A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate ...

The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing...

Key reconciliation techniques are employed to discard the effect of uncorrelated noise present at the communicating nodes of a reciprocal channel. Under a direct lineof-sight scenario, to randomize the channel, one of the communicating nodes shall be equipped with a RECAP antenna. The Linde-Buzo-Gray vector quantization is employed to the measured data, to support key generation. To eliminate t...

The objective of this paper is to extend, in the context of multicore architectures, the concepts of algorithms-by-tiles [Buttari et al., 2007] for Cholesky, LU, QR factorizations to the family of twosided factorizations. In particular, the bidiagonal reduction of a general, dense matrix is very often used as a pre-processing step for calculating the singular value decomposition. Furthermore, i...

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poinca...

Let A be an n × n symmetric matrix of bandwidth 2m + 1. The matrix need not be positive definite. In this paper we will present an algorithm for factoring A which preserves symmetry and the band structure and limits element growth in the factorization. With this factorization one may solve a linear system with A as the coefficient matrix and determine the inertia of A, the number of positive, n...

Phase diagrams of the two-dimensional one-band t-t8 Hubbard model are obtained within the two-patch and temperature-cutoff many-patch renormalization group approaches. At small t8 and at van Hove band fillings antiferromagnetism dominates, while with increasing t8 or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t85t/2 and close to van Hove band fillings the ...

The concept of S-permutation matrix is considered in this paper. It defines when two binary matrices are disjoint. For an arbitrary n × n S-permutation matrix, a lower band of the number of all disjoint with it S-permutation matrices is found. A formula for counting a lower band of the number of all disjoint pairs of n × n S-permutation matrices is formulated and proven. As a consequence, a low...

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tightbinding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width W and dimerizatio...