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81.
This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials. 相似文献
82.
83.
Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain
a decomposition of continuity. 相似文献
84.
Zarubitskii O. G. Budnik V. G. Omel'chuk A. A. Melekhin V. T. Opanasyuk V. P. Zakharchenko N. F. 《Russian Journal of Applied Chemistry》2002,75(4):558-561
Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry. 相似文献
85.
The procedure for calculating the dispersion of the refractive and absorption indices and thickness of an optical film, based on measurements of spectral dependence of the transmittance, is described. The film parameters are calculated using a solution of the approximation problem. The effect of the film model on the calculated values of the refractive and absorption indices is analyzed. 相似文献
86.
87.
The process of harmonic wave propagation is investigated in a semi-infinite rigidly-clamped elastic layer. An analytic solution of the problem is obtained by the superposition method. The wave field expansion in the form of a normal mode series for a corresponding infinite waveguide is established. According to residue theory, the explicit form of the expansion coefficients is established with physical requirements of the radiation conditions taken into account.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 3–10, 1988. 相似文献
88.
O. Babelon 《Communications in Mathematical Physics》2006,266(3):819-862
The classical Volterra model, equipped with the Faddeev-Takhtajan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so-called separated variables. Taking the continuum limit of these formulae, we obtain the Virasoro generators written as determinants of infinite matrices, the elements of which are constructed with a set of points lying on an infinite genus Riemann surface. The coordinates of these points are separated variables for an infinite set of Poisson commuting quantities including L
0. The scaling limit of the eigenvector can also be calculated explicitly, so that the associated Schroedinger equation is in fact exactly solvable. 相似文献
89.
V. De Sabbata C. Sivaram H.-H. v. Borzeszkowski H.-J. Treder 《Annalen der Physik》1991,503(7):497-502
It is shown that in gravitational theories with torsion one is led to commutation rules corresponding to Landau-Peierls type uncertainty relations. 相似文献
90.