Showing papers in "Annals of the West University of Timisoara: Mathematics and Computer Science in 2014"
TL;DR: In this paper, a generalized form of the extended Hurwitz-Lerch Zeta function is considered, which includes various integral representations, a differential formula, Mellin transforms and certain generating relations.
Abstract: Abstract Our purpose in this paper is to consider a generalized form of the extended Hurwitz-Lerch Zeta function. For this extended Hurwitz-Lerch Zeta function, we obtain some classical properties which includes various integral representations, a differential formula, Mellin transforms and certain generating relations. We further consider an application to probability distributions and also point out some important special cases of the main results.
18 citations
TL;DR: In this article, a brief description of these problems are made in terms of their denitions, followed by a comparative study of them, using both approaches: matrix geometry and graph theory.
Abstract: The bandwidth, average bandwidth, envelope, prole and antibandwidth of the matrices have been the subjects of study for at least 45 years. These problems have generated considerable interest over the years because of them practical relevance in ar- eas like: solving the system of equations, nite element methods, circuit design, hypertext layout, chemical kinetics, numerical geo- physics etc. In this paper a brief description of these problems are made in terms of their denitions, followed by a comparative study of them, using both approaches: matrix geometry and graph theory. Time evolution of the corresponding algorithms as well as a short description of them are made. The work also contains concrete real applications for which a large part of presented al- gorithms were developed.
12 citations
TL;DR: In this paper, the authors consider the solvability of nonlinear integral equations in the Banach algebra of continuous functions on a closed and bounded interval, using the measure of noncompactness and the suitable fixed point theorem for the product of two operators.
Abstract: In this paper, we study the existence of the solutions of a class of functional integral equations which contain a lot of classical nonlinear integral equations as special cases. We consider the solvability of the equations in the Banach algebra of continuous functions on a closed and bounded interval. The main tools here are the measure of noncompactness and the suitable fixed point theorem for the product of two operators in the Banach algebra. AMS Subject Classification (2010). Primary: 45M99, Sec- ondary: 47H09. Keywords. Nonlinear integral equation, Measure of noncompact- ness, Fixed point theorem, Banach algebra, Product of two oper- ators.
7 citations
TL;DR: In this article, a characterization of the (h, k)-trichotomy of an evolution operator in terms of (h and k)-dichotomy for two associated evolution operators is given.
Abstract: Abstract The paper considers some concepts of (h, k)-dichotomy and (h, k)-trichotomy for noninvertible evolution operators in Ba- nach spaces. A characterization of the (h, k)-trichotomy of an evolution operator in terms of (h, k)-dichotomy for two associated evolution operators is given. As applications of this result, charac- terizations for nonuniform exponential trichotomy and nonuniform polynomial trichotomy are obtained.
6 citations
TL;DR: New computable invariants, the "relevant level persistence numbers” and the “positive and negative bar codes” are introduced and explained, and how they are related to the bar codes for level persistence are explained.
Abstract: Persistence theory discussed in this paper is an appli- cation of algebraic topology (Morse Theory (29)) to Data Analysis, precisely to qualitative understanding of point cloud data, or PCD for short. PCD can be geometrized as a filtration of simplicial com- plexes (Vietoris-Rips complex (25) (36)) and the homology changes of these complexes provide qualitative information about the data. Bar codes describe the changes in homology with coefficients in a fixed field. When the coefficient field is Z2, the calculation of bar codes is done by ELZ algorithm (named after H. Edelsbrunner, D. Letscher, and A. Zomorodian (20)). When the coefficient field is R, we propose an algorithm based on the Hodge decomposi- tion (17). With Dan Burghelea and Tamal K. Dey we developed a persistence theory which involves level sets discussed in Section 4. We introduce and discuss new computable invariants, the "rel- evant level persistence numbers" and the "positive and negative bar codes", and explain how they are related to the bar codes for level persistence. We provide enhancements and modifications of ELZ algorithm to calculate such invariants and illustrate them by examples.
4 citations
TL;DR: In this article, the Hyers-Ulam stability on restricted domains of generalized Jensen functional equations was proved for the case where the Jensen functional equation is restricted to a restricted domain.
Abstract: Abstract We prove the Hyers-Ulam stability on restricted domains of generalized Jensen functional equation where . These results are applied to study of an asymptotic behavior of these functional equation.
3 citations
TL;DR: The necessary and sufficient conditions for conditional stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations were proved in this paper, where it is proved (necessary and sufficient) that
Abstract: Abstract It is proved (necessary and) suficient conditions for Ψ conditional stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations
3 citations
TL;DR: In this article, the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented, and some examples are given to exhibit different type of situation which show the requirements of conditions of their results.
Abstract: Abstract The aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.
3 citations
TL;DR: In this article, a characterization of exponential trichotomy for a cocycle over a semiflow in terms of exponential dichotomy of two associated cocycles over the same semiflow is given.
Abstract: The paper considers a concept of exponential trichotomy for cocycles over semiflows in Banach spaces and as a particular case the corresponding dichotomy concept. Our main objective is to give a characterization of exponential trichotomy for a cocycle over a semiflow in terms of exponential dichotomy of two associated cocycles over the same semiflow. AMS Subject Classification (2000). 34D05, 34D09
1 citations
TL;DR: In this paper, the notion of first countability of the hyperspace was studied and compared with that of the Euclidean plane in terms of the number of vertices of a hyperspace.
Abstract: In this paper the notion of first countability of the hyperspace $(\theta(X),\tau)$ has been studied and being compared with that of $X$.
1 citations
TL;DR: In this article, it is proved a necessary and sufficient condition for the existence of at least one Ψ-bounded solution of a linear non-homogeneous Lyapunov matrix differential equation.
Abstract: Abstract It is proved a necessary and sufficient condition for the existence of at least one Ψ- bounded solution of a linear non- homogeneous Lyapunov matrix differential equation. In addition, it is given a result in connection with the asymptotic behavior of the Ψ- bounded solutions of this equation.
TL;DR: In this article, the notions of N-subalgebras and N-lters based on Smarandache CI-algebra were introduced and their properties were investigated.
Abstract: In this paper, we introduce the notions of N- subalgebras and N-lters based on Smarandache CI-algebra and give a number of their properties. The relationship between N(Q;f)-subalgebras(lt ers) and N-subalgebras(lte rs) are also in- vestigated.
TL;DR: In this paper, the authors consider three general trichotomy concepts for noninvertible linear discrete-time systems in Banach spaces and characterizations of these concepts are obtained from the point of view of the projections sequences.
Abstract: Abstract This paper considers three general trichotomy concepts for noninvertible linear discrete-time systems in Banach spaces. Characterizations of these concepts are obtained from the point of view of the projections sequences. Some illustrative examples are given in order to prove that these concepts are distinct.
TL;DR: A x-coordinate recovery algorithm that can be used at any stage of a differential addition chain during the scalar multiplication of a point on the Edwards curve over the finite field Fp where p is an odd prime is presented.
Abstract: Abstract We present two computational approaches for the purpose of point compression and decompression on Edwards curves over the finite field Fp where p is an odd prime. The proposed algorithms allow compression and decompression for the x or y affine coordinates. We also present a x-coordinate recovery algorithm that can be used at any stage of a differential addition chain during the scalar multiplication of a point on the Edwards curve.
TL;DR: In this paper, the uniqueness of the form of factorizations of maximum length of a finite purely inseparable extension of a given field k of characteristic p > 0 was studied, where the data of m intermediate fields K1,K2, ···,Km of K/k such as K ≃ K 1 ⊗k K2 ⊆k K 2 ⊈k ···⊗ k Km.
Abstract: Résumé Let K/k be a finite purely inseparable extension of field k of characteristic p > 0. A factorization of length m of K/k is the data of m intermediate fields K1,K2, ··· ,Km of K/k such as K ≃ K1 ⊗k K2 ⊗k ···⊗k Km. In the present paper, we are especially interested in the uniqueness of the form of factorizations of maximum length.