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Markov operators acting on Polish spaces

Tomasz Szarek (1997)

Annales Polonici Mathematici

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

Karol Baron, Andrzej Lasota (1998)

Annales Polonici Mathematici

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

S. Ben Miled, A. Kebir, M. L. Hbid (2010)

Mathematical Modelling of Natural Phenomena

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

Ilmar Gahramanov (2015)

Archivum Mathematicum

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.

Matrix refinement equations: Continuity and smoothness

Xing-Gang He, Chun-Tai Liu (2007)

Czechoslovak Mathematical Journal

In this paper we give some criteria for the existence of compactly supported C k + α -solutions ( k is an integer and 0 ≤ α < 1 ) of matrix refinement equations. Several examples are presented to illustrate the general theory.

Maximal regularity of discrete and continuous time evolution equations

Sönke Blunck (2001)

Studia Mathematica

We consider the maximal regularity problem for the discrete time evolution equation u n + 1 - T u ₙ = f ₙ 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 ( T ⁿ ) n ∈ ℕ ₀ 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...

Maximizers for the Strichartz Inequality

Damiano Foschi (2007)

Journal of the European Mathematical Society

We compute explicitly the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrödinger equation and for the wave equation in the cases when the Lebesgue exponent is an even integer.

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Tianwei Zhang, Lijun Xu (2019)

Kybernetika

By using the semi-discrete method of differential equations, a new version of discrete analogue of stochastic shunting inhibitory cellular neural networks (SICNNs) is formulated, which gives a more accurate characterization for continuous-time stochastic SICNNs than that by Euler scheme. Firstly, the existence of the 2th mean almost periodic sequence solution of the discrete-time stochastic SICNNs is investigated with the help of Minkowski inequality, Hölder inequality and Krasnoselskii's fixed...

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