Numer czasopisma
Opuscula Mathematica
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ISSN: 1232-9274
e-ISSN:
Data wydania
2008
Rocznik
Vol. 28
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. 28 (2008)
Artykuły numeru (rel.)
Artykuł
Dostęp ograniczony
A note on a family of quadrature formulas and some applications
(2008) Bożek, Bogusław; Solak, Wiesław; Szydełko, Zbigniew
In this paper a construction of a one-parameter family of quadrature formulas is presented. This family contains the classical quadrature formulas: trapezoidal rule, mid-point rule and two-point Gauss rule. One can prove that for any continuous function there exists a parameter for which the value of quadrature formula is equal to the integral. Some applications of this family to the construction of cubature formulas, numerical solution of ordinary differential equations and integral equations are presented.
Artykuł
Dostęp ograniczony
On a complete lattice of retracts of a free monoid generated by three elements
(2008) Foryś, Wit
We prove that the family of retracts of a free monoid generated by three elements, partially ordered with respect to the inclusion, is a complete lattice.
Artykuł
Dostęp ograniczony
Application 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, Paweł
In 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.
Artykuł
Dostęp ograniczony
A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices
(2008) Pchelintseva, Irina
We consider self-adjoint unbounded Jacobi matrices with diagonal [formula] and off-diagonal entries [formula], where bn is a 2-periodical sequence of real numbers. Theparameter space is decomposed into several separate regions, where the spectrum of theoperator is either purely absolutely continuous or discrete. We study the situation wherethe spectral phase transition occurs, namely the case of b1b2 = 4. The main motive of thepaper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix.The pure point part of the spectrum is analyzed in detail.
Artykuł
Dostęp ograniczony
On a multivalued second order differential problem with Hukuhara derivative
(2008) Piszczek, Magdalena
Let K be a closed convex cone with the nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. Assume that continuous linear multifunctions H, ψ : K -> cc(K) are given. We consider the following problem D2 φ (t, x) = φ (t, H(x)), D φ (t,x) / (t=0) = {0}, φ (0, x) = ψ (x) for t ≥ 0 and [formula], where D φ (t, x) denotes the Hukuhara derivative of φ (t, x) with respect to t.
Artykuł
Dostęp ograniczony
On the Chaplyghin method for first order partial differential equations
(2008) Puźniakowska, Elżbieta
Classical solutions of initial problems for nonlinear first order partial differential equations are considered. It is shown that under natural assumptions on given functions, there exist Chaplyghin sequences and they are convergent. Error estimates for approximate solutions are given. The method of characteristics is used for the construction of approximate solutions.
Artykuł
Dostęp ograniczony
Approximate solutions of a singular integral equation with Cauchy kernels in the quarter plane
(2008) Pylak, Dorota
In the paper, we present explicit formulae for the solution of the singular integral equation with Cauchy kernels in the quarter plane. Next, Jacobi and Chebyshev polynomials are used to derive approximate solutions of this equation.
Artykuł
Dostęp ograniczony
Ergodic conditions and spectral properties for A-contractions
(2008) Suciu, Laurian; Suciu, Nicolae
In this paper the canonical representation of an A-contraction T on a Hilbert space H is used to obtain some conditions concerning the concept of A-ergodicity studied in [14-17]. The regular case and the case of R(A) closed are considered, and specifically, the TT*-contractions are studied. Some spectral properties are also given for certain particular class of A-isometries.