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. PDF |

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. PDF |

No. of downloads: 207

From a DieudonnÃ¨ 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. PDF |

No. of downloads: 189

Oscillation of even-order neutral differential equations via comparison principles

Author: J. DÅ¾urina / B. BaculÃ¬kovÃ¡

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. PDF |

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. PDF |

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. PDF |

No. of downloads: 168

On the crossing numbers of Cartesian products of paths with special graphs

Author: MariÃ¡n KleÅ¡Ä / Daniela KravecovÃ¡ / Jana PetrillovÃ¡

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. PDF |

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. PDF |

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) $. PDF |

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. PDF |

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. PDF |

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. PDF |

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. PDF |

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 $n$. PDF |

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. PDF |

No. of downloads: 161

High-order optimality conditions for degenerate variational problems

Author: Agnieszka PrusiÅ„ska / 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. PDF |

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. PDF |

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. PDF |