# Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science

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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 Open Access Quasi Subordinations for Bi-Univalent Functions With Symmetric Conjugate Points(Yıldız Technical University, 2024) Sakar, Fethiye Müge; Aydoğan, Melike; KARAHÜSEYİN, ZELİHAMany researchers have recently acquainted and researched several interesting subfamilies of bi-univalent function family delta and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar. In this current work, the subfamily F-delta,q(sc) (alpha, Xi) of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients vertical bar a(2)vertical bar, vertical bar a(3)vertical bar and besides related with these coefficients vertical bar a(3) - a(2)(2)vertical bar for functions belonging to this subfamily are derived. Further some corollaries are also presented.Publication Open Access Salih Zeki ve Asar-ı Bakiye'nin 1960'larda Yapılmış Bir Çevirisi(İstanbul Üniversitesi Edebiyat Fakültesi, 2005) ŞENKON, HÜLYATogether with the Kamus-i Riyaziyât (Encyclopaedia of Mathematics), the Asâr-ı Bâkiye is Salih Zeki’s major work on the history of mathematics and astronomy. The first volume covering the history of spherical trigonometry and the second treating the history of arithmetics were both published in Istanbul in 1913. The third volume on astronomy remained unpublished. A project of translating the first three volumes into modern Turkish was initiated by Nazım Terzioğlu (1912-1976) professor of mathematics at Istanbul University in early 1960s or possibly earlier. A commission composed of professors of mathematics, astronomy, physics and history of medicine was formed in 1961 to decide on the publication of Salih Zeki’s works. The manuscript of the Asâr-ı Bâkiye translation which consists of 411 type-written pages is actually kept in the archives of the Turkish Mathematical Society. The present paper aims to introduce this translation which could not be published for reasons unknown to us.Publication Open Access On Theta-Euclidean L-Fuzzy Ideals of Rings(TÜBİTAK, 2004) KOÇ, AYTEN; Balkanay, ErolIn this paper we define a theta-Euclidean level subset and a theta-Euclidean level ideal. We also give some properties of a theta-Euclidean level subset.Publication Open Access Stokastik Trendin Lokal Polinomal Yaklaşım ve Üstel Düzgünleştirme ile Bulunmasında Hata Kareleri Ortalamasının Karşılaştırılması(Marmara Üniversitesi, 2004) ÇAĞLAR, HATİCE NAZAN; ÇAĞLAR, SÜLEYMAN HİKMETÜstel düzgünleştirme modelleri stokastik trendin elde edilmesinde kullanılan en temel yöntemdir. Düzgünleştirme problemlerinde kullanılabilecek alternatif bir yöntemde Lokal Polinomal yaklaşımdır. Bizim çalışmamızda Lokal polinomlarda ağırlık fonksiyonu olarak Kernel fonksiyonları kullanılmıştır. Özellikle son yıllarda bu alanda yapılan bilimsel çalışmalarda Kernel fonksiyonları çok geniş yer tutmaktadır. Yapılan bu çalışmada Üstel düzgünleştirme ve Lokal Polinomal yaklaşım modelleri için hata kareleri ortalaması (HKO) karşılaştırılarak en uygun yöntem belirlenmeye çalışılmıştır. Bu amaçla stokastik trend Türkiye’deki altın fiyatları kullanılarak her iki yöntem için bulunmuş ve HKO lar hesaplanmıştır. Ayrıca üstel düzgünleştirmeyi sağlayan otlar için HKO lar araştırılmıştır.Publication Metadata only Analytic Functions With Conic Domains Associated With Certain Generalized q-integral Operator(Korean Mathematical Society, 2023) Ahuja, Om P.; ÇETİNKAYA, ASENA; Jain, Naveen KumarIn this paper, we define a new subclass of k-uniformly starlike functions of order-gamma (0 <= gamma < 1) by using certain generalized q integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q sufficient coefficient condition, q-Fekete-Szego inequalities, q-Bieberbach De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order-gamma by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.Publication Restricted Harmonic Multivalent Functions Associated With a (P,Q)-Analogue of Ruscheweyh Operator(Turkic World Mathematical Soc., 2023) Sharma, P.; Mishra, O.; Ahuja, O. P.; ÇETİNKAYA, AYŞENURThe aim of this paper is to introduce and investigate a new class of harmonic multivalent functions defined by (p,q)-analogue of Ruscheweyh operator for multivalent functions. For this new class, we obtain a (p,q)-coefficient inequality as a sufficient con-dition. Using this coefficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic multivalent functions to its sequences of partial sums. We further consider a subclass of our new class and for which we obtain (p,q)-analogue of coefficient characterization which in fact helps us to determine its properties such as distortion bounds, extreme points, convolutions and convexity conditions. In the last section on conclusion, it is pointed out that the results obtained in this paper may also be extended to some generalized classes.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 Restricted Cesaro Vector Lattices and Their Ideals of Finite Elements(Springer, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R. R.For the Cesaro matrix C = (c(nm))(n,m?N), where c(nm) = (1)/(n), if n = m and c(nm) = 0 otherwise, the Cesaro sequence spaces ces(0), ces(p) (for 1 < p < 8) and cesoo are defined. These spaces turn out to be real vector lattices and with respect to a corresponding (naturally introduced) norm they are all Banach lattices, and so possess (or not possess) some interesting properties. In particular, the relations to their generating ideals c(0), t(p) and t(8) are investigated. Finally the ideals of all finite, totally finite and selfmajorizing elements in ces(0), ces(p) (for 1 < p <8) and ces(8) are described in detail.Publication Restricted Bound on Hankel Determinants H(2)4 (F) and H(3)4 (F) for Lemniscate Starlike Functions(Honam Mathematical Soc., 2023) Kumar, Sushil; Rai, Pratima; ÇETİNKAYA, ASENAWe determine the upper bounds on fourth order Hankel de-terminants H4(2) (f) and H(3) 4 (f) for the class S*L of lemniscate starlike functions defined on the open unit disk which was introduced by Sok ' o l and Stankiewicz in [17].Publication Open Access On the Essential Element Graph of a Lattice(Matematikçiler Derneği, 2022) ÜLKER, ALPERLet mathcalL be a bounded lattice. The essential element graph of mathcalL is a simple undirected graph varepsilonmathcalL such that the elements x,y of mathcalL form an edge in varepsilonmathcalL, whenever xveey is an essential element of mathcalL. In this paper, we study properties of the essential elements of lattices and essential element graphs. We study the lattices whose zero-divisor graphs and incomparability graphs are isomorphic to its essential element graphs. Moreover, the line essential element graphs are investigated.Publication Open Access Exact Sequences of BCK-Modules(Fuat Usta, 2022) ÜLKER, ALPERBCK-modules were introduced as an action of a BCK-algebra over an Abelian group. Homomorphisms of BCK-modules form an exact sequence which is called BCK-sequence. In this paper, we study homomorphisms of BCK-modules. We show that this homomorphisms have a module structure. Moreover, we show that sequences of Hom functors are BCK-sequences.Publication Restricted Fekete-SzegÖ Inequalities for q-Starlike and q-Convex Functions Involving q-Analogue of Ruscheweyh-Type Differential Operator(Palestine Polytechnic University, 2022) Soni, Amit; ÇETİNKAYA, ASENAIn the present paper, the new generalized Ma-Minda type classes of q-starlike and q-convex functions are introduced by using Ruscheweyh-type q-differential operator. Denote by SRλq (φ) the class of q-starlike functions and CRλq (φ) the class of q-convex functions associated with Ruscheweyh-type q-differential operator, where φ is the function with positive real part. By making use of these classes, we obtain initial coefficient estimates and Fekete-Szegö inequalities for the classes SRλq (φ) and CRλq (φ), respectively. © Palestine Polytechnic University-PPU 2022.Publication Restricted The Effect of Loss and Optimization Functions on Bitcoin Rate Prediction in LSTM(Institute of Electrical and Electronics Engineers Inc., 2022) KIRCI, BERKE KAAN; BAYDOĞMUŞ, GÖZDE KARATAŞIn recent years, Bitcoin cryptocurrency has become a growing trend in the world. For this reason, researchers from many fields are examining various artificial intelligence models to predict Bitcoin rates. In particular, Deep Learning algorithms have been shown to outperform traditional models in predicting cryptocurrency rates. However, very few studies have examined the effect of parameters used in deep learning algorithms on the algorithm. Optimization and loss functions are very important, which affect the algorithm's ability to make a successful prediction. In this study, Long-Short Term Memory, a deep learning algorithm, is used to predict daily Bitcoin prices and the effect of optimization/loss functions on the accuracy rate is evaluated. Experimental results showed that the Long-Short Term Memory model made the best predictions as a result of working with the Adam optimization function and the Mean Square Error loss function. © 2022 IEEE.Publication Restricted Covid-19 Disease Detection with Improved Deep Learning Algorithms on X-Ray Data(Institute of Electrical and Electronics Engineers Inc., 2022) ÇİÇEKLİ, NAHİDE ZEYNEP; BAYDOĞMUŞ, GÖZDE KARATAŞThe COVID-19 pandemic has brought human life to a startling halt around the world from the moment it emerged and took thousands of lives. The health system has come to the point of collapse, many people in the world have died from being infected, and many people who have survived the disease have had permanent lung damage with the spread of COVID-19 in 212 countries and regions. In this study, an answer is sought to diagnose the disease-causing virus through Artificial Intelligence Algorithms. The aim of the study is to accelerate the diagnosis and treatment process of COVID-19 disease. Enhancements were made using Deep Learning methods, including CNN, VGG16, DenseNet121, and ResNet50. For this study, the disease was detected by using X-Ray images of patients with and without COVID-19 disease, and then it was evaluated how to increase the accuracy rate with the limited available data. To increase the accuracy rate, the results of data augmentation on the image data were examined and the time complexity of the algorithms with different layers was evaluated. As a result of the study, it was seen that data augmentation increased the performance rate in all algorithms and the ResNet50 algorithm was more successful than other algorithms. © 2022 IEEE.Publication Metadata only A New Topology Via a Topology(American Institute of Physics Inc., 2022) DAĞCI, FİKRİYE İNCE; Çakallı, HüseyinIn this extended abstract, we modify the definition of h-open set introduced in [1] by F. Abbas who neglects that the set of all h-open sets is a topology, and we show that the union of any family of h-open subsets of X is h-open that ensures that the set of all h-open subsets of a topological space (X, τ) forms a topology which is finer than τ, where a subset A of a topological space (X, τ) is said to be h-open if A ⊆ Int(A ∪ U) for every non-empty subset U of X such that U ∈ τ. We also give continuity type theorems. © 2022 American Institute of Physics Inc.. All rights reserved.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 Restricted Independent Domination Polynomial of Zero-Divisor Graphs of Commutative Rings(Springer, 2022) Gürsoy, Necla Kırcalı; ÜLKER, ALPER; Gürsoy, ArifAn independent dominating set of a graph is a vertex subset that is both dominating and independent set in the graph, i.e., a maximal independent set. Also, the independent domination polynomial is an ordinary generating function for the number of independent dominating sets in the graph. In this paper, we examine independent domination polynomials of zero-divisor graphs of the ring Z(n) where n is an element of {2p, p(2), p(alpha), pq, p(2)q, pqr) and their roots. Finally, we prove the log-concavity and unimodality of their independent domination polynomials.Publication Open Access Briot-Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function(MDPI, 2022) ÇETİNKAYA, ASENA; Cotirla, Luminita-IoanaWe define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot-Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot-Bouquet differential equations and observe that these solutions are the best dominant of the Briot-Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions.Publication Restricted On Spirallike Functions Related to Bounded Radius Rotation(The Honam Mathematical Society (호남수학회), 2022) ÇETİNKAYA, ASENA; Taştan, Hakan MeteIn the present paper, we prove the growth and distortion theorems for the spirallike functions class S-k(lambda) related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class S-k (lambda). Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.