Numer czasopisma
Opuscula Mathematica
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ISSN: 1232-9274
e-ISSN:
Data wydania
2009
Rocznik
Vol. 29
Numer
No. 2
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. 29 (2009)
Artykuły numeru (rel.)
Artykuł
Dostęp ograniczony
On some quadrature rules with Gregory end corrections
(2009) Bożek, Bogusław; Solak, Wiesław; Szydełko, Zbigniew
How can one compute the sum of an infinite series s := a1 + a2 + · · · ? If the series converges fast, i.e., if the term an tends to 0 fast, then we can use the known bounds on this convergence to estimate the desired sum by a finite sum a1 + a2 + · · ·+ an. However, the series often converges slowly. This is the case, e.g., for the series an = n−t that defines the Riemann zeta-function. In such cases, to compute s with a reasonable accuracy, we need unrealistically large values n, and thus, a large amount of computation. Usually, the n-th term of the series can be obtained by applying a smooth function f(x) to the value n: an = f(n). In such situations, we can get more accurate estimates if instead of using the upper bounds on the remainder infinite sum R = f(n + 1) + f(n + 2) + . . ., we approximate this remainder by the corresponding integral I of f(x) (from x = n + 1 to infinity), and find good bounds on the difference I − R. First, we derive sixth order quadrature formulas for functions whose 6th derivative is either always positive or always negative and then we use these quadrature formulas to get good bounds on I − R, and thus good approximations for the sum s of the infinite series. Several examples (including the Riemann zeta-function) show the efficiency of this new method. This paper continues the results from [3] and [2].
Artykuł
Dostęp ograniczony
On an evolution inclusion in non-separable Banach spaces
(2009) Cernea, Aurelian
We consider a Cauchy problem for a class of nonconvex evolution inclusions in non-separable Banach spaces under Filippov-type assumptions.We prove the existence of solutions.
Artykuł
Dostęp ograniczony
A note on Radon-Nikodym derivatives and similarity for completely bounded maps
(2009) Gheondea, Aurelian; Kavruk, Ali Şamil
We point out a relation between the Arveson's Radon-Nikodym derivative and known similarity results for completely bounded maps. We also consider Jordan type decompositions coming out from Wittstock's Decomposition Theorem and illustrate, by an example, the nonuniqueness of these decompositions.
Artykuł
Dostęp ograniczony
Continuous solutions of iterative equations of infinite order
(2009) Kapica, Rafał; Morawiec, Janusz
Given a probability space (Ω, A, P) and a complete separable metric space X, we consider continuous and bounded solutions ϕ: X → R of the equations ϕ(x) = ∫Ωϕ(f(x,ω))P(dω) and ϕ(x) = 1 − ∫Ωϕ(f(x,ω))P(dω), assuming that the given function f : X × Ω → X is controlled by a random variable L: Ω → (0,∞) with −∞ < ∫Ω log L(ω)P(dω) < 0. An application to a refinement type equation is also presented.
Artykuł
Dostęp ograniczony
A note on the p-domination number of trees
(2009) Lu, You; Hou, Xinmin; Xu, Jun-Ming
Let p be a positive integer and G = (V (G), E(G)) a graph. A p-dominating set of G is a subset S of V (G) such that every vertex not in S is dominated by at least p vertices in S. The p-domination number [formula] is the minimum cardinality among the p-dominating sets of G. Let T be a tree with order n ? 2 and p ? 2 a positive integer. A vertex of V (T) is a p-leaf if it has degree at most p - 1, while a p-support vertex is a vertex of degree at least p adjacent to a p-leaf. In this note, we show that [formula], where Lp(T) and Sp(T) are the sets of p-leaves and p-support vertices of T, respectively. Moreover, we characterize all trees attaining this lower bound.
Artykuł
Dostęp ograniczony
On the diameter of dot-critical graphs
(2009) Mojdeh, Doost Ali; Mirzamani, Somayeh
A graph G is k-dot-critical (totaly k-dot-critical) if G is dot-critical (totaly dot-critical) and the domination number is k. In the paper [T. Burtona, D. P. Sumner, Domination dot-critical graphs, Discrete Math, 306(2006), 11–18] the following question is posed: What are the best bounds for the diameter of a k-dot-critical graph and a totally k-dot-critical graph G with no critical vertices for k ≥ 4? We find the best bound for the diameter of a k-dot-critical graph, where k ∈ {4, 5, 6} and we give a family of k-dot-critical graphs (with no critical vertices) with sharp diameter 2k − 3 for even k ≥ 4.
Artykuł
Dostęp ograniczony
Vague BCK/BCI-algebras
(2009) Saeid, Arsham Borumand
In this note, by using the concept of vague sets, the notion of vague BCK/BCI-algebra is introduced. And the notions of α-cut and vague-cut are introduced and the relationships between these notions and crisp subalgebras are studied.
Artykuł
Dostęp ograniczony
Weyl-Titchmarsh type formula for Hermite operator with small perturbation
(2009) Simonov, Sergej A.
Small perturbations of the Jacobi matrix with weights √n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is an analogue of the classical Weyl-Titchmarsh formula for the Schrödinger operator on the half-line with summable potential. Additionally, a base of generalized eigenvectors for 'free' Hermite operator is studied and asymptotics of Plancherel-Rotach type are obtained.
Artykuł
Dostęp ograniczony
On the property of the BBGKY hierarchy solution in a cumulant representation
(2009) Stašenko, Mihail O; Gubal', Galina Mikolaïvna
We consider a one-dimensional nonsymmetric system of particles interacting via the hard-core potential. For this system, we prove that the BBGKY hierarchy solution in a cumulant representation is an equilibrium in the case of equilibrium initial data.