We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, and negative binomial distributions. Our results also establish connections between the entropy functions and to the Riemann z...

We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of Rn × R.

Analysis of data can be made by replacing observations by their ranks. The analysis produces inference for the regression model where the location parameters of the observations, i, i 1⁄4 1; 2; . . . ; n, are related by 1⁄4 X . Here X is an n by p matrix of explanatory variables and is a vector of p unknown regression parameters. The observations are replaced by their ranks and an approximation...

This note presents series expansions and nonlinear controllability results for Lagrangian systems subject to dissipative forces. The treatment relies on the assumption of dissipative forces of linear isotropic nature. The approach is based on the affine connection formalism for Lagrangian control systems, and on the homogeneity property of all relevant vector fields.

We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval Œ0;T  so that all signals issued from the domain leave it after time T . In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the ...

In this letter, a class of improved extreme learning machines (ELM) encoding a priori information is proposed to obtain better generalization performance and much faster convergence rate for function approximation. According to Fourier series expansion theory, the hidden neurons activation functions in the improved ELM are sine and cosine functions. In addition, the improved ELM analytically de...

We study the nuclear (A) dependence of the European Muon Collaboration (EMC) effect at high values of x (x ≥ 0.6). Our approach makes use of conventional nuclear degrees of freedom within the Relativistic Impulse Approximation. By performing a non-relativistic series expansion we demonstrate that relativistic corrections make a substantial contribution to the effect at x ∼ 0.6 and show that the...

In this article we proposed three explicit Improved Runge-Kutta (IRK) methods for solving first-order ordinary differential equations. These methods are two-step in nature and require lower number of stages compared to the classical RungeKutta method. Therefore the new scheme is computationally more efficient at achieving the same order of local accuracy. The order conditions of the new methods...

Let B(t), t ∈ [−1, 1], be the fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1 ) . In this paper we present the series representation

In a Galton-Watson branching process with o spring distribution (p0; p1; : : :) started with k individuals, the distribution of the total progeny is identical to the distribution of the rst passage time to k for a random walk started at 0 which takes steps of size j with probability pj+1 for j 1. The formula for this distribution is a probabilistic expression of the Lagrange inversion formula f...