Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 1On The Problem Of Schoenberg On Rn(University of Prishtina, 2024) Kushpel, Alexander; Taş, KenanArticle Citation - Scopus: 1On the Problem of Schoenberg On Rn(Univ Prishtines, 2024) Kushpel, Alexander; Tas, KenanIn 1946 Schoenberg introduced splines on R, which play now one of the central roles in Numerical Analysis, and posed the problem on spline interpolation. The main aim of this article is to establish explicit representations of fundamental splines on Rn and give a positive solution of the problem of Schoenberg on RnArticle Citation - Scopus: 45Interpolative Kannan-Meir Type Contraction(DergiPark, 2021) Karapınar, E.In this short manuscript, we revisit the renowned contraction’s of Meir-Keeler by involving the interpolation theory in the context of complete metric space. We provide a simple example to illustrate the validity of the observed result. © 2021, DergiPark. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3The Refinement-Schemes Unified Algorithms for Certain Nth Order Linear and Nonlinear Differential Equations With a Set of Constraints(Springer, 2021) Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; Ejaz, Syeda TehminaWe first present a generalized class of binary interpolating refinement schemes and their properties. Then the refinement-schemes-based unified algorithms for the solution of certain nth order linear and nonlinear differential equations with a set of constraints are presented. Moreover, several algorithms based on the refinement schemes for solving differential equations are the special cases of our algorithms.Article Citation - WoS: 2Citation - Scopus: 4Construction and Analysis of Unified 4-Point Interpolating Nonstationary Subdivision Surfaces(Springer, 2021) Mustafa, Ghulam; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Bari, MehwishSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having C1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence >= 3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409-420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.Article A 6-Point Subdivision Scheme and Its Applications for the Solution of 2nd Order Nonlinear Singularly Perturbed Boundary Value Problems(Amer inst Mathematical Sciences-aims, 2020) Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; Mustafa, Ghulam; Anjum, KaweetaIn this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.Article Interpolation of Exponential-Type Functions on a Uniform Grid by Shifts of a Basis Function(Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Kushpel, Alexander; Levesley, Jeremy; Sun, XinpingIn this paper, we present a new approach to solving the problem of interpolating a continuous function at (n + 1) equally-spaced points in the interval [0, 1], using shifts of a kernel on the (1/n)-spaced infinite grid. The archetypal example here is approximation using shifts of a Gaussian kernel. We present new results concerning interpolation of functions of exponential type, in particular, polynomials on the integer grid as a step en route to solve the general interpolation problem. For the Gaussian kernel we introduce a new class of polynomials, closely related to the probabilistic Hermite polynomials and show that evaluations of the polynomials at the integer points provide the coefficients of the interpolants. Finally we give a closed formula for the Gaussian interpolant of a continuous function on a uniform grid in the unit interval (assuming knowledge of the discrete moments of the Gaussian).Article Citation - WoS: 4Citation - Scopus: 4A Class of Refinement Schemes With Two Shape Control Parameters(Ieee-inst Electrical Electronics Engineers inc, 2020) Hameed, Rabia; Mahmood, Ayesha; Baleanu, Dumitru; Mustafa, GhulamA subdivision scheme defines a smooth curve or surface as the limit of a sequence of successive refinements of given polygon or mesh. These schemes take polygons or meshes as inputs and produce smooth curves or surfaces as outputs. In this paper, a class of combine refinement schemes with two shape control parameters is presented. These even and odd rules of these schemes have complexity three and four respectively. The even rule is designed to modify the vertices of the given polygon, whereas the odd rule is designed to insert a new point between every edge of the given polygon. These schemes can produce high order of continuous shapes than existing combine binary and ternary family of schemes. It has been observed that the schemes have interpolating and approximating behaviors depending on the values of parameters. These schemes have an interproximate behavior in the case of non-uniform setting of the parameters. These schemes can be considered as the generalized version of some of the interpolating and B-spline schemes. The theoretical as well as the numerical and graphical analysis of the shapes produced by these schemes are also presented.Article Citation - WoS: 16Citation - Scopus: 18On the Asymptotic Integration of a Class of Sublinear Fractional Differential Equations(Aip Publishing, 2009) Mustafa, Octavian G.; Baleanu, Dumitru; Bleanu, DumitruWe estimate the growth in time of the solutions to a class of nonlinear fractional differential equations D-0+(alpha)(x-x(0))=f(t,x) which includes D-0+(alpha)(x-x(0))=H(t)x(lambda) with lambda is an element of(0,1) for the case of slowly decaying coefficients H. The proof is based on the triple interpolation inequality on the real line and the growth estimate reads as x(t)=o(t(a alpha)) when t ->+infinity for 1>alpha>1-a>lambda>0. Our result can be thought of as a noninteger counterpart of the classical Bihari asymptotic integration result for nonlinear ordinary differential equations. By a carefully designed example we show that in some circumstances such an estimate is optimal.