OPUSCULA MATHEMATICA
Stały identyfikator URI dla tego zbioru
- 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.
Uwaga! Zasoby czasopisma w trakcie uzupełniania w Repozytorium. Dostęp do numerów: (Vol. 37/4 (2017) - Vol. 44/2 (2024):
https://journals.bg.agh.edu.pl/OPUSCULA/
New! Aktualny numer: 2024 - Vol. 44 - No. 6
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- ArtykułOtwarty dostęp(1,2)-PDS in graphs with the small number of vertices of large degrees(Wydawnictwa AGH, 2025) Bednarz, Urszula; Pirga, MateuszWe define and study a perfect $(1,2)$-dominating set which is a special case of a $(1,2)$-dominating set. We discuss the existence of a perfect $(1,2)$-dominating set in graphs with at most two vertices of maximum degree. In particular, we present a complete solution if the maximum degree equals $n-1$ or $n-2$.
- ArtykułDostęp ograniczony2-biplacement without fixed points of (p,q)-bipartite graphs(2005) Orchel, BeataIn 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 S*(G) of all 2-biplacements of G without fixed points is empty.
- ArtykułDostęp ograniczony2-hyperreflexivity and hyporeflexivity of power partial isometries(2016) Piwowarczyk, Kamila; Ptak, MarekPower partial isometries are not always hyperreflexive neither reflexive. In the present paper it will be shown that power partial isometries are always hyporeflexive and 2-hyperreflexive.
- ArtykułDostęp ograniczony2-splittable and cordial graphs(2010) Cichacz, SylwiaE. Miller and G.E. Stevens proved in [5] the existence of certain families of 2-splittable caterpillars. In this paper we characterize other families of 2-splittable caterpillars. Moreover, we show that for some of them there exists a friendly labeling inducing two isomorphic subgraphs.
- ArtykułDostęp ograniczony3-biplacement of bipartite graphs(2008) Adamus, Lech; Leśniak, Edyta; Orchel, BeataLet G = (L,R;E) be a bipartite graph with color classes L and R and edge set E. A set of two bijections {$\varphi_{1}$, $\varphi_{2}$}, $\varphi_{1}$,$\varphi_{2}$ : $\varphi_1{(L)}=\varphi_2{(L)}=L$, is said to be a 3-biplacement of G if $\varphi_1{(L)}=\varphi_2{(L)}=L$ and [formula], where [formula] are the maps defined on E, induced by $\varphi_{1}$, $\varphi_{2}$, respectively. We prove that if $\vert{L}\vert=p$, $\vert{R}\vert=q$, $3\leq{p}\leq{q}$, then every graph G = (L, R; E) of size at most p has a 3-biplacement.
- ArtykułDostęp ograniczonyThe 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.
- ArtykułDostęp ograniczonyAbout sign-constancy of Green's functions for impulsive second order delay equations(2014) Domoshnitsky, Alexander; Landsman, Guy; Yanetz, ShlomoWe consider the following second order differential equation with delay \[\begin{cases} (Lx)(t)\equiv{x''(t)+\sum_{j=1}^p {b_{j}(t)x(t-\theta_{j}(t))}}=f(t), \quad t\in[0,\omega],\\ x(t_j)=\gamma_{j}x(t_j-0), x'(t_j)=\delta_{j}x'(t_j-0), \quad j=1,2,\ldots,r. \end{cases}\] In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality \(\sum_{i=1}^p{b_i(t)\left(\frac{1}{4}+r\right)}\lt \frac{2}{\omega^2}\) is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case \(0\lt \gamma_i\leq{1}\), \(0\lt \delta_i\leq{1}\) for \(i=1,\ldots ,p\).
- ArtykułDostęp ograniczonyAn abstract nonlocal second order evolution problem(2012) Byszewski, Ludwik; Winiarska, TeresaThe aim of the paper is to prove theorems on the existence and uniqueness of mild and classical solutions of a semilinear evolution second order equation together with nonlocal conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied.
- ArtykułDostęp ograniczonyAffine extensions of functions with a closed graph(2015) Wójtowicz, Marek Antoni; Sieg, WaldemarLet A be a closed Gδ-subset of a normal space X. We prove that every function f0 : A → R with a closed graph can be extended to a function f : X → R with a closed graph, too. This is a consequence of a more general result which gives an affine and constructive method of obtaining such extensions.
- ArtykułDostęp ograniczonyAlgebraic construction of a coboundary of a given cycle(2007) Mazur, Marcin; Szybowski, JacekWe present an algebraic construction of the coboundary of a given cycle as a simpler alternative to the geometric one introduced in [4, 5].
- ArtykułDostęp ograniczonyAn algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup(2010) Liu, Min; Chang, Shih Sen; Zuo, PingIn this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
- ArtykułDostęp ograniczonyAlien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter(2015) Tanda, MikaWe compute alien derivatives of the WKB solutions of the Gauss hypergeometric differential equation with a large parameter and discuss the singularity structures of the Borel transforms of the WKB solution expressed in terms of its alien derivatives.
- ArtykułDostęp ograniczonyAll graphs with paired-domination number two less than their order(2013) Ulatowski, WłodzimierzLet G = (V,E) be a graph with no isolated vertices. A set S ⊆ V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number $\gamma_p(G)$ of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199–206] Haynes and Slater described graphs G with $\gamma_p(G)$ = n and also graphs with $\gamma_p(G)$ = n − 1. In this paper we show all graphs for which $\gamma_p(G)$ = n − 2.
- ArtykułOtwarty dostępAnalysis of a multiphase free boundary problem(Wydawnictwa AGH, 2024) Abdelouahab, Ahlem; Bensid, SabriIn this paper, we investigate a free boundary problem relevant in several applications, such as tumor growth models. Our problem is expressed as an elliptic equation involving discontinuous nonlinearities in a specified domain with a moving boundary. We establish the existence and uniqueness of solutions and provide a qualitative analysis of the free boundaries generated by the nonlinear term (inner boundaries). Furthermore, we analyze the dynamics of the outer region boundary. The final result demonstrates that under certain conditions, our problem is solvable in the neighborhood of a radial solution.
- ArtykułDostęp ograniczonyAnalysis of integrodifferential control system with pulse-width modulated sampler on Banach spaces(2012) Wang, JinRongThis paper studies steady-state control and stability for a class of integrodifferential control system with pulse-width modulated sampler on Banach spaces. The existence and stability of the steady-state for the integrodifferential control system with pulse-width modulated sampler are given. An example is given to illustrate the theory.
- ArtykułDostęp ograniczonyAnalytic continuation of solutions of some nonlinear convolution partial differential equations(2015) Tahara, HidetoshiThe paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
- ArtykułDostęp ograniczonyAndrzej Lasota's selected results(2008) Myjak, JózefIn this article we recall Andrzej Lasota's selected results which either indicated new directions of research, or layed the foundations for new approaches, or solved interesting problems. The area of mathematical interests of Professor Andrzej Lasota was very large: ordinary differential equations, partial differential equations, dynamical systems, multifunctions, differential inclusions, functional differential equations, equations with retarded arguments, ergodic theory, invariant measures, chaos, stochastic differential equations, control theory, fixed point theory, theory of Markov operators, theory of fractals, theory of dimensions, biomathematics. In all these branches he obtained original and essential results.
- ArtykułDostęp ograniczonyApplication of Chebyshev and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane(2008) Karczmarek, PawełIn this article Chebyshev and trigonometric polynomials are used to constructan approximate solution of a singular integral equation with a multiplicative Cauchy kernelin the half-plane.
- ArtykułDostęp ograniczonyApplication of Green's operator to quadratic variational problems(2006) Tsalyuk, Vadim Z.; Azbelev, Nikolay V.We use Green’s function of a suitable boundary value problem to convert the variational problem with quadratic functional and linear constraints to the equivalent unconstrained extremal problem in some subspace of the space [formula] of quadratically summable functions. We get the neccessary and sufficient criterion for unique solvability of the variational problem in terms of the spectrum of some integral Hilbert–Schmidt operator in [formula] with symmetric kernel. The numerical technique is proposed to estimate this criterion. The results are demonstrated on examples: 1) a variational problem with deviating argument, and 2) the problem of the critical force for the vertical pillar with additional support point (the qualities of the pillar may vary discontinuously along the pillar’s axis).
- ArtykułDostęp ograniczonyAn application of the Choquet theorem to the study of randomly-superinvariant measures(2012) Rajba, TeresaGiven a real valued random variable $\Theta$ we consider Borel measures $\mu$ on $\mathcal{B}{(\mathbb{R})}$, which satisfy the inequality $\mu(B)\geq{E\mu(B-\Theta)}$ $\mu(B)\geq{E\mu(B-\Theta)}$ $(B\in{\mathcal{B}{(\mathbb{R})}})$ (or the integral inequality $\mu(B)\geq{\int^\infty_{-\infty}}\mu(B-h)\gamma(dh)$).We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable $\Theta$.
