Local stability of the additive functional equation and its applications.
Local stability of the functional equation characterizing polynomial functions
Long-term behavior of solutions of the difference equation .
Lösung einer allgemeinen Funktionalgleichung mit fünf unbekannten Funktionen von verschiedenen Veränderlichenzahlen
Lösung einer Funktionalgleichung für Translationsflächen die ein zylindrisch-konisches Netz besitzen
Lower-dimensional decompositions using complex variables
The purpose of the present paper is to represent non-holomorphic functions depending on one or several complex variables by holomorphic and anti-holomorphic functions depending on only one complex variable. Similarly as in the case of functions of real variables, the obtained criteria can also be interpreted as conditions for the solvability of functional equations.
Lyapunov functions for linear nonautonomous dynamical equations on time scales.
Lyapunov inequalities for time scales.
Lyapunov stability theory for dynamic systems on time scales.
Mappings preserving regular hexahedrons.
Markov operators acting on Polish spaces
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
Markov operators on the space of vector measures; coloured fractals
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
Mathematical Modeling Describing the Effect of Fishing and Dispersion on Hermaphrodite Population Dynamics
In order to study the impact of fishing on a grouper population, we propose in this paper to model the dynamics of a grouper population in a fishing territory by using structured models. For that purpose, we have integrated the natural population growth, the fishing, the competition for shelter and the dispersion. The dispersion was considered as a consequence of the competition. First we prove, that the grouper stocks may be less sensitive to the...
Mathematical structures behind supersymmetric dualities
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.
Mathematical works of Jerzy Popenda.
Matrix method for solving linear complex vector functional equations.
Matrix refinement equations: Continuity and smoothness
In this paper we give some criteria for the existence of compactly supported -solutions ( is an integer and ) of matrix refinement equations. Several examples are presented to illustrate the general theory.
Matrix Refinement Equations: Existence and Uniqueness.
Matrix solutions of the functional equation of the gamma function.
Maximal regularity of discrete and continuous time evolution equations
We consider the maximal regularity problem for the discrete time evolution equation for all n ∈ ℕ₀, u₀ = 0, where T is a bounded operator on a UMD space X. We characterize the discrete maximal regularity of T by two types of conditions: firstly by R-boundedness properties of the discrete time semigroup and of the resolvent R(λ,T), secondly by the maximal regularity of the continuous time evolution equation u’(t) - Au(t) = f(t) for all t > 0, u(0) = 0, where A:= T - I. By recent results of...