Definition of the partition function of U(1) gauge theory is extended to a class of fourmanifolds containing all compact spaces and the asymptotically locally flat (ALF) ones including the multi-Taub–NUT sopaces. The partition function is calculated via zetafunction regularization and heat kernel techniques with special attention to its modular properties. In the compact case, compared with the...

Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits and significands, often referred to as Benford’s Law (BL) or, in a special case, as the First Digit Law. The invariance properties that characterize BL are developed in detail. Special attention is gi...

The UQV theory is a metaphysical theory that the universe is the consequence of the ultimate questioner’s vanity 1 . This theory builds on the NSTP (Non – Spatial Thinking Process) theoretical metaphysical semi-solipsism, the position, which specifically regards the NSTP theoretical superhuman mind as a personal philosophical questioning supermind. The UQV theory further speculates the existenc...

The technology required for eikonal scattering amplitude calculations in Matrix theory is developed. Using the entire supersymmetric completion of the v/r Matrix theory potential we compute the graviton–graviton scattering amplitude and find agreement with eleven dimensional supergravity at tree level.

the wisdom of crowds, an innovative theory described in social science, claims that the aggregate decisions made by a group will often be better than those of its individual members if the four fundamental criteria of this theory are satisfied. this theory used for in clustering problems. previous researches showed that this theory can significantly increase the stability and performance of lea...

in the study of one-dimensional spin chains with nearestneighbor antiferromagnetic exchange interaction J, following the conjecture by Haldane' that integer spin chains have a singlet ground state with a finite gap EH in the excitation spectrum, whereas the excitation spectrum for half-integer spins is gapless. More recently, the physics of S =1 open spin chains has received new attention stimu...

We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X)). The main theorem of local class field theory consists of the isomorphism theorem and existence theorem. In this section we consider the isomorphism theorem. An outline of one of the proofs is as follows. First, for the Brauer group Br(K), an isomorphism inv: Br(K) →̃Q/Z is established; it mainly...

Abstract. We construct a discrete model of the homotopy theory of S-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. P inherits a model structure from the model structures on the categories of simplicial sets and cyclic sets. We then show that there is a Quillen equivalence between P and the model category of S-spa...

U(1) gauge theory on R is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of SL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-ener...

Advances on the theory of M&S Achieving a widely accepted theoretical foundation with a sound computational framework in modeling and simulation (M&S) is still a hot topic. The path to a complete theory of M&S (TMS) crosses many well-established areas, such as systems theory, software engineering, automata theory, graph theory, etc. This special issue aims at highlighting the most recent advanc...