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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
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Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
Two families (type and type ) 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 ) and the Laguerre polynomials (type ), 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
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