Numer czasopisma
Opuscula Mathematica
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ISSN: 1232-9274
e-ISSN:
Data wydania
2010
Rocznik
Vol. 30
Numer
No. 1
Prawa dostępu
Dostęp: otwarty dostęp
Uwagi:
Prawa: CC BY 4.0 
Uznanie autorstwa 4.0 Międzynarodowe (CC BY 4.0)
Strony
Opis
Rocznik czasopisma (rel.)
Rocznik czasopisma
Opuscula Mathematica
Vol. 30 (2010)
Artykuły numeru (rel.)
Artykuł
Dostęp ograniczony
A study of chaos for processes under small perturbations II - rigorous proof of chaos
(2010) Oprocha, Piotr; Wilczyński, Paweł
In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation $ż=(1+{e}^{i{\kappa}t}|z|^{2}) {\overline{z}^{2}}-Ne^{-i\frac{\pi}3}$. Heteroclinic and homoclinic connections between two periodic solutions bifurcating from the stationary solution 0 present in the system when N = 0 are also discussed.
Artykuł
Dostęp ograniczony
Dominating sets and domination polynomials of certain graphs, II
(2010) Alikhani, Saeid; Peng, Yee Hock
The domination polynomial of a graph G of order n is the polynomial $D(G,x)=\sum_{i=\gamma{(G)}}^{n}{d(G,i)x^i}$ where d(G, i) is the number of dominating sets of G of size i, and $\gamma$(G) is the domination number of G. In this paper, we obtain some properties of the coefficients of D(G, x). Also, by study of the dominating sets and the domination polynomials of specific graphs denoted by G'(m), we obtain a relationship between the domination polynomial of graphs containing an induced path of length at least three, and the domination polynomial of related graphs obtained by replacing the path by shorter path. As examples of graphs G' (m), we study the dominating sets and domination polynomials of cycles and generalized theta graphs. Finally, we show that, $n\equiv0,2(mod3)$ and D(G, x) = D($C_n$, x), then G = $C_n$.
Artykuł
Dostęp ograniczony
Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener
(2010) Azócar Bates, Luis Antonio; Guerrero, José Atilio; Matkowski, Janusz; Merentes Díaz, Nelson José
We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.
Artykuł
Dostęp ograniczony
2-splittable and cordial graphs
(2010) Cichacz, Sylwia
E. 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.
Artykuł
Dostęp ograniczony
On some properties of the superposition operator on topological manifolds
(2010) Dronka, Janusz
In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
Artykuł
Dostęp ograniczony
Hyponormal differential operators with discrete spectrum
(2010) Ismailov, Zameddin I; Unluyol, Erdal
In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Artykuł
Dostęp ograniczony
Differential difference inequalities related to parabolic functional differential equations
(2010) Netka, Milena
Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.