Now showing items 1-10 of 12
Sign-changing Lyapunov functions in linear extensions of dynamical systems
In this note we consider sets of linear extensions of dynamical systems on a torus. We examine regularity of the systems by means of a given sign-changing Lyapunov function. The main result of the paper is to give ...
Another description of continuous solutions of a nonlinear functional inequality
The paper gives a general construction of all continuous solutions of inequality (1) ful lling one of conditions (5) or (26). This paper is a continuation of .
Riemann integrability of a nowhere continuous multifunction
We present an example of the Riemann integrable multifunction which is discontinuous at each point with respect to the Hausdorff metric. The constructed multifunction is neither lower nor upper semicontinuous.
Gauss's definition of the gamma function
The present paper gives a historical account on extending the factorial function to complex numbers by Gauss.
Annales Academiae Paedagogicae Cracoviensis. 63. Studia Mathematica 7
(Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków, 2008)
The harmonic Dirichlet problem in a planar domain with cracks
The harmonic Dirichlet problem in a planar domain with smooth cracks of an arbitrary shape is considered in case, when the solution is not continuous at the ends of the cracks. The well-posed formulation of the problem ...
The transmission problem for elliptic second order equations in a conical domain
The present article is a survey of our last results. We establish best possible estimates of the weak solutions to the transmission problem near conical boundary point. We study this problem for the Laplace operator ...
Optimal design of unbounded 2D composite materials with circular inclusions of different radii
Optimal design problem for 2D composite materials with different circular inclusions is studied on the base of the potential method combined with functional equation method. Exact geometric description of the optimal ...