In this paper the idea of -locally closed sets in generalized topological space is introduced and study some of their properties. We introduce the notion of (,’)locally closed continuous functions on generalized topological space and investigate some of their characterizations.

The paper considers the role of quantale algebra nuclei in representation of quotients of quantale algebras, and in factorization of quantale algebra homomorphisms. The set of all nuclei on a given quantale algebra is endowed with the structure of quantale semi-algebra.

In this paper, we first discuss the structure of the Ramond N = 2 superconformal algebras. Then we classify the modules of the intermediate series over Ramond N = 2 superconformal algebra.

We investigate the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal-free cylindric algebras. We prove that a Df2algebra is finitely representable iff it is finitely approximable, characterize finite projective Df2-algebras, and show that there are no non-trivial injectives and absolute retracts in Df2. We prove that every proper subvariety of Df2 is locally fini...

We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other. [MSC: 46J05, 46J10]

We introduce a notion of “hopfish algebra” structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras are examples of hopfish algebras. We find that a hopfish structure on the algebra of functions on a finite set G is closely related to a “hypergroupoid” structure on G. ...

Some simple Lie superalgebras, specific of characteristic 3, defined by S. Bouarroudj and D. Leites [BL06], will be related to the simple alternative and commutative superalgebras discovered by I.P. Shestakov [She97]. Throughout the paper, the ground field k will always be assumed to be of characteristic 6= 2. 1. Tits construction In 1966 [Tit66], Tits gave a unified construction of the excepti...

A harmonic mapping is a univalent function of one complex variable. We define family mappings on the unit disk whose images are rotationally symmetric “rosettes” with n cusps or nodes, \(n\ge 3\). These analogous to n-cusped hypocycloid, but modified by Gauss hypergeometric factors, both in analytic and co-analytic parts. Relative rotations an angle \(\beta \) anti-analytic parts lead graphs th...

Investigations were carried out on 43 serially sectioned human embryos of developmental stages 18 to 23. The homogeneous interzone of the future knee joint is observed in embryos at stage 18. During stage 19 this interzone is differentiated into dense, intensively stained, peripheral parts, which are the primordia of menisci and the medial portion, in which the cruciate ligaments are formed. Al...

A self-folding structure fabricated by additive manufacturing can be automatically folded into a demanding 3D shape by actuation mechanisms such as heating. However, 3D surfaces can only be fabricated by self-folding structures when they are flattenable. Most generally designed parts are not flattenable. To address the problem, we develop a shape optimization method to modify a non-flattenable ...