In this paper, we develop a new technique for constructing fuzzy ideals of semigroup. By using generalized Green's relations, star are constructed. It is shown that the ideal semigroup can be used to investigate relationship between sets and abundance regularity an arbitrary Appropriate examples such given in order illustrate technique. Finally, explain when satisfies conditions regularity.

We employ semigroup and spectral methods to analyze the linear stability of positive stationary solutions of a generalized size-structured Daphnia model. Using the regularity properties of the governing semigroup, we are able to formulate a general stability condition which permits an intuitively clear interpretation in a special case of model ingredients. Moreover, we derive a comprehensive in...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

We report about results revolving around Kostka–Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup, which we call Liskova semigroup. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among ...

Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the semigroup is contained in an ambit. In the convolution algebras constructed over ambitable semigroups, topological centres have a tractable characterization. 1...

In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in R associated with the generalized Hermite polynomials {Hμ n} and prove that it is weak type (1,1) with respect to dλμ(x) = |x|2μe−|x| 2 dx, for μ > −1/2 as well as bounded on L(dλμ) for p > 1.

We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.

The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...

Results from a nonlinear semigroup theory are applied to get existence and uniqueness for PDEs with hysteresis. The hysteresis nonlinearity considered is of the generalized play operator type, but can be easily extended to a generalized Prandtl-Ishlinskii operator of play type, both possibly discontinuous.