Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2005
Volume
Vol. 25
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 25 (2005)
Projects
Pages
Articles
A necessary and sufficient condition for sigma-Hurwitz stability of the convex combination of the polynomials
(2005) Białas, Stanisław
In the paper are given a necessary and sufficent condition for $\sigma$-Hurwitz stability of the convex combination of the polynomials.
Calculation of distribution of temperature in three-dimensional solid changing its shape during the process
(2005) Bożek, Bogusław; Mączka, Czesław
The present paper suplements and continues [Bożek B., Filipek R., Holly K., Mączka C.: Distribution of temperature in three-dimensional solids. Opuscula Mathematica 20 (2000), 27-40]. Galerkin method for the Fourier–Kirchhoff equation in the case when $\Omega(t)$ – equation domain, dependending on time $t$, is constructed. For special case $\Omega(t) \subset \mathbb{R}^2$ the computer program for above method is written. Binaries and sources of this program are available on http://wms.mat.agh.edu.pl/~bozek.
A note on geodesic and almost geodesic mappings of homogeneous Riemannian manifolds
(2005) Formella, Stanisław
Let $M$ be a differentiable manifold and denote by $\nabla$ and $\tilde{\nabla}$ two linear connections on $M$. $\nabla$ and $\tilde{\nabla}$ 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 $\nabla$ and $\tilde{\nabla}=\nabla-T$ 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 $(M,\tilde{\nabla})$, then the map is affine. If a naturally reductive manifold $(M,g)$ admits a nontrivial geodesic mapping onto a Riemannian manifold $(\overline{M},\overline{g})$ then both manifolds are of constant cutvature. We also give some results for almost geodesic mappings $(M,g) \to (M,\tilde{\nabla})$.
Convex compact family of polynomials and its stability
(2005) Góra, Michał
Let $P$ be a set of real polynomials of degree n. Set $P$ can be identified with some subset $P$ of $\mathbb{R}^n$ 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.
Solving equations by topological methods
(2005) Górniewicz, Lech
In 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.