In this paper, the concepts of hybrid pure hyperideals in ordered hypersemigroups are introduced and some algebraic properties studied. We characterize weakly regular terms hyperideals. Finally, we introduce prove that if such satisfy idempotent property.

We study the determinism checking problem for regular expressions extended with interleaving. There are two notions of determinism, i.e., strong and weak determinism. Interleaving allows child elements intermix in any order. Although interleaving does not increase the expressive power of regular expressions, its use makes the sizes of regular expressions be exponentially more succinct. We first...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

For any $h\in(1,2]$, we give an explicit construction of a compactly supported, uniformly continuous, and (weakly) divergence-free velocity field in $\mathbb{R}^2$ that weakly advects measure whose support is initially the origin but for positive times has Hausdorff dimension $h$. These velocities are continuous space-time locally Lipschitz except at one point satisfy conditions existence uniqu...

We introduce the notions of a generalised category and of an inductive generalised category over a band. Our purpose is to describe a class of semigroups which we name weakly B-orthodox. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids. Here B denotes a band of idempotents; we note that if B is a semilattice then a weakly B-or...

A multivariate ridge function is a of the form f ( x ) = g T , where univariate and ∈ R d . We show that recovery an unknown defined on hypercube [ − 1 ] with Lipschitz-regular profile suffers from curse dimensionality when error measured in L ∞ -norm, even if we allow randomized algorithms. If limited number components substantially larger than others, then not present problem weakly tractable...

It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, σ–centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on ω. Therefore the existence of such algebras is undecidable in ZFC. In ”forcing language” condition (a) says that there exists a non– trivial σ–centered for...

a Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan. b Department of Mathematics, Riphah International University Islamabad, Pakistan.  Corresponding Author's Email: [email protected] ABSTRACT: In this paper, we introduce the notions of soft intersectional ternary subsemirings and soft intersectional ideals in ternary semirings. We also discuss ...

In this paper we have generalized the concepts of   q   , -fuzzy ideals,   q   , -fuzzy quasi-ideals and   q   , -fuzzy bi-ideals by introducing the concepts of   k q   , -fuzzy ideals,   k q   , -fuzzy quasiideals and   k q   , -fuzzy bi-ideals in ternary semigroups and several related properties are investigated. Different characterizations of regular and weakly ...

We discuss regular production systems as a tool for analyzing tilings in general. As an application we give necessary and sufficient conditions for a generic triangle to admit a tiling of H and show that almost every triangle that admits a tiling is “weakly aperiodic.” We pause for a variety of other applications, such as non-quasi-isometric maps between regular tilings, aperiodic Archimedean t...