The article presents some simulations for a mathematical model that describes the bioremediation of polluted soil. The mathematical model is a reaction-diffusion system for the pollutant and for the bacteria. We made some two-dimensional simulations that show us how a small parameter affects the coupling and diffusion. The simulations help us to visualize both pollutant and bacteria evolution.
This paper deals with different types of generalized versions of fuzzy continuity, introducing the concept of \(fg{\alpha}^{\theta}\) - continuity, based on \(fg{\alpha}^{\theta}\) - closed sets and \(fg{\alpha}^{\theta}\) - open sets. Also, using \(fg{\alpha}^{\theta}\) - closed sets and \(fg{\alpha}^{\theta}\) - open sets, new types of fuzzy separation axioms and fuzzy compactness are studied. Some applications of \(fg{\alpha}^{\theta}\) - continuous functions are established.
We study algebraic classification and rigidity properties of ABC group actions on the three torus \(T^3\), by linear and affine transformations. The linear part of such an action is an ABC subgroup of SL(3, Z). We investigate when such a linear ABC action on \(T^3\) can be extended to an affine action that has no identity factors. For a particular class of such actions, we show KAM rigidity; the main reason for the existence of the conjugacy is KAM rigidity of the parabolic \(Z^2\) action inside the ABC group action.
In this paper, we prove a general common fixed point theorem for two pairs of mappings satisfying a new type of common limit range property in semimetric (symmetric) spaces. Our result relies on the use of an almost altering distance and of implicit relations and generalizes known results. As applications, we obtain new fixed point theorems for mappings satisfying contractive conditions of integral type and for C-class functions.
The notions of (α, β, γ)- order and (α, β, γ)- type have been introduced by B. Belaïdi and T. Biswas, as tools for the investigation of the growth of the solutions of linear differential equations with meromorphic coefficients. In this paper, the notions of (α, β, γ)- order and (α, β, γ)- type are used to estimate the growth of the Nevanlinna characteristic of a differential polynomial generated by a meromorphic function by comparison with the Nevanlinna characteristic of a composition of this function with another meromorphic function, one of these functions being entire function.
The aim of the paper is to identify the largest supertopological subrings, endowed with the uniform topology or with the m-topology, of the ring of real functions defined on a Tychonoff space X. Also, some special cases for the space X are investigated.