An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to original ones in compact matrix format. Keywords—Quadratic forms, characteristic function, multichannel communication systems.

The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and ...

We consider an inverse problem of identifying the support D of a source term in an elliptic equation −∆u(x) + q(x)χD(x)u(x) = 0, x ∈ Ω and u(x) = f(x), x ∈ ∂Ω. Here q is a given positive function and χD is the characteristic function of a subdomain D such that D ⊂ Ω. By using a Carleman estimate, we prove the global uniqueness in this inverse problem within convex hulls of polygons D’s.

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulæ for the distribution of the sum of n non-identically distributed uniform random variables in both the continuo...

We obtain a formula for the values of the characteristic function of a character sheaf, in terms of the representation theory of certain finite groups related to the Weyl group. This formula, a generalization of previous results due to Mœglin and Waldspurger, depends on knowledge of certain reductive subgroups that admit cuspidal character sheaves. For quasi-simple groups, we make the formula t...

In this paper, we introduce a new core concept for partition function games, to be called the strong-core, which reduces to the ordinary core if the worth of every coalition is independent of the partitions to which it belongs and the game is adequately represented by a characteristic function. It is nicely related to previous core concepts, but unlike them does not assume formation of a specif...

A goodness–of–fit test for two–component homoscedastic and homothetic mixtures of normal distributions is proposed. The tests are based on a weighted L2–type distance between the empirical characteristic function and its population counterpart, where in the latter, parameters are replaced by consistent estimators. Consequently the resulting tests are consistent against general alternatives. Whe...

soil hydraulic properties such as soil water characteristic curve are necessary prerequisite for modeling water movement and solute transport. direct methods of estimating these hydraulic properties are time consuming and costly. indirect methods, such as pedotransfer functions, estimate the hydraulic parameters using easy-to-measure soil properties like particle size distributions, bulk densit...