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...

We review determinations of the electric proton charge radius from a diverse set low-energy observables. explore under which conditions it can be related to Wilson coefficients appropriate effective field theories. This discussion is generalized other constants. provides us with unified framework deal constants associated its electromagnetic interactions. Unambiguous definitions these objects a...

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

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...

This thesis is concerned with the area of algebraic set theory. Algebraic set theory was invented by Joyal and Moerdijk [18] with the aim to study set theory from the perspective of category theory. The central notion is a category of classes, given by a triple (E ,S,Ps), consisting of a Heyting pretopos E , a particular class S of arrows of E that are called small maps and an endofunctor Ps : ...