here, the concept of quantum potential that has been illustrated in extended phase space (eps) in previous works is explored for its marginal behavior. unlike in configuration space, different representations of the quantum mechanics can be found in eps when exploiting appropriate canonical transformations. these canonical transformations revealed that there exist several representations in whi...

We describe a sensitive technique for measuring nonlinear refraction in a variety of materials that offers simplicity, sensitivity and speed. The transmittance of a sample is measured through a finite aperture in the far -field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinearity is easily deduced from such a transmittance ...

Abstract. Signed digit representations with base q and digits − q 2 , . . . , q 2 (and uniqueness being enforced by applying a special rule which decides whether −q/2 or q/2 should be taken) are considered with respect to counting the occurrences of a given (contiguous) subblock of length r. The average number of occurrences amongst the numbers 0, . . . , n−1 turns out to be const · log q n + δ...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...

This study aims to offer a critical analysis of V. S. Naipaul’s second Islamic travelogue Beyond Belief: Islamic Excursions Among the Converted Peoples (1998), which chronicles the author’s excursions to the 4 non-Arab Muslim countries of Indonesia, Iran, Pakistan, and Malaysia. This critique is presented, firstly, through problematizing the author’s theorization on the theme of Muslim conversi...