a graph of size n is said to be graceful when is possible toassign distinct integers from {0, 1, . . . , n} to its verticesand {|f(u)−f(v)| : uv ∈ e(g)} consists of n integers. inthis paper we present broader families of graceful graphs; these families are obtained via three different operations: the third power of a caterpillar, the symmetric product of g and k2 , and the disjoint :union: of g...

This study examined the probability of (a) being placed in a disciplinary alternative education setting for mandatory versus discretionary reasons and (b) returning within the same year among an ethnically diverse sample (African American, Caucasian, Hispanic) of middle and high school students (N=270). Participants were compared based on ethnicity, gender, grade level, and special education st...

let $g$ be a finite group and $gamma(g)$ the prime graph of $g$‎. ‎recently people have been using prime graphs to study simple groups‎. ‎naturally we pose a question‎: ‎can we use prime graphs to study almost‎ ‎simple groups or non-simple groups? in this paper some results in‎ ‎this respect are obtained and as follows‎: ‎$gcong s_p$ if and only‎ ‎if $|g|=|s_p|$ and $gamma(g)=gamma(s_p)$‎, ‎whe...

We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on [−1, 1] via the special form of the representation of the derivatives pn+1(x) by pk(x), k = 0, ..., n.

We present static cylindrically symmetric electrovac solutions in the framework of the Brans-Dicke theory and show that our solution yields some of the well-known solutions for special values of the parameters of the resulting metric functions.

We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special symmetric generalizations of the Hermite polynomials.

We introduce a new family of symmetric functions, which are defined in terms of ribbon tableaux and generalize Hall-Littlewood functions. We present a series of conjectures, and prove them in two special cases.

A new de(nition of a symmetric fractional B-spline is presented. This generalises the usual integer order B-spline, that becomes a special case of the new one. ? 2003 Elsevier B.V. All rights reserved.