average vector field method (PAVF) is derived for nonlinear Schrodinger equation (NLS) and strongly coupled Schrodinger equation (SCNLS). The NLS and the SCNLS is discretized in space by finite difference and is solved in time by PAVF method. Numerical results compare with the AVF method. The results indicate that PAVF method are more effective to preserve global energy.Publication Metadata only Ruscheweyh-type starlike functions of complex order associated with q-difference operator(SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND, 2019-11) Çetinkaya, AsenaIn this paper, we introduce three new subclasses of starlike functions of complex order by using Ruscheweyh-type q-differential operator. We investigate inclusion theorem, sufficient coefficient estimates, distortion bounds and radius of starlikeness for the functions belonging to these subclasses. Moreover, partial sums of these subclasses were obtained.Publication Open Access Smart home hecurity with the use of WSNs on future intelligent cities(2019-04) Dine, G.; ŞAHİNGÖZ, ÖZGÜR KORAYIn recent years, smart cities use some advanced technologies such as Cyber-Physical Systems and Internet of Things for improving the quality of human life by enabling extra security and communication abilities. In a recent survey of ICMA which is the world's leading association of professional city and county managers, ICMA emphasizes the importance of the safety and security benefits of smart cities by categorizing it as one of the five important motivating factors. Therefore, in this paper, we proposed a new security model for smart buildings and smart homes by using a hot topic research area of Cyber-Physical Systems: WSNs. With the use of this system, it is aimed to construct a smart security system by using a minimum number of sensor nodes with the increased coverage rate for smart buildings and homes.Publication Restricted Sombor Index of Zero-Divisor Graphs of Commutative Rings(Ovidius Univ Press, 2022) Gürsoy, Arif; ÜLKER, ALPER; Kırcali Gürsoy, NeclaIn this paper, we investigate the Sombor index of the zero-divisor graph of DOUBLE-STRUCK CAPITAL Z (n) which is denoted by Gamma(DOUBLE-STRUCK CAPITAL Z (n) ) for n is an element of {p(alpha), pq, p (2) q, pqr} where p, q and r are distinct prime numbers. Moreover, we introduce an algorithm which calculates the Sombor index of Gamma(DOUBLE-STRUCK CAPITAL Z (n) ). Finally, we give Sombor index of product of rings of integers modulo n.Publication Metadata only Spirallike and robertson functions of complex order with bounded boundary rotations(2019-06) Çetinkaya, Asena; Kahramaner, Yasemin; Ahuja, Om P.Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.