Dijkgraaf and Vafa have conjectured that the effective superpotentials for N = 1 four-dimensional supersymmetric gauge theories can be given by the planar diagrams of matrix models. We examine some special models with cubic and quartic tree level superpotentials for adjoint chiral superfield Φ. We consider the effective superpotentials for the classical vacuum Φ = 0 for U(N) and SO(N)/Sp(N) gau...

Sliding mode control (SMC) is an effective method of controlling systems with uncertainties which satisfy the socalled matching condition. However, how to effectively handle mismatched uncertainties of systems is still an ongoing research issue in SMC. Several methods have been proposed to design a stable sliding surface even if mismatched uncertainties exist in a system. Especially, it is pres...

Recommender systems have been widely utilized by online merchants and online advertisers to promote their products in order to improve profits. By evaluating customer interests based on their purchase history and relating it to commodities for sale these retailers could excavate out products which are most likely to be chosen by a specific customer. In this case, online ratings given by custome...

We study the leading quantum effects in the recently introduced Matrix Big Bang model. This amounts to a study of supersymmetric Yang-Mills theory compactified on the Milne orbifold. We find a one-loop potential that decays near the Big Bang. More surprisingly, the potential decays very rapidly at late times where it appears to be generated by D-brane effects. Usually, general covariance constr...

This paper presents the calculation of the reflectivity, transmissivity and optical constants of ultrathin Cu-Ni multilayer stacks using the characteristic effective medium approximation (CEMA) introduced in an earlier communication. Each of the Cu-Ni multilayer stacks has an identity period of 100 Å, Cu – 45 Å and Ni – 55 Å. Calculations of the reflectivity and transmissivity are executed via ...

Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative domains.

effective elastic properties for carbon nanotube reinforced composites are obtained through a variety of micromechanics techniques. an embedded carbon nanotube  in  a  polymer  matrix  and  its surrounding  interphase  is  replaced with an equivalent fiber for  predicting  the  mechanical  properties of  the  carbon  nanotube/polymer composite. the effects of an interphase layer between the nan...

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...

An implementation of Automatic Sparsity Detection (ASD) as a new source-to-source transformation is presented. Given a code for evaluation of a function, ASD generates code to evaluate the sparsity pattern of the function’s Jacobian by operations on bit-vectors. Similar to Automatic Differentiation (AD), there are forward and reverse modes of ASD. As ASD code has significantly fewer required va...

In this paper, we describe our development of GABLE, a Matlab implementation of the Geometric Algebra based on C̀ p,q (where p+ q = 3) and intended for tutorial purposes. Of particular note are the matrix representation of geometric objects, effective algorithms for this geometry (inversion, meet and join), and issues in efficiency and numerics.