TR-Dizin İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/396
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Article Solutions to Nonlinear Second-Order Three-Point Boundary Value Problems of Dynamic Equations on Time Scales(Tubitak Scientific & Technological Research Council Turkey, 2019-05-29) Dogan, AbdulkadirIn this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional p-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; 24: 295-304].Article New Proofs of Fejer's and Discrete Hermite-Hadamard Inequalities With Applications(Ankara Univ, Fac Sci, 2023-06-22) Sekin, Cagla; Tamar, Mehmet Emin; Aliyev, Ilham A.New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions f : [a, b] -> R about the midpoint c = (a+b)/2 are obtained and the reverse Hardy inequality for convex functions f : (0, infinity) -> (0, infinity) is established.Article Citation - WoS: 3Citation - Scopus: 3MicroRNA Prediction Based on 3D Graphical Representation of RNA Secondary Structures(Tubitak Scientific & Technological Research Council Turkey, 2019-08-05) Sacar Demirci, Muserref Duygu; Demirci, Müşerref Duygu SaçarMicroRNAs (miRNAs) are posttranscriptional regulators of gene expression. While a miRNA can target hundreds of messenger RNA (mRNAs), an mRNA can be targeted by different miRNAs, not to mention that a single miRNA might have various binding sites in an mRNA sequence. Therefore, it is quite involved to investigate miRNAs experimentally. Thus, machine learning (ML) is frequently used to overcome such challenges. The key parts of a ML analysis largely depend on the quality of input data and the capacity of the features describing the data. Previously, more than 1000 features were suggested for miRNAs. Here, it is shown that using 36 features representing the RNA secondary structure and its dynamic 3D graphical representation provides up to 98% accuracy values. In this study, a new approach for ML-based miRNA prediction is proposed. Thousands of models are generated through classification of known human miRNAs and pseudohairpins with 3 classifiers: decision tree, naive Bayes, and random forest. Although the method is based on human data, the best model was able to correctly assign 96% of nonhuman hairpins from MirGeneDB, suggesting that this approach might be useful for the analysis of miRNAs from other species.Article Existence of Positive Solutions for Nonlinear Multipoint P-Laplacian Dynamic Equations on Time Scales(Tubitak Scientific & Technological Research Council Turkey, 2020-05-08) Dogan, AbdulkadirIn this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.Article Citation - WoS: 1Citation - Scopus: 1Existence Results for a Class of Boundary Value Problems for Fractional Differential Equations(Tubitak Scientific & Technological Research Council Turkey, 2021-05-20) Dogan, AbdulkadirBy application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the LeraySchauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).Article Citation - WoS: 2Citation - Scopus: 3An Asymptotic-Numerical Hybrid Method for Singularly Perturbed System of Two-Point Reaction-Diffusion Boundary-Value Problems(Tubitak Scientific & Technological Research Council Turkey, 2019-01-18) Cengizci, Suleyman; Natesan, Srinivasan; Atay, Mehmet TankThis article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.