DSpace Collection: Mathematica Balkanica New Series, Vol. 26, 2012, Fasc. 1-2
http://hdl.handle.net/10525/2617
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On Some Generalizations of Classical Integral Transforms
http://hdl.handle.net/10525/2674
Title: On Some Generalizations of Classical Integral Transforms<br/><br/>Authors: Virchenko, Nina<br/><br/>Abstract: Using the generalized confluent hypergeometric function [6] some new integral transforms are introduced. They are generalizations of some classical integral transforms, such as the Laplace, Stieltjes, Widder-potential, Glasser etc. integral transforms. The basic properties of these generalized integral transforms and their inversion formulas are obtained. Some examples are also given.<br/><br/>Description: MSC 2010: 44A15, 44A20, 33C60Sun, 01 Jan 2012 00:00:00 GMTSO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions
http://hdl.handle.net/10525/2672
Title: SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions<br/><br/>Authors: Shilin, Ilya<br/><br/>Abstract: The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).<br/><br/>Description: MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40Sun, 01 Jan 2012 00:00:00 GMTOn a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series
http://hdl.handle.net/10525/2671
Title: On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series<br/><br/>Authors: Rakha, Medhat A.<br/><br/>Description: MSC 2010: 33C20Sun, 01 Jan 2012 00:00:00 GMTNumber Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants
http://hdl.handle.net/10525/2669
Title: Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants<br/><br/>Authors: Rajkovic, Predrag M.; Barry, Paul; Savic, Natasa<br/><br/>Abstract: This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases.<br/><br/>Description: MSC 2010: 11B83, 05A19, 33C45Sun, 01 Jan 2012 00:00:00 GMTGrowth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions
http://hdl.handle.net/10525/2667
Title: Growth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions<br/><br/>Authors: Polatoglu, Yasar; Aydogan, Melike; Yemisci, Arzu<br/><br/>Description: AMS Subj. Classification: 30C45Sun, 01 Jan 2012 00:00:00 GMTInequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions
http://hdl.handle.net/10525/2665
Title: Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions<br/><br/>Authors: Paneva-Konovska, Jordanka<br/><br/>Abstract: We consider some families of 3-index generalizations of the classical Mittag-Le²er functions and study the behaviour of these functions in domains of the complex plane. First, some inequalities in the complex plane and on its compact subsets are obtained. We also prove an asymptotic formula for the case of "large" values of the indices of these functions. Similar results have also been obtained by the author for the classical Bessel functions and their Wright's generalizations with 2, 3 and 4 parameters, as well as for the classical and multi-index Mittag-Le²er functions.<br/><br/>Description: MSC 2010: 33E12, 30A10, 30D15, 30E15Sun, 01 Jan 2012 00:00:00 GMTCalculus of Variations with Classical and Fractional Derivatives
http://hdl.handle.net/10525/2663
Title: Calculus of Variations with Classical and Fractional Derivatives<br/><br/>Authors: Odzijewicz, Tatiana; Torres, Delfim F. M.<br/><br/>Abstract: We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.<br/><br/>Description: MSC 2010: 49K05, 26A33Sun, 01 Jan 2012 00:00:00 GMTα-Mellin Transform and One of Its Applications
http://hdl.handle.net/10525/2661
Title: α-Mellin Transform and One of Its Applications<br/><br/>Authors: Nikolova, Yanka<br/><br/>Abstract: We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem 3 (α-Mellin transform of fractional R-L derivatives) are presented, and the proofs can be found in [5]. Now we prove some further properties of this integral transform, useful for its application to solving some fractional order differential equations.<br/><br/>Description: MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45Sun, 01 Jan 2012 00:00:00 GMTSpecial Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
http://hdl.handle.net/10525/2660
Title: Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type<br/><br/>Authors: Milovanovic, Gradimir V.; Cvetkovic, Aleksandar S.<br/><br/>Abstract: In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems with strong nonclassical weights on (0;+1), including a conjecture for an oscillatory weight on [¡1; 1]. Finally, we give some new results on orthogonal polynomials on radial rays in the complex plane.<br/><br/>Description: MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32Sun, 01 Jan 2012 00:00:00 GMTConflict-Controlled Processes Involving Fractional Differential Equations with Impulses
http://hdl.handle.net/10525/2658
Title: Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses<br/><br/>Authors: Matychyn, Ivan; Chikrii, Arkadii; Onyshchenko, Viktoriia<br/><br/>Abstract: Here we investigate a problem of approaching terminal (target) set by a system of impulse differential equations of fractional order in the sense of Caputo. The system is under control of two players pursuing opposite goals. The first player tries to bring the trajectory of the system to the terminal set in the shortest time, whereas the second player tries to maximally put off the instant when the trajectory hits the set, or even avoid this meeting at all. We derive analytical solution to the initial value problem for a fractional-order system involving impulse effects. As the main tool for investigation serves the Method of Resolving Functions based on the technique of inverse Minkowski functionals. By constructing and investigating special setvalued mappings and their selections, we obtain sufficient conditions for the game termination in a finite time. In so doing, we substantially apply the technique of L £ B-measurable setvalued mappings and their selections to ensure, as a result, superpositional measurability of the first player's controls.<br/><br/>Description: MSC 2010: 34A08, 34A37, 49N70Sun, 01 Jan 2012 00:00:00 GMTThe Deformed Trigonometric Functions of two Variables
http://hdl.handle.net/10525/2654
Title: The Deformed Trigonometric Functions of two Variables<br/><br/>Authors: Marinkovic, Sladjana; Stankovic, Miomir; Mulalic, Edin<br/><br/>Abstract: Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed sine and cosine functions and analyze their various properties. We give series expansions of these functions, formulas which have their similar counterparts in the classical trigonometry, and interesting difference and differential properties.<br/><br/>Description: MSC 2010: 33B10, 33E20Sun, 01 Jan 2012 00:00:00 GMTSome Completely Monotonic Properties for the (p, g)-Gamma Function
http://hdl.handle.net/10525/2653
Title: Some Completely Monotonic Properties for the (p, g)-Gamma Function<br/><br/>Authors: Krasniqi, Valmir; Merovci, Faton<br/><br/>Description: MSC 2010: 33B15, 26A51, 26A48Sun, 01 Jan 2012 00:00:00 GMTEPQ Model with Imperfect Quality Raw Material
http://hdl.handle.net/10525/2650
Title: EPQ Model with Imperfect Quality Raw Material<br/><br/>Authors: El-Kassar, Abdul-Nasser; Salameh, Moueen; Bitar, Mokarram<br/><br/>Abstract: The classical economic production model (EPQ) has been extended in many directions to incorporate factors encountered in real-life situations. In this paper, an EPQ model that accounts for the cost of raw material needed for production is examined. It is assumed that the raw material acquired from the supplier contains a percentage of imperfect quality items. At the beginning of the inventory cycle, the raw material is received instantaneously, and a 100% screening process for detecting the imperfect quality items is conducted. Two different scenarios are considered. In the first, the imperfect quality items of the raw material are sold at a discounted price at the end of the screening period. In the second scenario, the imperfect quality items are kept in stock until the end of the inventory cycle and returned to the supplier when the next order is received.<br/><br/>Description: MSC 2010: 26A33, 33E12, 33C60, 44A20Sun, 01 Jan 2012 00:00:00 GMTInverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation
http://hdl.handle.net/10525/2649
Title: Inverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation<br/><br/>Authors: Kalla, S.L.; Virchenko, N.; Alexandrovich, I.<br/><br/>Description: MSC 2010: 35J05, 33C10, 45D05Sun, 01 Jan 2012 00:00:00 GMTIntegral Representations of Functional Series with Members Containing Jacobi Polynomials
http://hdl.handle.net/10525/2647
Title: Integral Representations of Functional Series with Members Containing Jacobi Polynomials<br/><br/>Authors: Jankov, Dragana; Pogany, Tibor K.<br/><br/>Abstract: In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.<br/><br/>Description: MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10Sun, 01 Jan 2012 00:00:00 GMTExact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
http://hdl.handle.net/10525/2646
Title: Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations<br/><br/>Authors: Dimovski, Ivan; Tsankov, Yulian<br/><br/>Abstract: In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces to n one-dimensional cases. In the Duhamel representations of the solution are used multidimensional non-classical convolutions. This explicit representation may be used both for theoretical study, and for numerical calculation of the solution.<br/><br/>Description: MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05Sun, 01 Jan 2012 00:00:00 GMT