The \unsharpness problem" is solved by the construction of a nite Although this equation fails in general, it does hold under slightly stronger hypotheses. x1 In recent years various relation-algebraic formulations of the properties of pairs of projection functions naturally associated with direct products have appeared in the literature of computer science. Two particular relevant examples are...

By an ordered commutative semigroup of the first kind (abbreviated "o.c.s.I") we mean a system 5(o, <) consisting of a set 5 endowed with a binary operation o and a binary relation < such that the following axioms are satisfied. I. S is a commutative semigroup with respect to o, i.e. the associative law, a o (b o c) = (a o b)o c, and the commutative law, a o b = b o a, hold (a, b, c in S). II. ...

in this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup s . some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. different classes, regular, intra-regular, and simple ordered semigroups are   characterized by means of fuzzy sof...

Submicrometer patterns of adjacent, well-ordered and disordered domains were obtained using optical lithography by area-selective, photoinduced disordering transitions within block copolymer composite films. Enantiopure tartaric acid was blended with poly(ethylene oxide-block-tert-butyl acrylate), PEO-b-PtBA, copolymers to yield well-ordered films. In the presence of triphenylsulfonium triflate...

In this paper, we describe how checking whether a given property F is true for a product A1 ×A2 of partially ordered spaces can be reduced to checking several related properties of the original spaces Ai. This result can be useful in the analysis of properties of intervals [a, b] def = {x : a ≤ x ≤ b} over general partially ordered spaces – such as the space of all vectors with component-wise o...

Logic programs under answer set semantics have become popular as a knowledge representation formalism in Artificial Intelligence. In this paper we investigate the possibility of using answer sets for qualitative decision making. Our approach is based on an extension of the formalism, called logic programs with ordered disjunction (LPODs). These programs contain a new connective called ordered d...

We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic. 1. T0 and IS0. In this section, we introduce the system T0, and show that it corresponds to the...

The preparation of cation-ordered thin films correlated oxides is great interest for both fundamental and applied research. scientific long-term vision strongly motivated by the perspective studying electronic correlations in condensed matter without presence chemical or quenched disorder. A promising material platform provides double perovskite A2BB’O6 bulk samples with different types B/B’ or...

In this paper the author gives necessary and sufficient conditions under which to a stable weak isometry f in a directed group G there exists a direct decomposition G = A × B of G such that f(x) = x(A) − x(B) for each x ∈ G. Further, some results on weak isometries in partially ordered groups are established. Isometries in an abelian lattice ordered group (l-group) have been introduced and inve...

The software package SPuDS has previously been shown to accurately predict crystal structures of AMX(3) and A(1 - x)A'(x)MX(3) perovskites that have undergone octahedral tilting distortions. This paper describes the extension of this technique and its accuracy for A(2)MM'X(6) ordered double perovskites with the aristotype Fm\overline 3m cubic structure, as well as those that have undergone octa...