TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/4
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Article Citation - WoS: 17Citation - Scopus: 19Lebesgue-Stieltjes Measure on Time Scales(Scientific Technical Research Council Turkey-Tubitak, 2009-01-01) Deniz, Ash; Ufuktepe, ÜnalThe theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory oil time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes Delta and del-measures and by using these measures, we define ail integral adapted to time scales, specifically Lebesgue-Stieltjes Delta-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes Delta-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes Delta-integral.Article Citation - WoS: 3Citation - Scopus: 3A Reduced Computational Matrix Approach With Convergence Estimation for Solving Model Differential Equations Involving Specific Nonlinearities of Quartic Type(Scientific Technical Research Council Turkey-Tubitak, 2020-01-20) Kürkçü, ÖmÜr KıvançThis study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-alpha, matrix equations, and Chebyshev-Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-alpha. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled methodology involving the proposed method and Laplace-Pade technique. The convergence estimation is established via residual function. Numerical and graphical results are indicated to discuss the validity and efficiency of the method.Article Citation - WoS: 4Citation - Scopus: 4On the Hilbert Formulas and of Change of Integration Order for Some Singular Integrals in the Unit Circle(Scientific Technical Research Council Turkey-Tubitak, 2018-05-08) Bory Reyes, Juan; Abreu Blaya, Ricardo; Perez De La Rosa, Marco Antonio; Schneider, Baruch; Rosa, Marco Antonio Perez De La; Reyes, Juan Bory; Blaya, Ricardo AbreuWe obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory when alpha is a complex number. Such formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincare-Bertrand formula for the alpha-hyperholomorphic singular integrals in the unit circle is presented.Article Citation - WoS: 11Citation - Scopus: 11A Novel Graph-Operational Matrix Method for Solving Multidelay Fractional Differential Equations With Variable Coefficients and a Numerical Comparative Survey of Fractional Derivative Types(Scientific Technical Research Council Turkey-Tubitak, 2019-01-18) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, MehmetIn this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.Article Citation - WoS: 11Citation - Scopus: 14Legendre Wavelet Solution of High Order Nonlinear Ordinary Delay Differential Equations(Scientific Technical Research Council Turkey-Tubitak, 2019-05-29) Gumgum, Sevin; Ersoy Ozdek, Demet; Ozaltun, Gokce; Özdek, Demet ErsoyThe purpose of this paper is to illustrate the use of the Legendre wavelet method in the solution of high-order nonlinear ordinary differential equations with variable and proportional delays. The main advantage of using Legendre polynomials lies in the orthonormality property, which enables a decrease in the computational cost and runtime. The method is applied to five differential equations up to sixth order, and the results are compared with the exact solutions and other numerical solutions when available. The accuracy of the method is presented in terms of absolute errors. The numerical results demonstrate that the method is accurate, effectual and simple to apply.Article Enlarging Multiword Expression Dataset by Co-Training(Scientific Technical Research Council Turkey-Tubitak, 2018-09-28) Kumova Metin, Senem; Metin, Senem KumovaIn multiword expressions (MWEs), multiple words unite to build a new unit in language. When MWE identification is accepted as a binary classification task, one of the most important factors in performance is to train the classifier with enough number of labelled samples. Since manual labelling is a time-consuming task, the performances of MWE recognition studies are limited with the size of the training sets. In this study, we propose the comparison-based and common-decision co-training approaches in order to enlarge the MWE dataset. In the experiments, the performances of the proposed approaches were compared to those of the standard co-training [1] and manual labelling where statistical and linguistic features are employed as two different views of the MWE dataset [2]. A number of tests with different settings were performed on a Turkish MWE dataset. Ten different classifiers were utilized in the experiments and the best performing classifier pair was observed to be the SMO-SMO pair. The experimental results showed that the common-decision co-training approach is an alternative to hand-labeling of large MWE datasets and both newly proposed approaches outperform the standard co-training [2] when the training set is to be enlarged in MWE classification.Article Citation - Scopus: 1Performance Analysis and Feature Selection for Network-Based Intrusion Detection With Deep Learning(Scientific Technical Research Council Turkey-Tubitak, 2021) Caner, Serhat; Erdogmus, Nesli; Erten, Y. MuratAn intrusion detection system is an automated monitoring tool that analyzes network traffic and detects malicious activities by looking out either for known patterns of attacks or for an anomaly. In this study, intrusion detection and classification performances of different deep learning based systems are examined. For this purpose, 24 deep neural networks with four different architectures are trained and evaluated on CICIDS2017 dataset. Furthermore, the best performing model is utilized to inspect raw network traffic features and rank them with respect to their contributions to success rates. By selecting features with respect to their ranks, sets of varying size from 3 to 77 are assessed in terms of classification accuracy and time efficiency. The results show that recurrent neural networks with a certain level of complexity can achieve comparable success rates with state-of-the-art systems using a small feature set of size 9; while the average time required to classify a test sample is halved compared to the complete set.