OPUSCULA MATHEMATICA

Permanent URI for this communityhttps://repo.agh.edu.pl/handle/AGH/102755

Adres wydawniczy: Kraków : Wydawnictwa AGH, 2005-
O czasopiśmie: http://www.opuscula.agh.edu.pl/
ISSN: 1232-9274 e-ISSN: 2300-6919
DOI: http://dx.doi.org/10.7494/OpMath

The journal Opuscula Mathematica publishes original research articles that are of significant importance in all areas of Discrete Mathematics, Functional Analysis, Differential Equations, Mathematical Physics, Nonlinear Analysis, Numerical Analysis, Probability Theory and Statistics, Theory of Optimal Control and Optimization, Financial Mathematics and Mathematical Economic Theory, Operations Research, and other areas of Applied Mathematics.

New! Aktualny numer: 2026 - Vol. 46 - No. 2

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Now showing 1 - 20 of 1034

Access status: Open Access ,
On intertwining and ω-hyponormal operators
(2005) Otieno, M. O.
Given $A, B\in B(H)$, the algebra of operators on a Hilbert Space $H$, define $\delta_{A,B}: B(H) \to B(H)$ and $\Delta_{A,B}: B(H) \to B(H)$ by $\delta_{A,B}(X)=AX-XB$ and $\Delta_{A,B}(X)=AXB-X$. In this note, our task is a twofold one. We show firstly that if $A$ and $B^{*}$ are contractions with $C_{.}o$ completely non unitary parts such that $X \in \ker \Delta_{A,B}$, then $X \in \ker \Delta_{A*,B*}$. Secondly, it is shown that if $A$ and $B^{*}$ are $w$-hyponormal operators such that $X \in \ker \delta_{A,B}$ and $Y \in \ker \delta_{B,A}$, where $X$ and $Y$ are quasi-affinities, then $A$ and $B$ are unitarily equivalent normal operators. A $w$-hyponormal operator compactly quasi-similar to an isometry is unitary is also proved.
Access status: Open Access ,
A necessary and sufficient condition for sigma-Hurwitz stability of the convex combination of the polynomials
(2005) Białas, Stanisław
In the paper are given a necessary and sufficent condition for $\sigma$-Hurwitz stability of the convex combination of the polynomials.
Access status: Open Access ,
A note on inductive limit model of Bargmann space of infinite order
(2005) Stochel, Jerzy
It is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction $a=(a_1,a_2,\ldots) \in l^2$ are inductive limits of the creation and annihilation operator acting on Bargmann space of $n$-th order.
Access status: Open Access ,
On some application of biorthogonal spline systems to integral equations
(2005) Wronicz, Zygmunt
We consider an operator $P_N: L_p(I) \to S_n(\Delta_N)$, such that $P_Nf=f$ for $f\in S_n(\Delta_N)$, where $S_n(\Delta_N)$ is the space of splines of degree $n$ with respect to a given partition $\Delta_N$ of the interval $I$. This operator is defined by means of a system of step functions biorthogonal to $B$-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the approximation of the solution of this equation are given.
Access status: Open Access ,
A note on self-complementary hypergraphs
(2005) Zwonek, Małgorzata
In the paper we desribe all self-complementary hypergraphs. It turns out that such hypergraphs exist if and only if the number of vertices of the hypergraph is of the form $n=2^k$. This answers a conjecture posed by A. Szymański (see [3]).
Access status: Open Access ,
Recovering a part of potential by partial information on spectra of boundary problems
(2005) Pivovarčik, Vâčeslav
Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm-Liouville equation on $[0,a]$ with real potential $q(x)\in L_2(0,a)$, 2) a certain part of the spectrum of the Dirichlet problem for the same equation on $[\frac{a}{3},a]$ and 3) the potential on $[0,\frac{a}{3}]$. The aim is to find the potential on $[\frac{a}{3},a]$.
Access status: Open Access ,
A singular nonlinear boundary value problem with Neumann conditions
(2005) Janus, Julian
We study the existence of solutions for the equations $x^{\prime\prime}\pm g(t,x)=h(t)$, $t\in (0,1)$ with Neumann boundary conditions, where $g:[0,1] \times (0,+\infty) \to [0,+\infty)$ and $h:[0,1] \to \mathbb{R}$ are continuous and $g(t,\cdot)$ is singular at $0$ for each $t\in [0,1]$.
Access status: Open Access ,
Numerical approximations of difference functional equations and applications
(2005) Kamont, Zdzisław
We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear ﬁrst order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Access status: Open Access ,
A note on self-complementary 4-uniform hypergraphs
(2005) Szymański, Artur
We prove that a permutation $\theta$ is complementing permutation for a $4$-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of $\theta$ is a multiple of $8$, (ii) $\theta$ has $1$, $2$ or $3$ fixed points, and all other cycles have length a multiple of $8$, (iii) $\theta$ has $1$ cycle of length $2$, and all other cycles have length a multiple of $8$, (iv) $\theta$ has $1$ fixed point, $1$ cycle of length $2$, and all other cycles have length a multiple of $8$, (v) $\theta$ has $1$ cycle of length $3$, and all other cycles have length a multiple of $8$. Moreover, we present algorithms for generating every possible $3$ and $4$-uniform self-complementary hypergraphs.
Access status: Open Access ,
Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type
(2005) Zabawa, Tomasz
The Dirichlet problem for an inﬁnite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin’s method of lower and upper functions.
Access status: Open Access ,
Calculation of distribution of temperature in three-dimensional solid changing its shape during the process
(2005) Bożek, Bogusław; Mączka, Czesław
The present paper suplements and continues [Bożek B., Filipek R., Holly K., Mączka C.: Distribution of temperature in three-dimensional solids. Opuscula Mathematica 20 (2000), 27-40]. Galerkin method for the Fourier–Kirchhoff equation in the case when $\Omega(t)$ – equation domain, dependending on time $t$, is constructed. For special case $\Omega(t) \subset \mathbb{R}^2$ the computer program for above method is written. Binaries and sources of this program are available on http://wms.mat.agh.edu.pl/~bozek.
Access status: Open Access ,
Independent set dominating sets in bipartite graphs
(2005) Zelinka, Bohdan
The paper continues the study of independent set dominating sets in graphs which was started by E. Sampathkumar. A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called a set dominating set (shortly sd-set) in $G$, if for each set $X \subseteq V(G)-D$ there exists a set $Y \subseteq D$ such that the subgraph $X \cup Y$ of $G$ induced by $\langle X \cup Y\rangle$ is connected. The minimum number of vertices of an sd-set in $G$ is called the set domination number $\gamma_s(G)$ of $G$. An sd-set $D$ in $G$ such that $|D|=\gamma_s(G)$ is called a $\gamma_s$-set in $G$. In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.
Access status: Open Access ,
The Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter
(2005) Mee, Cornelis van der; Pivovarčik, Vâčeslav
We present the complete version including proofs of the results announced in [1]. Namely, for the problem of small transversal vibrations of a damped string of nonuniform stiffness with one end ﬁxed we give the description of the spectrum and solve the inverse problem: ﬁnd the conditions which should be satisﬁed by a sequence of complex numbers to be the spectrum of a damped string.
Access status: Open Access ,
On the structure of characteristic surfaces related with partial differential equations of first and higher orders. Part 1
(2005) Prikarpats'ka, Natalâ K.; Pytel-Kudela, Marzena
The geometric structure of characteristic surfaces related with partial differential equations of ﬁrst and higher orders is studied making use the vector ﬁeld technique on hypersurfaces. It is shown, that corresponding characteristics are deﬁned uniquely up to some smooth tensor ﬁelds, thereby supplying additonal information about the suitable set of their solutions. In particular, it may be very useful for studying asymptotic properties of solutions to our partial differential equations under some boundary conditions.
Access status: Open Access ,
A sufficient condition for Schur stability of the convex combination of the polynomials
(2005) Białas, Stanisław
In this paper is given a simple suffcient condition for Schur stability of the convex combination of the real polynomials.
Access status: Open Access ,
2-biplacement without fixed points of (p,q)-bipartite graphs
(2005) Orchel, Beata
In this paper we consider 2-biplacement without fixed points of paths and $(p, q)$-bipartite graphs of small size. We give all $(p, q)$-bipartite graphs $G$ of size q for which the set $\mathcal{S}^{*}(G)$ of all 2-biplacements of $G$ without fixed points is empty.
Access status: Open Access ,
Solution of the Stieltjes truncated matrix moment problem
(2005) Adamân, Vadim Movsevovič; Tkačenko, Igor M.
The truncated Stieltjes matrix moment problem consisting in the description of all matrix distributions $\boldsymbol{\sigma}(t)$ on $[0,\infty)$ with given first $2n+1$ power moments $(\mathbf{C}_j)_{n=0}^j$ is solved using known results on the corresponding Hamburger problem for which $\boldsymbol{\sigma}(t)$ are defined on $(-\infty,\infty)$. The criterion of solvability of the Stieltjes problem is given and all its solutions in the non-degenerate case are described by selection of the appropriate solutions among those of the Hamburger problem for the same set of moments. The results on extensions of non-negative operators are used and a purely algebraic algorithm for the solution of both Hamburger and Stieltjes problems is proposed.
Access status: Open Access ,
A note on geodesic and almost geodesic mappings of homogeneous Riemannian manifolds
(2005) Formella, Stanisław
Let $M$ be a differentiable manifold and denote by $\nabla$ and $\tilde{\nabla}$ two linear connections on $M$. $\nabla$ and $\tilde{\nabla}$ are said to be geodesically equivalent if and only if they have the same geodesics. A Riemannian manifold $(M,g)$ is a naturally reductive homogeneous manifold if and only if $\nabla$ and $\tilde{\nabla}=\nabla-T$ are geodesically equivalent, where $T$ is a homogeneous structure on $(M,g)$ ([Tricerri F., Vanhecke L., Homogeneous Structure on Riemannian Manifolds. London Math. Soc. Lecture Note Series, vol. 83, Cambridge Univ. Press 1983]). In the present paper we prove that if it is possible to map geodesically a homogeneous Riemannian manifold $(M,g)$ onto $(M,\tilde{\nabla})$, then the map is affine. If a naturally reductive manifold $(M,g)$ admits a nontrivial geodesic mapping onto a Riemannian manifold $(\overline{M},\overline{g})$ then both manifolds are of constant cutvature. We also give some results for almost geodesic mappings $(M,g) \to (M,\tilde{\nabla})$.
Access status: Open Access ,
Monotone iteration for infinite systems of parabolic equations
(2005) Pudełko, Anna
In the paper the Cauchy problem for an inﬁnite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on diffenential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.
Access status: Open Access ,
The Abel summation of the Kontorovich-Lebedev integral representation
(2005) Cojuhari, Petru A.; Gomilko, Aleksandr M.
A new result on the summation of the Kontorovich–Lebedev integral representation in the sense of Abel mean is given.