This paper deals with a dynamical system that generalizes the Kepler-Coulomb system and the Hartmann system. It is shown that the Schrödinger equation for this generalized KeplerCoulomb system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic and spheroidal) are studied in detail. It is found that the coef...

Representation theory for the Jordanian quantum algebra Uh(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of Uh(sl(2)) on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the gener...

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra Uq,p(ŝl2). The algebra Uq,p(ŝl2) has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra Uq(ŝl2) and a Heisenberg algebra. This yields a systematic construction of both finite and infinite-dimensional dynamical repre...

In this article the full set of irreducible unitary holomorphic representations of U (p, q) is determined. For a general Hermitian symmetric space G/K of the noncompact type the set of irreducible unitary representations of G on scalar valued holomorphic functions has been found by Wallach [14] and by Rossi and Vergne [11]. For the groups Mp(n, ~) and SU(n, n) unitary irreducible representation...

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint ⊗ adjoint → adjoint. We present a practical method for the determination of these quantum...

The theory of apolarity was first developed by Clebsch, Lasker, Richw x mond, Sylvester, and Wakeford 10, 17, 20 . They were first interested in studying homogeneous polynomials of degree p and in q variables, and in expressing them as sums of pth powers of linear terms. The problem is to minimize the number of pth powers which are required in such a sum. For instance, a result due to Sylvester...

background: some studies have shown the possible role of protein‑energy malnutrition (pem) in persistence of endemic goiter in iodine replenished areas. the present study was conducted to assess the association between pem and goiter in schoolchildren of isfahan, iran. methods: in a cross‑sectional study using multistage cluster random‑sampling, 2331 schoolchildren with age ranged from 6‑13 yea...

OBJECTIVE To develop a simple clinical scoring system for severity of illness to help prioritize care and predict outcome in emergency department. METHODS Prospective hospital based observational study. Out of a total of 874 children who attended emergency department in one year, 777 were included in the study. Data was collected at the time of admission in emergency department. The baseline ...

BACKGROUND Signs of Inflammation in Children that can Kill (SICK score) is a new severity-of-illness score. It uses the physical signs of the Systemic Inflammatory Response Syndrome (SIRS) and its continuum--the Multiple Organ Dysfunction Syndrome (MODS). The development of the score used multiple logistic regression model coefficients converted to integer scores that have been published earlie...