Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science

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

Browse

Now showing 1 - 20 of 22

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.
Open Access
Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial
(MDPI, 2020) Aydoğan, S. Melike; Karahüseyin, Zeliha
In 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.
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 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.
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
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.
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 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.
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.
Restricted
Generalizations for Certain Bazilevic Functions
(SEAMS - Southeast Asian Mathematical Society, 2021) YAVUZ, EMEL; DAYMAZ, TUĞBA; Owa, Shigeyoshi
For analytic functions f(z) in the open unit disk U, an interesting class A(alpha, beta, gamma) is considered. The object of the present paper is to discuss some properties for f(z) in the class A(alpha, beta, gamma) and the class A(alpha, beta, infinity) for gamma -> infinity.
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, 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
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 KORAY
In 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.
Restricted
Independent Domination Polynomial of Zero-Divisor Graphs of Commutative Rings
(Springer, 2022) Gürsoy, Necla Kırcalı; ÜLKER, ALPER; Gürsoy, Arif
An 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.
Restricted
Minimal Generators of Annihilators of Even Neat Elements in the Exterior Algebra
(Scientific Technical Research Council Turkey-TUBITAK, 2022) ESİN, SONGÜL
This paper deals with an exterior algebra of a vector space whose base field is of positive characteristic. In this work, a minimal set of generators forming the annihilator of even neat elements of such an exterior algebra is exhibited. The annihilator of some special type of even neat elements is determined to prove the conjecture established in [3]. Moreover, a vector space basis for the annihilators under consideration is calculated.
Metadata only
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.
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.
Metadata only
On Group Analysis of Optimal Control Problems in Economic Growth Models
(American Institute of Mathematical Sciences, 2020) POLAT, GÜLDEN GÜN; Özer, Teoman
The optimal control problems in economic growth theory are analyzed by considering the Pontryagin's maximum principle for both current and present value Hamiltonian functions based on the theory of Lie groups. As a result of these necessary conditions, two coupled first-order differential equations are obtained for two different economic growth models. The first integrals and the analytical solutions (closed-form solutions) of two different economic growth models are analyzed via the group theory including Lie point symmetries, Jacobi last multiplier, Prelle-Singer method,_-symmetry and the mathematical relations among them.
Open Access
On Ramsey Dynamical Model and Closed-Form Solutions
(Springer Nature, 2021) POLAT, GÜLDEN GÜN; Özer, Teoman
This 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.
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
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.
Unknown
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.
Restricted
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.

Browse

Browsing Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science by Language "en"