for 1 <; i < k. L. Carlitz [2] first derived the generating function for restricted bipartite partitions. Subsequently Carlitz and Roselle [3] enumerated certain special families of these partitions e.g., restricted bipartite partitions where the m< and % are all odd. Finally both Roselle [4] and Andrews [1] have obtained different generalizations for multipartite partitions. All these results ...

The site perimeter enumeration of polyominoes that are both columnand row-convex is a well-understood problem that always yields algebraic generating functions. Counting more general families of polyominoes is a far more difficult problem. Here Mireille BousquetMélou and Andrew Rechnitzer enumerate (by their site perimeter) the simplest family of polyominoes that are not fully convex—bargraphs....

Families of kernels that are useful in a variety of early vision algorithms may be obtained by rotating and scaling in a continuum a `template' kernel. These multi-scale multi-orientation family may be approximated by linear interpolation of a discrete nite set of appropriatèbasis' kernels. A scheme for generating such a basis together with the appropriate interpolation weights is described. Un...

We consider several types of pure grammars and systems as language acceptors and compare them to their generating counterparts. In contrast with the case (considered in earlier papers of the authors) encountered when admitting nonterminals in these classical string rewriting mechanisms , we get incomparability results between language families generated and accepted by numerous types of pure gr...

In recent years, many works on the subject of fractional calculus contain interesting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis ( such as ordinary and partial differential equations, integral equations, summation of series, etc.). The main object of this paper is to construct multivariable extension of Jacobi polynomia...

Despite recent efforts to develop automated protein structure determination protocols, structural genomics projects are slow in generating fold assignments for complete proteomes, and spatial structures remain unknown for many protein families. Alternative cheap and fast methods to assign folds using prediction algorithms continue to provide valuable structural information for many proteins. Th...

The purpose of this paper is to construct a unified generating function involving the families higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using their functional equations, we investigate some properties these Moreover, derive several connected formulas relations including Miller–Lee polynomials, Laguerre Lagrange Hermite–Miller–Lee

Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where restrictions are put on the locations where rotations are permitted, and provide upper bounds on distances between trees with a fixed number of nodes with respect to se...

Using data obtained during a retrospective interview study of 30 women who had undergone genetic testing-BRCA1/2 mutation searching-this paper describes how women, previously diagnosed with breast/ovarian cancer, perceive their role in generating genetic information about themselves and their families. It observes that when describing their motivations for undergoing DNA testing and their exper...

Bennett et al. [2] presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a single square partition or with several partitions with only one part. The cardinalities of those families of partitions are the Catalan and ballot numbers, respectively. In this paper we present a non-recursive descrip...