Moral conditions for methodologically rational decisions

The study’s main thesis is that respect for some moral values is a condition for methodologically rational decisions, namely, decisions which do not satisfy the condition are either not methodologically rational at all, or not fully rational. The paper shows supporting arguments for the thesis in terms of the philosophical theories by Aristotle, Immanuel Kant, Tadeusz Kotarbiński, Max Weber, Jean-Paul Sartre and some other thinkers. Their presentation undergoes phenomenological analysis of the phenomenon of decision making

A General-Theory Of Asymptotic Consistency For Subset-Selection With Applications

Mathematic

Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement

Two families (type $A$ and type $B$) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type $A$) and the Laguerre polynomials (type $B$), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl.Comment: AMS-LaTeX v1.2 (with amssymb.sty), 34 page

Properties of some families of hypergeometric orthogonal polynomials in several variables

Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of multivariable Wilson, continuous Hahn and Jacobi type polynomials, respectively. For each class of polynomials we provide systems of difference (or differential) equations, recurrence relations, and expressions for the norms of the polynomials in terms of the norm of the constant polynomial.Comment: 42 pages, AMSLaTeX 1.1 with amssym

Self-dual Koornwinder-Macdonald polynomials

We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify Macdonald's normalization conjectures for these polynomials.Comment: 21 pages, AMSLaTeX 1.1 with amssym