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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Citation - WoS: 1
Analysis of Joint Reliability Importance in Linear M-Consecutive L-Out System
(Ankara Univ, Fac Sci, 2020) Kan, Cihangir; Ozkut, Murat
Combinatorial techniques have an important role to compute the joint reliability importance (JRI) of some coherent systems. We obtain combi- natorial formula for calculation of the JRI of two components in a generalised version of consecutive type systems consisting of n linearly ordered components such that system fails if and only if (i§) there are at least m l-overlapping runs of k consecutive failed components (n m(k l) + l; l < k). Overlapping runs mean having common elements which is denoted by l: We concentrate on both s-independent & identical components and exchangeable components. Explicit combinatorial formulae are provided for computing the JRI of the above mentioned cases. For both cases, we also compare the results with lin- ear m-consecutive-k-out-of-n:F system (nonoverlapping case when l = 0). In addition, some numerical and illustrative examples are presented.
Bibliometric Analysis on Methods and Tools Developed for DGE Analysis: Current Trends and Future Perspectives
(2025) Kochan, Necla
Diferansiyel gen ekspresyonu (DGE) analizi, yeni nesil dizileme teknolojilerinin ortaya çıkışıyla önemli bir ilgi kazanmıştır. Bu durum, DGE analizi için çeşitli yöntemlerin ve araçların geliştirilmesine yol açmıştır. Bu çalışmada, Biblioshiny ve VOSviewer yazılımları kullanılarak, incelenen dönem boyunca eğilimleri araştırmak amacıyla bibliyometrik analiz yapılmıştır. 2005-2023 yılları arasında Web of Science veri tabanından, diferansiyel gen ekspresyonu ile ilgili terimleri konu alan ilgili makaleler taranmıştır. İncelenen dönem boyunca yayımlanan eğilimleri göstermek için Biblioshiny ve VOSviewer yazılımları kullanılarak ağ haritaları oluşturulmuştur. Toplamda 729 çalışma, DGE analizi metodolojilerindeki, araçlarındaki ve paketlerindeki eğilimleri ortaya koymak amacıyla incelenmiştir. Bu amaçla, ülke, kurum, kaynak, yazar ve anahtar kelime üretkenliği açısından eş-yazarlık, bibliyografik eşleşme ve eş-oluşum analizleri yapılmıştır. 2005 yılından sonra çıktı ve atıf sayılarında artış gözlenmiştir. Çalışma süresince ABD ve Çin, DGE analizine en çok katkı sağlayan ülkeler olarak öne çıkmıştır. Zamansal çalışmalar, belirli aralıklarla bir miktar azalma olmakla birlikte, zaman içinde yayınlarda önemli bir artış olduğunu ortaya koymuştur. En büyük düşüş, 2008 ile 2010 yılları arasında gözlenmiştir. Bu düşüşlere rağmen, DGE analizi, herhangi bir hastalığın mekanizmalarını, gen işlevlerini ve terapötik hedefleri anlamadaki temel rolü nedeniyle genomikte kritik bir konu olmaya devam etmektedir. Bu eğilim, mevcut yöntemlerin ve araçların, çeşitli hastalıklarla ilişkili anahtar bilgilendirici genleri tanımlamak için yeterince güçlü kabul edildiğini göstermektedir.
Characterization of Distributions by Using the Conditional Expectations of Generalized Order Statistics
(2008) Yıldız, Tuğba; Bayramoğlu, İsmihan
In this study, some continuous distributions through the proper- ties of conditional expectations of generalized order statistics are characterized. Let $X_{1:n:m:k},...,X_{n:n:m:k}$ be the generalized order statistics, where n $nin Bbb{N},k>0;m_1,...,m_{n-1}in Bbb{R},M_r = sumlimits_{j=r}^{n-1}mj,1leq rleq n-1,gamma_r= k+n-r+M_r > 0$ for all $rin {1,...,n-1}$ and let m = ${m_1,...,m_{n-1}}$, if n =arbitrary, if n = 1. Characterization theorems for a general class of distributions are presented in terms of the function $E {g(X_{j:n:m:m+1)| X_{j-p:n:m:m+1} = X,_{j+q:n:m:m+1} = y}$ = A(x; y); where k = m+1, p and q are positive integers such that $p+1leq jleq n-q$ and g(.), A(., .) is a real valued function satisfying certain regularity conditions.
Chebyshev Polynomial Solution for the Sir Model of Covid 19
(2023) Özdek, Demet
In this study, we deal with solving numerically initial value problem of a mathematical model of COVID-19 pandemic in Turkey. This model is a SIR model consisting of a nonlinear system of differential equations. In order to solve these equations, a collocation approach based on the Chebyshev polynomials is used. Chebyshev polynomials are orthonormal polynomials and the orthonormality reduces the computation cost of the method as an advantage. Another advantage is that the present method does not require any discretization of the domain. So the method is easy to implement. The main idea of the method is to convert the model to a system of nonlinear algebraic equations. For this we write the approximate solution of the system and its first derivative as the truncated series of Chebyshev polynomials with unknown coefficients in matrix forms and then utilizing the collocation points, the SIR model is converted to a system of the nonlinear equations. The obtained system is solved for the unknown coefficients of the assumed Chebyshev polynomial solution by MATLAB, and so the approximate solution is obtained. In order to check the robustness of the method, residual error of the solution is reviewed. The results show that the method is efficient and accurate.
A Copula-Based Classification Using Agglomerated Feature Selection_Extraction: An Application in Cervical Cancer Diagnostic
(Ankara University, Faculty of Science, 2025) Kochan, Necla; Sheikhi, Ayyub
The use of gene-expression datasets has significantly enhanced our understanding of complex diseases such as cancer. The importance of the relationship between genes in analyzing such datasets has been highlighted, indicating their crucial role in diagnosing the disease accurately. In this study, we investigate the associated copulas between attributes to extract fundamental block-related components. Subsequently, we perform a classification algorithm based on these components to classify a labeled target variable. Specifically, examining the practical implications and effectiveness of our approach in real-world scenarios, we provide a novel illustrative application in cervical cancer classification.
Citation - WoS: 1
Citation - Scopus: 1
Distinguishability of a Source Function in a Time Fractional Inhomogeneous Parabolic Equation With Robin Boundary Condition
(Hacettepe Univ, Fac Sci, 2018) Özbilge Kahveci, Ebru; Demir, Ali
This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output mappings in the linear time fractional inhomogeneous parabolic equation D(t)(alpha)u(x, t) = (k(x)u(x))(x) + F(x, t) 0 < alpha <= 1, with Robin boundary conditions u(0, t) = psi(0)(t), u(x)(1,t ) = gamma(u(1, t) - psi(1)(t)). By defining the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] the inverse problem is reduced to the problem of their invertibility. Hence, the main purpose of this study is to investigate the distinguishability of the input-output mappings Phi[.] and Psi[.]. Moreover, the measured output data f(t) and h(t) can be determined analytically by a series representation, which implies that the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] can be described explicitly.
Gegenbauer Parameter Effect on Gegenbauer Wavelet Solutions of Lane-Emden Equations
(2024) Özdek, Demet
In this study, we aim to solve Lane-Emden equations numerically by the Gegenbauer wavelet method. This method is mainly based on orthonormal Gegenbauer polynomials and takes advantage of orthonormality which reduces the computational cost. As a further advantage, Gegenbauer polynomials are associated with a real parameter allowing them to be defined as Legendre polynomials or Chebyshev polynomials for some values. Although this provides an opportunity to be able to analyze the problem under consideration from a wide point of view, the effect of the Gegenbauer parameter on the solution of Lane-Emden equations has not been studied so far. This study demonstrates the robustness of the Gegenbauer wavelet method on three problems of Lane-Emden equations considering different values of this parameter.
Göl Kirliliği Probleminin Çözümü için Hızlı ve Güvenilir Bir Sayısal Yaklaşım
(2025) Gümgüm, Sevin
Su, hava gibi çevrenin temel bileşenlerinden biridir ve su kaynaklarının bozulması tüm canlı organizmaları tehdit etmektedir. Bu nedenle su kirliliği sorununu araştırmak büyük önem taşımaktadır. Göller, su kaynaklarının büyük bir bölümünü oluşturmaktadır. Bu çalışmanın amacı, üç adet birbiriyle bağlantılı gölden oluşan bir sistemdeki kirlilik dinamiklerini Gegenbauer dalgacık yöntemi ile analiz etmektir. Problem, her bir göldeki kirlilik oranının zamana göre değişimini temsil eden üç doğrusal diferansiyel denklem sistemi ile modellenmiştir. Zaman türevlerine, kesikli Gegenbauer dalgacık serisiyle yaklaşılmış ve diferansiyel denklem sistemi, cebirsel denklem sistemine dönüştürülmüştür. Elde edilen sayısal sonuçlar, literatürde mevcut diğer sayısal sonuçlarla karşılaştırılarak önerilen tekniğin güvenilir ve hızlı olduğu gösterilmiştir. Ayrıca, yöntemin yüksek doğruluk sağladığı ve bu nedenle diğer ekolojik olayların çözümünde de kullanılabileceği ortaya konmuştur.
Heterojen Araç Filolu Çok Depolu Araç Rotalama Problemi için Görsel Etkileşimli Sezgisel Çözüm Yöntemleri
(2016) Tütüncü, Gözde Yazgı
Araç Rotalama Problemleri (ARP) her birine belli büyüklükteki ve nitelikteki ürün ya da yolcuların araç filosu ile ulaştırılması gereken birçok sayıda müşteri ya da durak içerir. ARP yöneylem araştırması ve yönetim bilimleri disiplinlerinin hem akademik araştırma hem de uygulama açısından en önemli alanlarından birisidir. Gerçek hayatta ARP problemleri temel ARP ?nin ötesinde ek kısıtlar ve zorluklar içermektedir. Bu projede gerçek hayatta çokça rastlanan ve birçok tedarik firması tarafından göz önüne alınıp önemsenen Heterojen Araç- filolu Çok-depolu Araç Rotalama Problemi (HAÇARP) ve HAÇARP ?in yaygın kullanımlı bir versiyonu olan Geri-toplamalı HAÇARP (GHAÇARP) ele alınmıştır. Onaylanan Bütçe: Bu projede öncelikle HAÇARP için yeni sezgisel yöntemler geliştirilmiş, geliştirilen sezgiseller literatürdeki karşılaştırmalı problem örnekleriyle test edilmiş ve gerçek hayat problemlerini çözmek üzere uygulamaya sunulmuştur. Daha sonra GHAÇARP için yeni bir matematiksel model önerilmiş, gerçek hayat problemlerini baz alan yeni problem örnekleri oluşturulmuş veönerilen model kullanılarak bu problemlerin gevşetilmiş çözümleri elde edilmiştir. Buna ek olarak, HAÇARP için geliştirilen yeni sezgisel yöntemler göz önüne alınarak GHAÇARP için de yeni bir sezgisel geliştirilmiş ve önerilen problem örnekleriyle test edilmiş ve gerçek hayat problemlerini çözmek üzere uygulamaya sunulmuştur. Sonuç olarakgünlük hayatta çeşitli firmalarca kullanılabilir, farklı araç rotalama problemlerinin çözümü için uyarlanabilir, görsel etkileşimli ve sezgisel yöntemlere dayalı ve ele alınan problemleri iyi sonuçlarla çözebilen bir Karar Destek Sistemi geliştirilmiştir
Laguerre Wavelet Method for Solving Troesch Equation
(2019) Gümgüm, Sevin
The purpose of this paper is to illustrate the use of the Laguerre wavelet method in thesolution of Troesch’s equation, which is a stiff nonlinear equation. The unknownfunction is approximated by Laguerre wavelets and the equation is transformed into asystem of algebraic equations. One of the advantages of the method is that it does notrequire the linearization of the nonlinear term. The problem is solved for differentvalues of Troesch’s parameter (??) and the results are compared with both the analyticaland other numerical results to validate the accuracy of the method.
Citation - WoS: 17
Citation - Scopus: 19
Lebesgue-Stieltjes Measure on Time Scales
(Scientific Technical Research Council Turkey-Tubitak, 2009) Deniz, Ash; Ufuktepe, Ünal
The 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.
The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics
(2019) Kürkçü, Ömür Kıvanç; Dönmez Demir, Duygu; Sezer, Mehmet; Çınardalı, Tuğçe
In this study, the Legendre operational matrix method based on collocation points is introduced to solve high order ordinary differentialequations with some nonlinear terms arising in physics and mechanics. This technique transforms the nonlinear differential equationinto a matrix equation with unknown Legendre coefficients via mixed conditions. This solution of this matrix equation yields theLegendre coefficients of the solution function. Thus, the approximate solution is obtained in terms of Legendre polynomials. Some testproblems together with residual error estimation are given to show the usefulness and applicability of the method and the numericalresults are compared.
Citation - WoS: 11
Citation - Scopus: 14
Legendre Wavelet Solution of High Order Nonlinear Ordinary Delay Differential Equations
(Scientific Technical Research Council Turkey-Tubitak, 2019) Gumgum, Sevin; Ersoy Ozdek, Demet; Ozaltun, Gokce
The 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.
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations
(2020) Gümgüm, Sevin; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Bayku S Sava Saner Il, Nurcan
This paper presents the Lucas polynomial solution of second-order nonlinearordinary differential equations with mixed conditions. Lucas matrix method is based oncollocation points together with truncated Lucas series. The main advantage of the methodis that it has a simple structure to deal with the nonlinear algebraic system obtained frommatrix relations. The method is applied to four problems. In the first two problems, exactsolutions are obtained. The last two problems, Bratu and Duffing equations are solvednumerically; the results are compared with the exact solutions and some other numericalsolutions. It is observed that the application of the method results in either the exact oraccurate numerical solutions.
Citation - WoS: 11
Lucas Polynomial Solution for Neutral Differential Equations With Proportional Delays
(Turkic World Mathematical Soc, 2020) Gümgüm, Sevin; Savasaneril, N. Baykus; Kurkcu, O. K.; Sezer, M.
This paper proposes a combined operational matrix approach based on Lucas and Taylor polynomials for the solution of neutral type differential equations with proportional delays. The advantage of the proposed method is the ease of its application. The method facilitates the solution of the given problem by reducing it to a matrix equation. Illustrative examples are validated by means of absolute errors. Residual error estimation is presented to improve the solutions. Presented in graphs and tables the results are compared with the existing methods in literature.
Citation - WoS: 17
Citation - Scopus: 20
Lucas Polynomial Solution of Nonlinear Differential Equations With Variable Delays
(Hacettepe Univ, Fac Sci, 2020) Gumgum, Sevin; Savasaneril, Nurcan Baykus; Kürkçü, ÖmÜr Kıvanç; Sezer, Mehmet; Kürkҫü, Ömür Kıvanҫ
In this study, a novel matrix method based on Lucas series and collocation points has been used to solve nonlinear differential equations with variable delays. The application of the method converts the nonlinear equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Lucas coefficients. The method is tested on three problems to show that it allows both analytical and approximate solutions.
The Mrl Function of the K-Out System With Nonidentical Components in the System Level
(2006) Gürler, Selma; Bayramoğlu, İsmihan
A k-out-of-n system is working if at least k of its n components are operating. The system breaks down at the time of the (n-k+1) th component failure. Since all components start working at the same time, this approach leads to a kind of redundancy called active redundancy of n-k components. Important particular cases of k-out-of-n system are parallel and series systems corresponding to k=1 and k=n, respectively. In this paper, we consider the mean residual life (MRL) function of a parallel and k-out-of-n systems consisting of n components having independent and nonidentically distributed lifetimes. We provide new representations of the MRL function for such systems. The MRL functions of systems consisting of components having exponential and power distributed lifetimes are presented. Also we introduce a numerical example to study the effect of increasing the system level and various parameters on the mean residual life of the systems. Further, the relation between the mean residual life for the system and the mean residual life of its components is investigated.
A New Epsilon-Local Dependence Measure and Dependence Maps
(2007) Bayramoğlu, İsmihan; Üçer, H. Burcu
In the present work, we introduce a new local dependence function characterizing dependence structure between two random variables in an $varepsilon$-neighborhood of a particular point from the domain of underlying bivariate distribution and investigate its properties. As an example the local dependence function for Farlie-Gumbel-Morgenstern distribution is provided. Also, we construct dependence maps for some pairs of random variables. We use the estimator of local dependence function to construct the dependence map. Permutation test algorithm is applied for P=500 to obtain more accurate result in dependence map and also several examples are provided.
A NEW NUMERICAL METHOD FOR SOLVING DELAY INTEGRAL EQUATIONS WITH VARIABLE BOUNDS BY USING GENERALIZED MOTT POLYNOMIALS
(2018) Kürkçü, Ömür Kıvanç
In this study, the delay integral equations with variable bounds are considered and their approximate solutions are obtained byusing a new numerical method based on matrices, collocation points and the generalized Mott polynomials including aparameter- ? . An error analysis technique consisting of the residual function is performed. The numerical examples are appliedto illustrate the practicability and usability of the method. The behavior of the solutions is monitored in terms of the parameter-? . The accuracy of the method is scrutinized for different values of N and also the numerical results are discussed in figuresand tables.
Citation - WoS: 11
Citation - Scopus: 11
A 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) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
In 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.

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