1,721,475 research outputs found
On the Invariant Manifolds of the Fixed Point of a Second-Order Nonlinear Difference Equation
No full textTuran, Mehmet/0000-0002-1718-3902This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equationx(n+ 1)=alpha+beta x(n- 1)+x(n- 1)/x(n), where alpha> 0,0 <=beta<1$0\leqslant \beta and the initial conditionsx(- 1)andx(0)are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples
The Truncated <i>q</I>-bernstein Polynomials in the Case <i>q</I> > 1
No full textTuran, Mehmet/0000-0002-1718-3902The truncated q-Bernstein polynomials B-n,B-m,B-q (f; x), n is an element of N, and m is an element of N-0 emerge naturally when the q-Bernstein polynomials of functions vanishing in some neighbourhood of 0 are considered. In this paper, the convergence of the truncated q-polynomials on [0, 1] is studied. To support the theoretical results, some numerical examples are provided
On the Dynamics of a Second Order Nonlinear Difference Equation
Full text linkBu tezde iki keyfi parametre içeren ikinci dereceden özel bir rasyonel fark denklemi ele alınmıştır. Bu denklem bazı dinamik yapıları incelenmiştir: pozitif çözümlerin kararlılık ve yarı döngü analizleri; periyodik çözümlerin varlığı; denge noktasının yerel ve global kararlılık analizleri yapılmıştır. Bu tez dört bölümden oluşmaktadır. İlk bölümde fark denklemleri hakkında tarihsel bilgi, bunların bazı modellemeleri, ve yakın zamanda yapılmış bazı çalışmalar verilmiştir. İkinci bölümde, diziler ve fark denklemleriyle ilgili bilinen tanımlar ve sonuçlar gösterilmiştir. Asıl sonuçlar Bölüm 3'te sunulmuştur. Son bölümde kısa bir sonuç yazılmıştır.In this thesis, a certain second order fractional difference equation containing two arbitrary parameters is handled. The issue equation is investigated with aspects of some dynamics structures: the boundedness character and semi-cycle analysis of positive solutions are examined; existence of periodic solutions is studied; local and global stability analysis of the fixed point are performed. This thesis consists of four chapters. In the first chapter, historical information about difference equations, some modelings with them, and some recent studies are given. In the second chapter, basic concepts and known results concerning the sequences and difference equations are provided. Main results are presented in Chapter 3. A short conclusion is written down in the last chapter
On the Powers of the Kummer Distribution
No full textTuran, Mehmet/0000-0002-1718-3902The Kummer distribution is a probability distribution, whose density is given by f (x) = cx (alpha-1)(1 + delta x)(-gamma) e(-beta x), X > 0, where alpha, beta, delta > 0, gamma is an element of R and C is a normalizing constant. In this paper, the distributions of random variable X-P, p > 0, where X has the Kummer distribution, are considered with the conditions being IFR/DFR, some properties of moments depending on the parameters and the moment-(in) determinacy. In the case of moment-indeterminacy, exemplary Stieltjes classes are constructed.Science Citation Index Expande
On the Dynamics of the Nonlinear Difference Equation <i>xn</I>+1 = Α Plus Β<i>xn</I>-1 + <i>xn</I>-1
No full textTuran, Mehmet/0000-0002-1718-3902The boundedness and semi-cycle analysis of positive solutions, existence of period-2 solutions, and local and global asymptotic stability of the recursive sequence x(n+1) = alpha + beta x(n-1) + x(n-1)/x(n), n = 0,1,... are investigated where alpha is an element of [0, infinity), beta is an element of [0, 1) and the initial conditions x(-1) and x(0) are arbitrary positive real numbers. The paper concludes with some numerical examples to illustrate the theoretical results
Optimization of Central Pattern Generators
Full text linkGünümüzde insanlar gibi dinamik ve sağlam hareket edebilen insan robotunu bulmak en zor görevlerden biridir. İki ayaklı hareketi araştıran birçok araştırma olmasına rağmen, günümüzde insan yetenekleri olan robot bulunmamaktadır. Bu tezde robotlarda iki ayaklı hareket için Merkezi Örüntü Üreteçlerin (CPG) optimizasyonu ile ilgili olarak, üç matematiksel yapı tartışılmıştır. Ayrıca, bu tezde iki serbestlik dereceli bir bacakta ritmik hareket elde etmek için CPG'lerin, bağlantısız, tek yönlü veya çift yönlü bağlantılı gibi farklı şekillerde eşleşmeleri incelenmiştir. CPG'lerin üç matematiksel yapısı için de kararlılık analizi yapılmıştır. Bu tezde ele alınan farklı yapılardaki farklı eşleştirmeler arasından üçüncü yapıda çift yönlü eşleştirme en iyi sonucu vermiştir. Yapılardaki parametreler kararlılık bölgesinden seçildiği zaman, herhangi bir duyusal geribildirim olmaksızın önemli sonuçların elde edildiği gözlemlenmiştir.Up to this day, it is one of the most difficult tasks to find the humanoid robot that is able to move as dynamic and robust as humans do. Although there are many researches that have investigated bipedal locomotion, at current date, there is no robots with human's capabilities. In this study, with regard to the optimization of the CPGs for bipedal locomotion in robots, three mathematical structures are discussed. This thesis also investigates how different couplings of the CPGs such as uncoupled, unidirectional, bidirectional, are used to produce rhythmic patterns for one leg with two degrees of freedom. In each case of three types of the CPGs, stability analyzes is done. Bidirectional two CPGs of the third type give us the best performance comparing with all other cases studied here. When the parameters are taken from the stability region, it is seen that significant results are achieved without any sensory feedback
On the Moment-Determinacy of Power Lindley Distribution and Some Applications To Software Metrics
No full textTuran, Mehmet/0000-0002-1718-3902; Ostrovska, Sofiya/0000-0003-1842-7953The Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E. Ghitany et at who initiated the investigation of its properties and possible applications. In this article, new results on the power Lindley distribution are presented. The focus of this work is on the moment-(in)determinacy of the distribution for various values of the parameters. Afterwards, certain applications are provided to describe data sets of software metrics
Bifurcation of Discontinuous Limit Cycles of the Van Der Pol Equation
No full textAkhmet, Marat/0000-0002-2985-286X; Turan, Mehmet/0000-0002-1718-3902In this paper, we apply the methods of B-equivalence and psi-substitution to prove the existence of discontinuous limit cycle for the Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. The main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to demonstrate the theoretical results as well as application opportunities. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.Scientific and Technological Research Council of Turkey (TUBITAK) [111T320]This work was supported by the Grant 111T320 from the Scientific and Technological Research Council of Turkey (TUBITAK)
Stability Analysis of an Epidemic Model With Vaccination and Time Delay
Full text linkTuran, Mehmet/0000-0002-1718-3902This paper presents an epidemic model with varying population, incorporating a new vaccination strategy and time delay. It investigates the impact of vaccination with respect to vaccine efficacy and the time required to see the effects, followed by determining how to control the spread of the disease according to the basic reproduction ratio of the disease. Some numerical simulations are provided to illustrate the theoretical results
Bifurcation of Three-Dimensional Discontinuous Cycles
No full textAkhmet, Marat/0000-0002-2985-286X; Turan, Mehmet/0000-0002-1718-3902We consider three-dimensional discontinuous dynamical systems with non-fixed moments of impacts. Existence of the center manifold is proved for the system. The result is applied for the extension of the planar Hopf bifurcation theorem [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163-178]. Illustrative examples are constructed for the theory. (C) 2009 Elsevier Ltd. All rights reserved.Scientific and Technological Research Council of Turkey (TUBITAK) [106T418]This work was supported by Grant 106T418 from the Scientific and Technological Research Council of Turkey (TUBITAK)
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