Generalized Bose-Einstein and Fermi-Dirac distributions in nonextensive quantum statistics have been discussed by the maximum-entropy method (MEM) with the optimum Lagrange multiplier based on the exact integral representation [A. K. Rajagopal, R. S. Mendes, and E. K. Lenzi, Phys. Rev. Lett. 80, 3907 (1998)]. It has been shown that the (q-1) expansion in the exact approach agrees with the resul...

Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...

We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace’s equation which arises in the context of the Calogero-Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials and the constraints on the coefficients of expansion are derived. These constraints involve generalized binomial coefficients defined through Jack polynomials...

In neurological circles today the name James Taylor (1859-1946) is probably remembered mainly for his role in editing the Selected Writings of John Hughlings Jackson, the most readily available source of Jackson's contributions to neurological knowledge. Taylors' own neurological achievements are largely or entirely forgotten, but in his day he was an influential figure whose career linked the ...

Braided differential operators ∂ are obtained by differentiating the addition law on the braided covector spaces introduced previously (such as the braided addition law on the quantum plane). These are affiliated to a Yang-Baxter matrix R. The quantum eigenfunctions expR(x|v) of the ∂ i (braided-plane waves) are introduced in the free case where the position components xi are totally noncommuti...

Generalized random processes by various types of continuity are considered and classified as generalized random processes (GRPs) of type (I) and (II). Structure theorems for Hilbert space valued generalized random processes are obtained: Series expansion theorems for GRPs (I) considered as elements of the spaces L(A, S(H)−1) are derived, and structure representation theorems for GRPs (II) on K{...

Two new recursive approaches have been developed to provide accurate estimates for posterior moments of both parameters and system states while making use of the generalized polynomial-chaos framework for uncertainty propagation. The main idea of the generalized polynomial-chaos method is to expand random state and input parameter variables involved in a stochastic differential/difference equat...

We propose a fully Bayesian methodology for generalized kernel mixed models (GKMMs), which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of a generalized kernel model (GKM). This mixture prior allows a fraction of the components of the regres...

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent stationary Gaussian processes with uncertain hyper-parameters describe uncertainties of the model structure and parameters while Karhunnen-Loeve expansion is ado...

The pseudoperturbative shifted l expansion technique PSLET [16-19] is generalized for states with arbitrary number of nodal zeros. Boundstates energy eigenvalues for two truncated coulombic potentials are calculated using PSLET. In contrast with shifted large-N expansion technique, PSLET results compare excellently with those from direct numerical integration.