A Sequence of Matrix Valued Orthogonal Polynomials Associated to Spherical Functions

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, with respect to a weight W, that are eigenfunctions of a second-order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We also find other second-order differential operator E symmetric with respect to W and we describe the algebra generated by D and E.     

Short Disjoint Paths in Locally Connected Graphs

Chartrand and Pippert proved that a connected, locally k-connected graph is (k + 1)-connected. We investigate the lengths of k + 1 disjoint paths between two vertices in locally k-connected graphs with respect to several graph parameters, e.g. the k-diameter of a graph. We also give a generalization of the mentioned result. This research was partly done on a visit to the Institute of Systems Science of Academia Sinica (Beijing, China) under the project ME 418 of the Czech Ministery of Education. These authors are partly supported by the project LN00A056 of the Czech Ministery of Education.     

Spinning analytic discs and domains of dependence

In this paper we introduce a new technique of spinning analytic discs, which allows us to control the direction of CR extension of CR functions from rigid CR manifolds. Received: 30 January 1998     

Pre-Regge calculus: Topology via logic

Spacetime is simulated by a pattern space — a finite topological space homotopically equivalent to the spacetime simulated. Unlike the Regge calculus, we ignore metrical properties. A calculus based on Boolean arithmetic is suggested to describe the changing of global topology of the pattern spaces, and is suitable for computer realization.     

Calcia-supported lanthanide oxides. I. Preparation and characterization

Ln₂O₃-CaO systems, where Ln=La, Sm, have been prepared by impregnation of calcia with aqueous solutions of Ln nitrates or by mixing both oxides. Decomposition at 1073 K leads to a slight decrease in the specific surface area when starting from Ln₂O₃, but to a sharp decrease when starting from the nitrates.     

Constraints on cosmologically regenerated gravitinos

Cosmological constraints on the regenerated abundance of gravitinos as a function of the maximum reheating temperature T_h are examined. We combine the bound that arises in order for stable photinos produced by gravitino decays to not overdominate the mass density of the universe together with that inferred from the distortions produced in the cosmic microwave background radiation as well as constraints from the observed deuterium and ³He abundances. This suffices to constrain T_h to be below between 10¹⁷ and 10¹⁰ GeV for gravitions in the mass below ～ 10 TeV. More massive gravitinos, however, could be produced at T_h<10¹⁴ GeV.     

Birefringence measurements of liquid crystals and an application: An achromatic waveplate

We demonstrate a quarter wave phase retarder consisting of two layers of different liquid crystals (LCs). The phase retardation does not differ by more than ±5% from the target value π/2 within a spectral interval of 200 nm in the visible range. These values are comparable to the data for commercial two layer crystalline retarders which are much more expensive, especially if large apertures are required. In order to design the LC retarder we measured the birefringence of the LC within the entire visible spectrum using a published technique which does not consider interference effects due to reflections within indium-tin oxide coated LC cells. We show that these effects do not affect the results adversely provided that the birefringence data are taken over a broad spectral range.     

Extension and approximation of CR functions on tube manifolds

A complete generalization of the classical Bochner theorem for infinite tubes is given.