We study the enumeration problem for different kind of tree parking functions introduced recently, called functions, distributions, prime and rooted labelled trees important combinatorial families including ordered, unordered binary trees. Using decompositions underlying structures yields, after solving resulting equations, implicit characterizations suitable generating total number such size n...

We have developed a transfer matrix algorithm for the enumeration of compact self-avoiding walks on rectangular strips of the square lattice. The algorithm is easily adapted to other shapes or generalized to problems such as interacting walks. These models are relevant in the study of globular proteins.  2001 Elsevier Science B.V. All rights reserved. PACS: 05.50.+q; 02.70.Rw; 61.25.Hq

In this paper we consider the numerical solution of large-scale projected generalized continuous-time and discrete-time Sylvester equations with low-rank right-hand sides. First, we present the results on the sufficient conditions for the existence, uniqueness, and analytic formula of the solutions of these equations. Second, we review the low-rank alternating direction implicit method and the ...

Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born rad...

In this paper, we prove the strong convergence of an implicit iterative scheme with errors to a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings in convex metric spaces. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces. With the help of an example we compare implicit iteration used in our re...