Properties of certain q-orthogonal polynomials are connected to the qoscillator algebra. The Wall and q-Laguerre polynomials are shown to arise as matrix elements of q-exponentials of the generators in a representation of this algebra. A realization is presented where the continuous q-Hermite polynomials form a basis of the representation space. Various identities are interpreted within this model. In particular, the connection formula between the continuous big q-Hermite polynomials and the continuous q-Hermite polynomials is thus obtained, and two generating functions for these last polynomials are algebraically derived.

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We apply the ~justernik-Snirelman theory, a derivative of Morse theory, to the Skyrmion-Skyrmion potential in the two-flavor Skyrme model to look for the existence of new, static, classical solutions in the sector with baryon number two. Concomitantly, we present a systematic method for obtaining an expansion of this potential, in inverse powers of the separation, when the separation is large.

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A general discussion of nonrelativistic multichannel scattering for nonlocal potentials is presented. The approach is based on the extensive use of the Fredholm determinants that are associated with the integral equations occurring at various points of the theory. Special attention is paid to situations where confining potentials are present, as in nonrelativistic quark models of hadron-hadron interactions. Some standard results of multichannel scattering theory for local potentials and one-channel theory for nonlocal ones are generalized in this context, including Levinson s theorem.PACS number(s): 24. 10.Cn, 12.40.Aa