We theoretically show that an astigmatic transformation of nth-order edge dislocation (a zero-intensity straight line) produces n optical elliptical vortices (spiral dislocations) with unit topological charge at the double focal distance from cylindrical lens, located on a line perpendicular to dislocation, points whose coordinates are roots Hermite polynomial. The orbital angular momentum is p...

Given integers N n 0, we consider the least squares problem of nding the vector of coeecients ~ P with respect to a polynomial basis P N j=0 wn(zj) 2 jf(zj) ? P (zj)j 2. Here a perturbation of the values f(zj) leads to some perturbation of the coeecient vector ~ P. We denote by n the maximal magniication of relative errors, i.e., the Euclidean condition number of the underlying weighted Vanderm...

All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising rst-order clauses have involved inverting the clausal subsumption relationship. However , even Plotkin realised that this approach was incomplete. Since inversion of subsumption is central to many Inductive Logic Programming approaches, this form of incomple...

In this paper, we consider the relationships between the second order linear recurrences and the permanents and determinants of tridiagonal matrices. 1. Introduction The well-known Fibonacci, Lucas and Pell numbers can be generalized as follows: Let A and B be nonzero, relatively prime integers such that D = A 4B 6= 0: De…ne sequences fung and fvng by, for all n 2 (see [10]), un = Aun 1 Bun 2 (...

In this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.