Many combinatorial configurations (for example, perfect codes, latin squares and hypercubes, combinatorial designs and their q-ary generalizations — subspace designs) can be defined as an eigenfunction on a graph with some discrete restrictions. The study of these configurations often leads to the question about the minimum possible difference between two configurations from the same class (it ...

Zonal ‡ow helps reduce and control the level of ion temperature gradient (ITG) turbulence in a tokamak. The collisional damping of zonal ‡ow has been estimated by Hinton and Rosenbluth (H-R). Their calculation shows that the damping of zonal ‡ow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, H-R calculated the neoclassi...

The Fokker–Planck equation is solved by the method of distributed approximating functionals via forward time propagation. Numerical schemes involving higher-order terms in Dt are discussed for the time discretization. Three typical examples ~a Wiener process, an Ornstein–Uhlenbeck process, and a bistable diffusion model! are used to test the accuracy and reliability of the present approach, whi...

New theoretical results from large-scale relativistic close coupling calculations reveal the precise effect of resonances in collisional excitation of x-ray lines of Ne-like Fe XVII. By employing the Breit-Pauli R-matrix method and an 89-level eigenfunction expansion, including up to n = 4 levels, significant resonance enhancement of the collision strengths of forbidden and intercombination tra...

We find a close relationship between the discrete KarhunenLoeve transform (KLT) and the discrete prolate spheroidal wave functions (DPSWF). We show that the DPSWF form a natural basis for an expansion of the eigenfunctions of the KLT in the frequency domain, and then determine more general conditions that any set of functions must obey to be a valid basis. We also present approximate solutions ...

A method for solving various half-space multigroup transport problems for the case of a general transfer matrix is explained. A non-linear integral equation for the emergent distribution of the albedo problem is derived. Then, by using the full-range completeness of the infinite medium eigenfunctions, the distribution inside the half-space is obtained from the emergent distribution. Finally, th...

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...