The Schrödinger equation for the four-dimensional double singular oscillator is separable in Eulerian, doble polar and spheroidal coordinates in IR. It is shown that the coefficients for the expansion of double polar basis in terms of the Eulerian basis can be expressed through the Clebsch-Gordan coefficients of the group SU(2) analytically continued to real values of their arguments. The coeff...

BACKGROUND The purpose of the present study was to develop and evaluate a risk score to predict people at high risk of cardiovascular autonomic dysfunction neuropathy (CAN) in Chinese population. METHODS AND MATERIALS A population-based sample of 2,092 individuals aged 30-80 years, without previously diagnosed CAN, was surveyed between 2011 and 2012. All participants underwent short-term HRV ...

In order to develop a practical risk score for 90-day mortality following surgical lung biopsy (SLB) for interstitial lung disease (ILD) we reviewed 311 consecutive patients undergoing SLB for ILD between 2002 and 2009. Postoperative complication, 30-day and 90-day mortality rates were 11.5%, 9% and 10.6% respectively. Univariable and multivariable analyses, validated by bootstrap statistics, w...

We show that for every set of discrete polynomials yn(x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials zk(ξ(t)) of degrees k = s−a and k = b− s− 1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative f...

We develop exact expressions for the coefficients of series representations of translations and rotations of local and multipole fundamental solutions of the Helmholtz equation in spherical coordinates. These expressions are based on the derivation of recurrence relations, some of which, to our knowledge, are presented here for the first time. The symmetry and other properties of the coefficien...

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), Uq(sl2) and the enveloping algebra of the 3-dimensional Heisenberg Lie algebra. In a torsion-free case we describe the finite-dimensional simple modules, in particular their dimensions and pr...

Computer codes are developed to calculate Clebsch–Gordan coefficients of SU(3) in both SU(2)and SO(3)-coupled bases. The efficiency of this code derives from the use of vector coherent state theory to evaluate the required coefficients directly without recursion relations. The approach extends to other compact semi-simple Lie groups. The codes are given in subroutine form so that users can inco...

We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t . We prove the first nontrivial degree formula and use it to show that existence of morphisms between algebraic varieties for which these numbers are not divisible by q give information on the degree of such morphisms or on zero c...

Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...