Authors:Zhinan Xia, Zihui Li, Dingjiang Wang Abstract: In this paper, we introduce the concept of pseudo affine-periodic functionvia measure theory, that is measure pseudo $(Q, T)$-affine-periodic function.Existence, uniqueness of measure pseudo $(Q, T)$-affine-periodic solutionfor semilinear differential equations are investigated.The working tools are based on the Banach contraction mapping principleand Leray-Schauder alternative theorem.Finally, an example is presented to illustrate the main findings. PubDate: 2018-04-10 Issue No:Vol. 23 (2018)
Authors:Gabriel Bengochea, Luis Verde-Star, Manuel Ortigueira Abstract: We apply a general algebraic operational method to obtain solutions of ordinary differential equations. The solutions are expressed as series of scaled Hermite polynomials. We present some examples that show that the solutions obtained as truncated Hermite series give acceptable approximations to the exact solutions on intervals larger than the corresponding intervals for the solutions obtained as truncated Taylor series. Our method is algebraic and doesn't use any integral transforms. PubDate: 2018-04-10 Issue No:Vol. 23 (2018)
Authors:Tibor K Pogany, Saralees Nadarajah Abstract: An exact expression is established for thecharacteristic function of the order statistics of theStudent's $t$ distribution.The expression is a single infinite sum of terms involving themodified Bessel function of the second kind.It is simpler and yet more general than previously known expressions. PubDate: 2018-04-10 Issue No:Vol. 23 (2018)
Authors:Tomislav Marošević Abstract: Hausdorff distance can be used in various areas, where the problems of shape matching and comparison appear. We look at the Hausdorff distance between two hyperspheres in $\mathbb{R}^n$. With respect to different geometric objects, the Hausdorff distance between a segment and a hypersphere in $\mathbb{R}^n$ is given, too. Using the Mahalanobis distance, a modified Hausdorff distance between a segment and an ellipse in the plane, and generally between a segment and a hyper-ellipsoid in $\mathbb{R}^n$ is adopted. Finally, the modified Hausdorff distance between ellipses is obtained. PubDate: 2018-04-03 Issue No:Vol. 23 (2018)
Authors:Şule Yüksel Güngör, Nurhayat İspir Abstract: We dene the max-product (nonlinear) Bernstein-Chlodowsky operators andobtain some upper estimates of approximation error for some subclasses of functions. Wealso investigate the shape-preserving properties for these operators. PubDate: 2018-01-21 Issue No:Vol. 23 (2018)
Authors:Fatemeh Zarmehi, Ali Tavakoli Abstract: This paper deals with solving boundary value problems by Galerkin's method in which we use Gabor frames as trial and test functions. We show that, the preconditioned stiffness matrix resulted by discretization is compressible and its sparsity pattern involves a bounded polyhedron structure. Moreover, we introduce an adaptive Richardson iterative method to solve the resulting system and we also show that by choosing a suitable smoothing parameter, the method would be convergent. PubDate: 2018-01-18 Issue No:Vol. 23 (2018)
Authors:Nurettin Irmak, Kálmán Liptai, László Szalay Abstract: In this paper, we solve a few diophantine equations linked to balancing numbers and factorials. The basic problem $B_y=x!$ has only the one nontrivial solution $B_2=6=3!$, but it is a direct consequence of a theorem of F.~Luca. The more difficult problem $B_y=x_2!/x_1!$ is still open, but we solve it under different conditions. Two related problems are also studied. PubDate: 2017-12-13 Issue No:Vol. 23 (2017)
Authors:Trapti Neer, Ana Maria Acu, Purshottam Agrawal Abstract: This paper is in continuation of our work in [24], wherein we studied someapproximation properties of the Stancu-Durrmeyer operators based on q-integers. Here,we construct a bivariate generalization of these operators and study the rate of convergenceby means of the complete modulus of continuity and the partial moduli of continuity andthe degree of approximation with the aid of the Peetre's K functional. Subsequently, wedene the GBS(Generalized Boolean Sum) operators of Stancu- Durrmeyer type and givethe rate of approximation by means of the mixed modulus of smoothness and the Lipschitzclass of Bogel-continuous functions. PubDate: 2017-11-02 Issue No:Vol. 23 (2017)
Authors:Neven Grbac, Nevena Jurčević Peček Abstract: In this paper we study the reducibility of certain class of parabolically induced representations of $p$-adic hermitian quaternionic groups. We use the Jacquet modules techniques and the theory of $R$-groups to extend the reducibility results of Tadi\'{c} for split classical groups to the case of arbitrary hermitian quaternionic group.
Authors:Ufuk Öztürk, Esra Betül Koç Öztürk, Emilija Milojko Nešović Abstract: In this paper, we define equiformDarboux helices in Galilean space $\mathbb{G}_{3}$ and obtain their explicit parameter equations. We show that equiform Darboux helices have only non-isotropic axis and characterize equiform Darboux vectors of equiform Darboux helices in terms of equiform rectifying curves. We prove that an equiform Darboux vector of an equiform Darboux helix $\alpha$ is an equiform Darboux helix, if an admissible curve $\alpha$ is a rectifying curve. We also prove that there are no equiform curves of the constant precession and give some examples of the equiform Darboux helices. PubDate: 2017-10-17 Issue No:Vol. 23 (2017)
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