A hermitian integral kernel in N-space may be mapped to a corresponding Hamiltonian in 2N-space by the Wigner transformation. Linear simplectic transformation on the phase space of the Hamiltonian yields a new kernel whose spectrum is unchanged and whose eigenfunctions follow from an explicit unitary transformation. If an integral kernel has a Wigner transform whose surfaces of constant value a...

Monte Carlo criticality calculations use the power iteration method to determine the eigenvalue (keff) and eigenfunction (fission source distribution) of the fundamental mode. A recently proposed method for accelerating convergence of the Monte Carlo power iteration using Wielandt’s method has been implemented in a test version of MCNP5. The method is shown to provide dramatic improvements in c...

The multiplicity of the fractional Fourier transform (FRT), which is intrinsic in any fractional operator, has been claimed by several authors, but never systematically developed. The paper starts with a general FRT definition, based on eigenfunctions and eigenvalues of the ordinary Fourier transform, which allows us to generate all possible definitions. The multiplicity is due to different cho...

We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them. It is also shown that the eigenvalues emerge from the threshold of essential spectrum as the window passes through certain critical shapes. We prove the nec...

(∆− λ)f = T for a Γ-invariant distribution T on H, compactly-supported on Γ\H. The three main examples for T are described in detail below. That is, a slight roughness is tolerated in f at the support of the Γ-invariant distribution T . Three natural types of target distributions T are: (i) T is supported at a single point on Γ\H, (ii) T is supported on a closed geodesic on Γ\H, (iii) T evaluat...

In this paper we examine a spatially two–dimensional forced, damped Boussinesq equation with quadratic nonlinearity. This equation describes small, nonlinear oscillations of a circular, elastic membrane in the presence of viscosity. The eigenfunction expansion method is used for the purpose of constructing solutions for small initial data analytically. The constructive method enables us to perf...

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the ‘classical’ orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and ...

1. Introduction. The main purpose of this article is to give a stronger counterexample to the " hot spots " conjecture than the one presented in Burdzy and Werner [7]. Along the way we define and partly analyze a new process, which we call fiber Brownian motion, and which may have some interest of its own. Consider a Euclidean domain that has a discrete spectrum for the Laplacian with Neumann b...

We prove the “hot spots” conjecture of J. Rauch in the case that the domain Ω is a planar convex domain satisfying diam(Ω)2/|Ω| < 1.378. Specifically, we show that an eigenfunction corresponding to the lowest nonzero eigenvalue of the Neumann Laplacian on Ω attains its maximum (minimum) at points on ∂Ω. When Ω is a disk, diam(Ω)2/|Ω| t 1.273. Hence, the above condition indicates that Ω is a nea...

Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility χ(q) and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of ...