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- ArtykułDostęp ograniczonyThe Sturm-Liouville inverse spectral problem with boundary conditions depending on the spectral parameter(2005) Mee, Cornelis van der; Pivovarčik, VâčeslavWe 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.
- ArtykułDostęp ograniczonyOn some application of biorthogonal spline systems to integral equations(2005) Wronicz, ZygmuntWe consider an operator PN : LP(I) - Sn(deltaN), such that PN f = f for f mem Sn(deltaN), where Sn(deltaN) is the space of splines of degree n with repect to a given partition deltaN 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 aproximation of the solution of this equation are given.
- ArtykułDostęp ograniczonyA note on geodesic and almost geodesic mappings of homogeneous Riemannian manifolds(2005) Formella, StanisławLet M be a differentiable manifold and denote by ∇ and ∇~ two linear connections on M. ∇ and ∇~ 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 ∇ and ∇~=∇−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,∇~), then the map is affine. If a naturally reductive manifold (M,g) admits a nontrivial geodesic mapping onto a Riemannian manifold (M¯¯¯¯¯,g¯¯¯) then both manifolds are of constant cutvature. We also give some results for almost geodesic mappings (M,g)→(M,∇~).
- ArtykułDostęp ograniczonyA singular nonlinear boundary value problem with Neumann conditions(2005) Janus, JulianWe study the existence of solutions for the equations x" plmin g(t, x) = h(t), t ∊ (0, 1) with Neumann boundary conditions, where g: [0, 1] x (0, +∞) → [0, +∞] and h: [0, 1] → R are continuous and g(t, ·) is singular at 0 for each t ∊ [0, 1].
- ArtykułDostęp ograniczonyCalculation of distribution of temperature in three-dimensional solid changing its shape during the process(2005) Bożek, Bogusław; Mączka, CzesławThe present paper suplements and continues [2]. Galerkin method for the Fourier-Kirchoff equation in the case when Omega(t) - equation domain, dependending on time t, is constructed. For special case Omega(t) rcup R2 the computer program for above method is written. Binaries and sources of this program are available on http://wms.mat.agh.edu.pl/~bozek.
- ArtykułDostęp ograniczonyA note on inductive limit model of Bargmann space of infinite order(2005) Stochel, JerzyIt is shown that the generalized creation and annihilation operators on Bargmann space of infinite order in a direction a = (a₁, a₂, ...) ∊ l² are inductive limits of the creation and annihilation operator acting on Bargmann space on n-th order
- ArtykułDostęp ograniczonySolving equations by topological methods(2005) Górniewicz, LechIn this this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in diffrential equations.
- ArtykułDostęp ograniczonyConvex compact family of polynomials and its stability(2005) Góra, MichałLet P be a set of real polynomials of degree n. Set P can be identified with some subset P of Rn consists of vectors of coefficients of P. If P as a polytope, then to ascertain whether the entire family of polynomials P is stable or not, it suffices to examine the stability of the one-dimensional boundary sets of P. In present paper, we extend this result to convex compact polonomial families. Examples are presented to illustrate the results.
- ArtykułDostęp ograniczonyA necessary and sufficient condition for sigma-Hurwitz stability of the convex combination of the polynomials(2005) Białas, StanisławIn the paper are given a necessary and sufficent condition for sigma-Hurwitz stability of the convex combination of the polynomials.
- ArtykułDostęp ograniczonyExistence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type(2005) Zabawa, Tomasz SThe 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
- ArtykułDostęp ograniczonyThe geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal fiber bundles and some applications. Part 1(2005) Prikarpats'kìj, Ârema A.; Samojlenko, Anatolij Mihajlovič; Prykarpatski, AnatolijThe canonical reduction method on canonically symplectic manifolds is analized in detail, the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are stated. Some results devoted to studying geometrical properties of nonabelian Yang–Mills type gauge field quations are presented.
- ArtykułDostęp ograniczonyOn the structure of characteristic surfaces related with partial differential equations of first and higher orders. P. 1(2005) Prikarpats'ka, Natalâ K; Pytel-Kudela, MarzenaThe 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.
- ArtykułDostęp ograniczonyA note on self-complementary 4-uniform hypergraphs(2005) Szymański, ArturWe 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 hypergraph.
- ArtykułDostęp ograniczonyThe exact values of nonsquare constants for a class of Orlicz spaces(2005) Wang, JincaiWe extend the MDelta-condition from [10] and introduce the PhiDelta-condition at zero. Next we discuss nonsquare constant in Orlicz spaces generated by an N-function Phi(u) which satisfy PhiDelta-condition. We obtain exact value of nonsquare constant in this class of Orlicz spaces equipped with the Luxemburg norm.
- ArtykułDostęp ograniczonyMonotone iteration for infinite systems of parabolic equations(2005) Pudełko, AnnaIn 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.
- ArtykułDostęp ograniczonyOn intertwining and ω-hyponormal operators(2005) Otieno, M OGiven A, B mem B(H), the algebra of operators on a Hilbert Spaces H, define deltaA,B : B(H) arr B(H) and DeltaA,B : B(H) arr B(H) by deltaA,B(X) = AX - XB and DeltaA,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 mem ker DeltaA,B, then X mem ker DeltaA*,B*. Secondly, it is shown that if A and B* are ω-hyponormal operators such that X mem ker deltaA,B and Y mem ker deltaB,A, where X and Y are quasi-affinities, then A and B are unitarily equivalent normal operators. A ω-hyponormal operator compactly quasi-similar to an isometry is unitary is also proved.
- 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 ograniczonyTopological approach to chain recurrence in continuous dynamical systems(2005) Oprocha, PiotrIn this paper we present equivalent definitions of chain recurrent set for continuous dynamical systems. This definitions allow us to define chain recurrent set in topological spaces.
- ArtykułDostęp ograniczonyA note on self-complementary hypergraphs(2005) Zwonek, MałgorzataIn 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 = 2k. This answers a conjecture posed by A. Szymański (see [3]).
- ArtykułDostęp ograniczonyIndependent set dominating sets in bipartite graphs(2005) Zelinka, BohdanThe 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 ikkeq V(G) - D there exists a set Y ikkeq D such that the subgraph X cup Y of G induced X cup Y is connected. The minimum number of vertices of an sd-set in G is called the set domination number gammas (G) of G. An sd-set D in G such that /D/ = gammas(G) is called a gammas-set in G. In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.