in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for c...

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

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.

A system of linear equations with integer coefficients is partition regular over a subset S of the reals if, whenever S \ {0} is finitely coloured, there is a solution to the system contained in one colour class. It has been known for some time that there is an infinite system of linear equations that is partition regular over R but not over Q, and it was recently shown (answering a long-standi...

Polymorphic traits are central to many fundamental discoveries in evolution, yet why they are found in some species and not others remains poorly understood. We use the African genus Protea-within which more than 40% of species have co-occurring pink and white floral colour morphs-to ask whether convergent evolution and ecological similarity could explain the genus-wide pattern of polymorphism....