23.04.2017   




Print Edition: ISSN 1584 - 2851
Online Edition: ISSN 1843 - 4401


Carpathian J. Math. is a category A journal in the CNCSIS classification

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Contents (PDF)
Vol. 30 (2014), No. 3, 15 October 2014
 
Well posed problem in sense of Hadamard, for a source produced acoustic perturbation propagation in a lined duct, carrying a gas flow
Author: Agneta M. Balint / Ștefan Balint
Abstract: The purpose of this paper is to replace Brambley's concept of "well posed differential equation" (J. Sound Vibr., 322 (2009) 1026-1037), related to the source produced acoustic perturbation propagation in a rectangular lined duct carrying a gas flow, with that of "well posed problem in Hadamard sense". The reason is that the concept introduced by Brambley is confusing, i.e. the same equation can be well posed or ill posed depending on the functional framework. For the source produced acoustic perturbation (SPAP) propagation problem the concept of "well posed problem in Hadamard sense" is defined as follows: for any SPAP, from a given set of SPAP-s , there exists a unique solution to the problem of propagation and the solution depends continuously on the SPAP. Necessary or sufficient conditions are derived for that the propagation problem be well posed in sense of Hadamard.
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No. of downloads: 283
The Bernstein quadrature formula revised
Author: Dan Bărbosu / Gheorghe Ardelean
Abstract: Starting with the Bernstein approximation formula on the interval $[a,b]$ a corresponding composite quadrature formula is constructed. Its coefficients and an estimation for the remainder term are determined. Numerical examples are also presented.
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No. of downloads: 207
From a Dieudonnè theorem concerning the Cauchy problem to an open problem in the theory of weakly Picard operators
Author: Vasile Berinde / Mădălina Păcurar / Ioan A. Rus
Abstract: Let $(X, d)$ be a complete metric space and let $f:X\to X$ be a self operator. In this paper we study the following two problems: Problem 1. Let $f$ be such that its fixed points set is a singleton, i.e., $F_f=\{x^*\}$. Under which conditions the next implication does hold: $f$ is asymptotically regular $\Rightarrow$ $f$ is a Picard operator? Problem 2. Let $f$ be such that, $F_f\neq\phi$. Under which conditions the following implication does hold: $f$ is asymptotically regular $\Rightarrow$ $f$ is a weakly Picard operator? The case of operators defined on a linear $L^*$-space is also studied.
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No. of downloads: 189
Oscillation of even-order neutral differential equations via comparison principles
Author: J. Džurina / B. Baculìková
Abstract: In the paper we offer oscillation criteria for even-order neutral differential equations \[ \left(r(t)\big[z^{(n-1)}(t)\big]^{\gamma} \right)'+q(t)x^{\gamma}(\sigma(t))=0, \] where $z(t)=x(t)+p(t)x(\tau(t)).$ Establishing a generalization of Philos and Staikos lemma, we introduce new comparison principles for reducing the examination of the properties of the higher order differential equation onto oscillation of the first order delay differential equations. The results obtained are easily verifiable.
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No. of downloads: 194
Modular $G$-graded algebras and $G$-algebras of endomorphisms
Author: Dana Debora Gliția
Abstract: We study Clifford Theory and field extensions for strongly group-graded algebras. In [Turull, A., Clifford theory and endoisomorphisms, J. Algebra 371 (2012), 510--520] and [Turull, A., Endoisomorphisms yield mo-dule and character correspondences, J. Algebra 394 (2013), 7--50] the author introduced the notion of endoisomorphism showing that there is a natural connection between it and Clifford Theory of finite group algebras. An endoisomorphism is an isomorphism between $G$-algebras of endomorphisms, where $G$ is a finite group. We consider here endoisomorphisms between modules over strongly $G$-graded algebras. An endoisomorphism induces equivalences of categories with some good compatibility properties.
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No. of downloads: 173
Infinitely differentiable functions represented into Newton interpolating series
Author: G. Groza / M. Jianu / N. Pop
Abstract: We study infinitely differentiable functions which are representable into a Newton interpolating series at a suitable interpolation sequence with terms in $[0,1]$. Applications of this series to approximate the solution of boundary value problems for linear systems of differential equations are presented.
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No. of downloads: 168
On the crossing numbers of Cartesian products of paths with special graphs
Author: Marián Klešč / Daniela Kravecová / Jana Petrillová
Abstract: There are known exact results of the crossing numbers of the Cartesian product of all graphs of order at most four with paths, cycles and stars. Moreover, for the path $P_n$ of length $n$, the crossing numbers of Cartesian products $G \Box P_n$ for all connected graphs $G$ on five vertices and for forty graphs $G$ on six vertices are known. In this paper, we extend these results by determining the crossing numbers of the Cartesian products $G \Box P_n$ for six other graphs $G$ of order six.
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No. of downloads: 281
Hyers-Ulam stability of some partial differential equations
Author: Nicolaie Lungu / Dorian Popa
Abstract: In this paper we obtain a Hyers-Ulam stability result for a first order partial differential equation in Banach spaces. As a consequence follows stability results for an $n$ order partial differential equation.
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No. of downloads: 167
Greedoids on vertex sets of $B$-joins of graphs
Author: Vadim E. Levit / Eugen Mândrescu
Abstract: Let $\Psi(G)$ be the family of all local maximum stable sets of graph $G$, i.e., $S\in\Psi(G)$ if $S$ is a maximum stable set of the subgraph induced by $S\cup N(S)$, where $N(S)$ is the neighborhood of $S$. It was shown that $\Psi(G)$ is a greedoid for every forest $G$. The cases of bipartite graphs, triangle-free graphs, and well-covered graphs. If $G_{1}$, $G_{2}$ are two disjoint graphs, and $B$ is a bipartite graph having $E(B)$ as an edge set and bipartition $\left\{V(G_{1}),V(G_{2})\right\}$, then by $B$-join of $G_{1},G_{2}$ we mean the graph $B\left(G_{1},G_{2}\right)$ whose vertex set is $V(G_{1})\cup V(G_{2})$ and edge set is $E(G_{1})\cup E(G_{2})\cup E\left( B\right) $. In this paper we present several necessary and sufficient conditions for $\Psi(B\left( G_{1},G_{2}\right) )$ to form a greedoid, an antimatroid, and a matroid, in terms of $\Psi(G_{1})$, $\Psi(G_{2})$ and $E\left( B\right) $.
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No. of downloads: 159
On the comparison of fisher information of some probability distributions
Author: Ion Mihoc / Cristina Ioana Fătu
Abstract: In 1998 Gupta, R. C., Gupta, P. L. and Gupta, R. D. have introduced the exponentiated exponential distribution (or the generalized exponential distribution) as a generalization of the standard exponential distribution. The mathematical properties of this distribution have been studied in detail by Gupta and Kundu (2001). The aim of this paper is to establish some relations concerning the Fisher's information of the generalized exponential distribution and the similar information corresponding in the case of the weighted version.
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No. of downloads: 174
On the topological structure of the set of singularities for interpolatory product integration rules
Author: Alexandru I. Mitrea
Abstract: This paper highlights the phenomenon of double condensation of singularities for interpolatory product integration rules, related to a class of projection operators (including Lagrange and Sturm-Liouville projections), associated to the Banach space of real continuous functions defined on a compact set in $\mathbb{R}$ of positive measure.
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No. of downloads: 161
The theory of some asymptotic fixed point theorems
Author: Anton S. Mureșan
Abstract: In this paper we present the theory about some fixed point theorems for convex contraction mappings. We give some results on data dependence of fixed points, on sequences of ope\-ra\-tors and fixed points, on well-possedness of fixed point problem, on limit shadowing property and on Ulam-Hyers stability for equations of fixed points.
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No. of downloads: 186
A Volterra functional-integral equation, via weakly Picard operators' technique
Author: Viorica Mureșan
Abstract: In this paper we consider a Volterra functional-integral equation with linear modifications of the arguments. We use weakly Picard operator's technique and we obtain existence and data dependence results for the solutions.
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No. of downloads: 153
Simultaneous extensions of polyadic groups
Author: Vasile Pop
Abstract: The reduction of two polyadic groups of arbitrary arity to the same group was studied by I. Corovei, I. Purdea and V. Pop. In this paper we give necessary and sufficient conditions under which two polyadic groups of $(m+1)$ and $(n+1)$ arity can be extended to the same $(k+1)$-group, where $k$ is multiple of $m$ and $n$.
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No. of downloads: 157
Best constant in Hyers-Ulam stability of some functional equations
Author: Dorian Popa / Ioan Rața
Abstract: We obtain the infimum of Hyers-Ulam constants for Cauchy, Jensen and Quadratic functional equations. Moreover, in each case the infimum is itself a Hyers-Ulam constant.
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No. of downloads: 161
High-order optimality conditions for degenerate variational problems
Author: Agnieszka Prusińska / Ewa Szczepanik / Alexey A. Tret'yakov
Abstract: The paper is devoted to the class of singular calculus of variations problems with constraints which are not regular mappings at the solution point. Methods of the $p$-regularity theory are used for investigation of isoperimetric and Lagrange singular problems. Necessary conditions for optimality in $p$-regular calculus of variations problem are presented.
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No. of downloads: 144
Approximation processes and asymptotic relations
Author: Ioan Rața
Abstract: The paper is concerned with two approximation processes: general King operators and Campiti-Metafune operators. They are related by similar Voronovskaja formulas. Their shape preserving and global smoothness preserving properties are investigated and compared.
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No. of downloads: 181
A new central configuration in the planar $N$-body problem
Author: Agnieszka Siluszyk
Abstract: B. Elmabsout [C. R. Acad. Sci. 329, Serie II (1991)] has proved that a central configuration of $2n$ bodies located on two concentric regular $n$-gons exists iff the polygons are homotetic or similar with an angle equal to $\frac{\pi}{n}$ and the masses on the same polygon are equal. In this paper we study the existence of a planar central configuration which consists of $3n$ bodies also situated on two regular polygons, the "interior" $n$-gon with equal masses and the "exterior" $2n$-gon with masses of two quantities, and these quantities alternate.
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No. of downloads: 159


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