Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science
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Publication Open Access Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial(MDPI, 2020) Aydoğan, S. Melike; Karahüseyin, ZelihaIn the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete-Szego problem of this subclass is also acquired. Further, some special cases of our results are designated.Publication 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.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 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 Open Access Increasing the Performance of Machine Learning-Based IDSs on an Imbalanced and Up-to-Date Dataset(IEEE, 2020) BAYDOĞMUŞ, GÖZDE KARATAŞ; Demir, Önder; ŞAHİNGÖZ, ÖZGÜR KORAYIn recent years, due to the extensive use of the Internet, the number of networked computers has been increasing in our daily lives. Weaknesses of the servers enable hackers to intrude on computers by using not only known but also new attack-types, which are more sophisticated and harder to detect. To protect the computers from them, Intrusion Detection System (IDS), which is trained with some machine learning techniques by using a pre-collected dataset, is one of the most preferred protection mechanisms. The used datasets were collected during a limited period in some specific networks and generally don & x2019;t contain up-to-date data. Additionally, they are imbalanced and cannot hold sufficient data for all types of attacks. These imbalanced and outdated datasets decrease the efficiency of current IDSs, especially for rarely encountered attack types. In this paper, we propose six machine-learning-based IDSs by using K Nearest Neighbor, Random Forest, Gradient Boosting, Adaboost, Decision Tree, and Linear Discriminant Analysis algorithms. To implement a more realistic IDS, an up-to-date security dataset, CSE-CIC-IDS2018, is used instead of older and mostly worked datasets. The selected dataset is also imbalanced. Therefore, to increase the efficiency of the system depending on attack types and to decrease missed intrusions and false alarms, the imbalance ratio is reduced by using a synthetic data generation model called Synthetic Minority Oversampling TEchnique (SMOTE). Data generation is performed for minor classes, and their numbers are increased to the average data size via this technique. Experimental results demonstrated that the proposed approach considerably increases the detection rate for rarely encountered intrusions.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 On Ramsey Dynamical Model and Closed-Form Solutions(Springer Nature, 2021) POLAT, GÜLDEN GÜN; Özer, TeomanThis study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions of maximum principle are analyzed and then first integrals and corresponding closed-form (analytical) solutions are determined by using Lie point symmetries in conjunction with Prelle-Singer and Jacobi last multiplier methods. Additionally, associated lambda-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.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 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 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 Saldırı Tespit Sistemlerinde Makine Öğrenmesi Modellerinin Karşılaştırılması(Erzincan Binali Yıldırım Üniversitesi, Fen Bilimleri Enstitüsü, 2019) ÇEBİ, CEM BERKE; BULUT, FATMA SENA; FIRAT, HAZAL; BAYDOĞMUŞ, GÖZDE KARATAŞ; ŞAHİNGÖZ, ÖZGÜR KORAYSon yıllardaki gelişen teknolojiler neticesinde her türlü hesaplama cihazının İnternete bağlanması sağlanmıştır. Bu sayede birçok gerçek dünya problemi yeni ağ düzenine aktarılsa da bu tam-kontrol sağlanamayan sanal platform çok sayıda güvenlik açığı içermektedir. Günümüzde ağ yöneticilerin ana görevlerinden biride bu açıkları kapatmak ve sorumlu oldukları bilgisayar ağını saldırılardan korumaktır. Güvenlik duvarlarının kullanımı dışarıdan yapılan saldırıları ciddi boyutta engellese de içeriden yapılabilecek veya daha önceden karşılaşılmayan tipten saldırılara karşı zafiyetler içermektedir. Saldırı Tespit Sistemleri (STS) bu zafiyetleri ortadan kaldırmak için öncelikle tercih edilebilecek uygulamalardır. Son geliştirilen STSleri incelendiğinde dinamik bir güvenlik mekanizması geliştirmek adına özellikle Makine Öğrenmesi tabanlı sistemlere ağırlık verildiği görülmektedir. Bilgisayar donanımları ve paralel hesaplama teknolojilerinde ortaya çıkan gelişmeler ve Büyük Veri işleme teknolojilerinin, Makine Öğrenmesi tabanlı sistemlerle uyumlu kullanıldığı görülmektedir. Bu çalışmada yedi farklı makine öğrenimi algoritmaları kullanarak STSlerin geliştirilmesi amaçlanmıştır. Elde edilen sonuçlar başarım, eğitim süreleri ve çalıştırma süreleri açısından karşılaştırılarak farklı kriterlere göre uygun algoritmanın ortaya konmuştur. Bu karşılaştırma için genel kabul gören NSL-KDD veri setinden faydalanılmıştır. Başarım sonuçlarına bakınca Adaboost algoritmasının en yüksek doğruluk oranına ulaştığı görülmektedir. Ancak gerek eğitim süresi gerekse çalışma zamanı performansı göz önüne alınınca Karar Ağacı algoritmasının daha yüksek performans gösterdiği, doğruluk oranı değeri itibarı ile de Adaboost’a yakın değere sahip olduğu görülmektedir.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 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 Open Access Structure Preserving Schemes for Coupled Nonlinear Schrödinger Equation(Institute of Physics, 2024) AKKOYUNLU, CANAN; ŞAYLAN, PELİNThe 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.