Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science
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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 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 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 Generalizations for Certain Bazilevic Functions(SEAMS - Southeast Asian Mathematical Society, 2021) YAVUZ, EMEL; DAYMAZ, TUĞBA; Owa, ShigeyoshiFor 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.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 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 Restricted Minimal Generators of Annihilators of Even Neat Elements in the Exterior Algebra(Scientific Technical Research Council Turkey-TUBITAK, 2022) ESİN, SONGÜLThis 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.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.