Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators

Biquaternionic Vekua-type equations arising from the factorization of linear second order elliptic operators are studied. Some concepts from classical pseudoanalytic function theory are generalized onto the considered spatial case. The derivative and antiderivative of a spatial pseudoanalytic function are introduced and their applications to the second order elliptic equations are considered.Comment: 17 page

Zakharov-Shabat system and hyperbolic pseudoanalytic function theory

In [1] a hyperbolic analogue of pseudoanalytic function theory was developed. In the present contribution we show that one of the central objects of the inverse problem method the Zakharov-Shabat system is closely related to a hyperbolic Vekua equation for which among other results a generating sequence and hence a complete system of formal powers can be constructed explicitly.Comment: 9 page

An analogue of the Sommerfeld radiation condition for the Dirac operator

A simple radiation condition at infinity for time-harmonic massive Dirac spinors is proposed. This condition allows an analogue of the Cauchy integral formula in unbounded domains for null-solutions of the Dirac equation to be proved. The result is obtained with the aid of methods of quaternionic analysis.Comment: 15 pages, 1 figur

B Spectroscopy at Tevatron

Recent results on heavy flavor spectroscopy from the CDF and D0 experiments are reported in this contribution. Using up to 1 fb-1 of accumulated luminosity per experiment, properties of X(3872), excited B** states, and the B_c meson are measured. Also included are measurements of production rates for ground state b hadrons in ppbar collisions.Comment: This paper reflects the presentation on B spectroscopy at the Flavor Physics and CP Violation'06 conference in Vancouver, Apr 9-12, 2006. To be published in conferences proceeding

Wave polynomials, transmutations and Cauchy's problem for the Klein-Gordon equation

We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein-Gordon equation with a variable coefficient. Using the transmutation (transformation) operators and their recently discovered mapping properties we prove the completeness of the generalized wave polynomials and use them for an explicit construction of the solution of the Cauchy problem for the Klein-Gordon equation. Based on this result we develop a numerical method for solving the Cauchy problem and test its performance.Comment: 31 pages, 8 figures (16 graphs