We review exact results obtained for R couplings in maximally supersymmetric type II string theories. These couplings offer a privileged scene to understand the rules of semiclassical calculus in string theory. Upon expansion in weak string coupling, they reveal an infinite sum of non-perturbative e−1/g effects that can be imputed to euclidean D-branes wrapped on cycles of the compactification ...

OVERVIEW When a body (or object) travels through space, the equations and that give the body’s coordinates as functions of time serve as parametric equations for the body’s motion and path. With vector notation, we can condense these into a single equation that gives the body’s position as a vector function of time. For an object moving in the xy-plane, the component function h(t) is zero for a...

We join Cardelli's and Mitchell's approaches to polymorphic subtyping by introducing a new uniied calculus G that subsumes both Cardelli-inspired systems with rigid subtyping on the one hand, and the more liberal Mitchell's containment calculus F Mit88] on the other. Up until now both approaches were considered incompatible, since F-provable containments between functional and universal types a...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...

1 1 INTRODUCTION 2 1 Introduction Classical calculus is a basic tool in analysis. We use it so often that we forget that its construction needed considerable time and effort. Especially in the last decade, the progresses made in the field of analysis in metric spaces make us reconsider this calculus. Along this line of thought, all started with the definition of Pansu derivative [24] and its ve...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

We show how to reduce the uniication problem modulo-conversion and a rst-order equational theory E, into a rst-order uni-cation problem in a union of two non-disjoint equational theories including E and a calculus of explicit substitutions. A rule-based uniica-tion procedure in this combined theory is described and may be viewed as an extension of the one initially designed by G. Dowek, T. Hard...

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss...