A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

Abstract We examine four different notions of variation for real-valued functions defined on the compact ring integers a non-Archimedean local field, with an emphasis regularity properties finite variation, and establishing Koksma inequalities. The first version is due to Taibleson, second Beer, remaining two are new. Taibleson simplest these, but it coarse measure irregularity does not admit i...

We provide a construction of the moduli space stable coherent sheaves in world non-archimedean geometry, where we use notion Berkovich analytic spaces. The motivation for our is Tony Yue Yu’s enumerative geometry Gromov—Witten theory. using spaces will give rise to version Donaldson—Thomas invariants. In this paper over field $${\mathbb{K}}$$ . machinery formal schemes, that is, define and cons...

Abstract This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in non-Archimedean ring Colombeau generalized numbers this journal. We study one variable hyper-power series by analyzing notion radius convergence and proving classical results such as algebraic operations, composition reciprocal series. then define real analytic functions, considering their deri...

Let L be an ample line bundle on a (geometrically reduced) projective variety X over any complete valued field. Our main result describes the leading asymptotics of determinant cohomology large powers L, with respect to supnorm continuous metric Berkovich analytification L. As consequence, we establish in this setting existence transfinite diameters and equidistribution Fekete points, following...

A ring with identity is said to be clean if every element can be written as a sum of a unit and an idempotent. The study of clean rings has been at the forefront of ring theory over the past decade. The theory of partially-ordered groups has a nice and long history and since there are several ways of relating a ring to a (unital) partially-ordered group it became apparent that there ought to be...

This paper is to contributive to the model theory of ordered abelian groups (o.a.g. for short). The basic elements to build up the algebraic structure of the o.a.g-s are the archimedean groups: By Hahn's embedding theorem every o.a.g. can be represented as a subgroup of the Hahn-product of archimedean o.a.g.s. Archimedean is not a first-order concept but there exists a first-order model theory ...

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

In this paper, we introduce some new classes of proximal contraction mappings and establish  best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...

A new algorithm for classification of DMUs to efficient and inefficient units in data envelopment analysis is presented. This algorithm uses the non-Archimedean Charnes-Cooper-Rhodes[1] (CCR) model. Also, it applies an assurance value for the non-Archimedean                          using only simple computations on inputs and outputs of DMUs (see [18]). The convergence and efficiency of the ne...