The aim of this paper is to design appropriate nonstandard finite difference (NSFD) schemes for two population mathematical models based on coupled nonlinear ordinary differential equations. Our work clarifies existing constructions NSFD these models, which are not in full compliance with Mickens' methodology. We select the denominator functions discrete first-order derivatives depending existe...

This paper concerns the nonstandard problem of uniform deconvolution for nonperiodic functions over the real line. New algorithms are developed for this nonstandard statistical problem and integrated mean squared error bounds are established. We show that the upper bound of the integrated mean squared error for our new procedure is the same as for the standard case; hence these new estimators a...

The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation U ′ q(son) (which does not coincide with the Drinfel’d-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son(C)) of the Lie algebra son(C) when q is not a root of unity. These representations are exhausted by irreducible representations...

We analyze a class of predator-prey models with BeddingtonDeAngelis type functional response. The models incorporate the mutual interference between predators, which stabilizes predator-prey interactions even when only a linear intrinsic growth rate of the prey population is considered. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative feat...

Predator-prey systems with linear and logistic intrinsic growth rate of the prey are analyzed. The models incorporate the mutual interference between predators into the functional response which stabilizes predatorprey interactions in the system. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous pred...

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations.A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two nonstandard formulations, that numerous F...

Fuzziness or uncertainties arise due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of susceptible, infectious recovered are uncertain the different degrees in susceptibility, infectivity recovery among individuals population. differences can arise, when population groups under consideration having distinct h...

We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of finite-dimensional C*-algebras and completely positive maps. In particular, the new category contains both quantum and classical channels, providing elegant abs...

The present research is a contribution to W -Catalan combinatorics, which concerns generalizations of objects counted by the Catalan number to an arbitrary finite Coxeter group W. Triangulations of a polygon are a special case of the combinatorial clusters appearing in the theory of cluster algebras of finite type. Planar diagrams analogous to triangulations encode the combinatorics of clusters...