lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

the interaction of magnesium hydrate at the phosphate oxygen atom of the pyrimidine nucleotides (cmp,ump,dtmp) were studied at the hartree-fock level theory. we used lanl2dz basis set for mg and 6-31g* basis set for atoms.the basis set superposition error (bsse) begins to converge for used method/basis set. the gauge-invariant atomic orbital (giao) method and the continuous-set-of-gauge-transfo...

Very often, these computations involve collections of data, for example, a class management system might store a collection of students, or a server might need to track the set of computers it can directly communicate with on the network. Furthermore, these computations can frequently be phrased in terms of manipulations of or queries over these data, for example, generating pairs of students f...

I. The Role of Set Theory in Mathematics A. A Common Language and Framework B. Foundational Role II. Basic Ideas A. Membership and Extensionality B. Basic Operations on Sets III. The Iterative Concept of Sets A. Sets and Rank B. Proper Classes IV. Embedding Mathematics in Set Theory A. Functions and Relations B. Natural Numbers C. Other Number Systems V. Infinite Sets A. Cardinal Numbers B. Ord...

Set Theory deals with the fundamental concepts of sets and functions used everywhere in mathematics. Cantor initiated the study of set theory with his investigations on the cardinality of sets of real numbers. In particular, he proved that there are different infinite cardinalities: the quantity of natural numbers is strictly smaller than the quantity of real numbers. Cantor formalized and stud...

Notes on set theory, mainly forcing. The first four sections closely follow the lecture notes Williams [8] and the book Kunen [4]. The last section covers topics from various sources, as indicated there. Hopefully, all errors are mine. 1. The Suslin problem 1.1. The Suslin hypothesis. Recall that R is the unique dense, complete and separable order without endpoints (up to isomorphism). It follo...

Very often, these computations involve collections of data, for example, a class management system might store a collection of students, or a server might need to track the set of computers it can directly communicate with on the network. Furthermore, these computations can frequently be phrased in terms of manipulations of or queries over these data, for example, generating pairs of students f...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...