Let f (x) = 1+ ∑n=1 anx n be a formal power series with complex coefficients. Let {rn}n=1 be a sequence of nonzero integers. The Integer Power Product Expansion of f (x), denoted ZPPE, is ∏k=1(1+wkx k)rk . Integer Power Product Expansions enumerate partitions of multi-sets. The coefficients {wk}k=1 themselves possess interesting algebraic structure. This algebraic structure provides a lower bou...

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any...

High-speed computational procedures for space radiation shielding have relied on asymptotic expansions in terms of the off-axis scatter and replacement of the general geometry problem by a collection of flat plates. This type of solution was derived for application to human rated systems in which the radius of the shielded volume is large compared to the off-axis diffusion limiting leakage at l...

In this paper we consider some asymptotic aspects related to the proole of a reactive solute, which is injected from a well (radius > 0) into a three-dimensional porous medium. We present a convergence result for # 0 as well as the large time behaviour. Regarding the latter we show that the solute proole evolves in a self-similar way towards a stationary distribution and we give an estimate for...

In this paper we solve the asymptotic counting problem for unlabeled k-trees. By applying a proper singularity analysis of generating functions we show that the numbers Un of unlabeled k-trees of size n are asymptotically given by Un ∼ ckn(ρ1k) , where ck > 0 and ρ1k > 0 denotes the radius of convergence of the generating function U(z) = ∑ n≥0 Unz . Furthermore we prove that the number of leave...

We consider the following superlinear elliptic equation on Sn  ε∆Snu− u+ f(u) = 0 in D; u > 0 in D and u = 0 on ∂D, where D is a geodesic ball on Sn with geodesic radius θ1, and ∆Sn is the Laplace-Beltrami operator on Sn. We prove that for any θ ∈ ( 2 , π) and for any positive integer N ≥ 1, there exist at least 2N + 1 solutions to the above problem for ε sufficiently small. Moreover, the asym...

The eigenvalue problem for an irreducible nonnegative matrix A = a ij ] in the max algebra system is A x = x, where (A x) i = max j (a ij x j) and turns out to be the maximum circuit geometric mean, (A). A power method algorithm is given to compute (A) and eigenvector x. This method generalizes and simpliies an algorithm due to Braker and Olsder. The algorithm is developed by using results on t...

A front tracking method for inviscid gas dynamics is presented. The key constructions and algorithms used in the code are described and the interrelations between shock capturing, interface dynamics, computational geometry, grid construction, and parallelism are discussed for the code as a whole. Validation is carried out by comparing the single mode bubble velocity for Rayleigh–Taylor instabil...

We compute the decay of the autocorrelation function of the observable |vx| in the Sinai billiard and of the observable vx in the associated Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We consider the standard configuration where the disks is centered inside a unit square. The asymptotic decay is found to be C(t) ∼ c(R)/t. An explicit expression is given for the prefact...

This paper investigates the mean stability of a class of discrete-time stochastic switched linear systems using the Lp-norm joint spectral radius of the probability distributions governing the switched systems. First we prove a converse Lyapunov theorem that shows the equivalence between the mean stability and the existence of a homogeneous Lyapunov function. Then we show that, when p goes to ∞...