Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science

Permanent URI for this collectionhttps://hdl.handle.net/11413/6787

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On the Harary Index of Γ(Zn)
(Bayram Sahin, 2024) Gürsoy, Arif; ÜLKER, ALPER; Kircali Gürsoy, Necla
In this work, the Harary index of zero-divisor graphs of rings Zn are calculated when n is a member of the set {2p, p2, pλ, pq, p2 q, pqr} where p, q and r are distinct prime numbers and λ is an integer number. We give the formulas for computing the Harary index of Γ(Zn). Moreover, the Harary index of graphs for products of rings were computed. © 2024, Bayram Sahin. All rights reserved.
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Sheffer Stroke Operation on L-Algebras via an Algorithmic Approach
(Springer Science and Business Media Deutschland GmbH, 2024) Gürsoy, Necla Kırcalı; Öner, Tahsin; Gürsoy, Arif; ÜLKER, ALPER
In this study, we introduce the Sheffer stroke L-algebra and prove some fundamental theorems, propositions and lemmas of Sheffer Stroke L-algebras. The notions of filter and ultrafilter for Sheffer stroke L-algebra are studied. We give subalgebra and normal subset definitions of a Sheffer stroke L-algebras. Moreover, a homomorphism between Sheffer stroke L-algebras is introduced and isomorphism theorems are presented. Finally, we give three new algorithms for Sheffer stroke L-algebras. Thus, it is contributed to researchers on different application areas by presenting an algorithmic approach on this subject, for the first time in the literature. © The Author(s) 2024.
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Optical Soliton Solution of the Perturbed Fokas-Lenells Equation Having the Cubic-Quintic-Septic Law of Self-Phase Modulation in the Presence of Chromatic and Spatiotemporal Dispersions
(Springer Science and Business Media Deutschland GmbH, 2024) UÇAR, MEHMET FATİH; Özışık, Müslüm; Seçer, Aydın; Bayram, Mustafa
This study presents the optical soliton solutions of the Fokas-Lenells equation, which is a significant model for nonlinear optics. The new Kudryashov method is used to obtain the optical solutions in the form of the Fokas-Lenells equation, including the perturbation term and cubic-quintic-septic law nonlinearities. By implementing the method effectively, bright and singular soliton solutions are gained, and graphical presentations were created to analyze the effects of problem parameters on the bright soliton form. The investigated problem parameters include septic law nonlinearity, group velocity dispersion, and spatiotemporal dispersion terms.
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A Study on Harmonic Functions
(Proceedings of the Bulgarian Academy of Sciences, 2024) UÇAR, MEHMET FATİH; Uçar, Hatice Esra Özkan
The class of functions that have bounded boundary rotation and bounded radius rotation are the generalization of the convex and the starlike functions, respectively. The concept of such functions was introduced by LOWNER [1]. But he did not use the present terminology. It was PAATERO [2,3] who systematically developed their properties and made an exhaustive study of the class of functions that have bounded boundary rotation. We will examine in this paper, the subclass of S-H H that is related to the class of functions that have bounded radius rotation.
Open Access
Structure Preserving Schemes for Coupled Nonlinear Schrödinger Equation
(Institute of Physics, 2024) AKKOYUNLU, CANAN; ŞAYLAN, PELİN
The numerical solution of CNLS equations are studied for periodic wave solutions. We use the first order partitioned average vector field method, the second order partitioned average vector field composition method and plus method. The nonlinear implicit schemes preserve the energy and the momentum. The results show that the methods are successful to get approximation. © 2024 Institute of Physics Publishing. All rights reserved.
Open Access
A Discussion of Bisexual Populations With Wolbachia Infection as an Evolution Algebra
(Taylor and Francis Ltd., 2024) ESİN, SONGÜL; Kanuni M.; Özdinç B.
In this paper, Wolbachia infection in a bisexual and diploid population with a fixed cytoplasmic incompatibility rate w and maternal transmission rate d is studied as an evolution algebra. As the cytoplasmic incompatibility (CI) of the population causes deaths in the offspring, the evolution algebra of this model is not baric, and is a dibaric algebra if and only if the cytoplasmic incompatibility rate w is 1 and (Formula presented.). The idempotent elements are given in terms of d and w. Moreover, this algebra has no absolute nilpotent elements when CI expression (Formula presented.). © 2024 Taylor & Francis Group, LLC.
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, Şerife
In 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.
Open Access
Quasi Subordinations for Bi-Univalent Functions With Symmetric Conjugate Points
(Yıldız Technical University, 2024) Sakar, Fethiye Müge; Aydoğan, Melike; KARAHÜSEYİN, ZELİHA
Many 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.
Open Access
Salih Zeki ve Asar-ı Bakiye'nin 1960'larda Yapılmış Bir Çevirisi
(İstanbul Üniversitesi Edebiyat Fakültesi, 2005) ŞENKON, HÜLYA
Together 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.
Open Access
On Theta-Euclidean L-Fuzzy Ideals of Rings
(TÜBİTAK, 2004) KOÇ, AYTEN; Balkanay, Erol
In 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.
Open Access
Stokastik Trendin Lokal Polinomal Yaklaşım ve Üstel Düzgünleştirme ile Bulunmasında Hata Kareleri Ortalamasının Karşılaştırılması
(Marmara Üniversitesi, 2004) ÇAĞLAR, HATİCE NAZAN; ÇAĞLAR, SÜLEYMAN HİKMET
Üstel 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.
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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, AYŞENUR
The 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.
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.
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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.
Open Access
On the Essential Element Graph of a Lattice
(Matematikçiler Derneği, 2022) ÜLKER, ALPER
Let 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.
Open Access
Exact Sequences of BCK-Modules
(Fuat Usta, 2022) ÜLKER, ALPER
BCK-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.
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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 KARATAŞ
In 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.
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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 KARATAŞ
The 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.
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A New Topology Via a Topology
(American Institute of Physics Inc., 2022) DAĞCI, FİKRİYE İNCE; Çakallı, Hüseyin
In 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.
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Sombor Index of Zero-Divisor Graphs of Commutative Rings
(Ovidius Univ Press, 2022) Gürsoy, Arif; ÜLKER, ALPER; Kırcali Gürsoy, Necla
In 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.