1.1. Stirling’s formula. Laplace’s approach to Stirling’s formula is noteworthy first, because it makes a direct connection with the Gaussian (normal) distribution (whereas in other approaches the Gaussian distribution enters indirectly, or not at all), and second, because it provides a general strategy for the asymptotic approximation of a large class of integrals with a large parameter. Stirl...

Let C(n; N) = R H N tr Z 2n (dZ) denote a matrix integral by a U(N)-invariant gaussian measure on the space H N of hermitian N N matrices. The integral is known to be always a positive integer. We derive a simple combinatorial interpretation of this integral in terms of rook conngurations on Ferrers boards. The formula C(n; N) = (2n ? 1)!! n X k=0 N k + 1 n k 2 k found by J. Harer and D. Zagier...

We show that the Sudakov factor from the resummation of double logarithms ln(s/k T ) contained in the distribution functions is responsible for the kT smearing mechanism employed in the next-to-leading-order QCD (αα 2 s) calculations of direct photon production. s is the center-of-mass energy, and kT the transverse momentum carried by a parton in a colliding hadron. This factor exhibits the app...

This paper gives necessary conditions and slightly stronger sufficient conditions for a holomorphic function to be the Segal-Bargmann transform of a function in L(R, ρ), where ρ is a Gaussian measure. The proof relies on a family of inversion formulas for the Segal-Bargmann transform, which can be “tuned” to give the best estimates for a given value of p. I also give a single necessary-and-suff...

We describe three different methods to compute all those characters of a finite group that have certain properties of transitive permutation characters. First, a combinatorial approach can be used to enumerate vectors of multiplicities. Secondly, these characters can be found as certain integral solutions of a system of inequalities. Thirdly, they are calculated via Gaussian elimination. The me...

The concepts of regular generalized functions in Gaussian analysis are presented. Spaces of regular generalized functions are characterized and their probabilistic structure is worked out. Finally, these concepts are applied to a nonlinear (Verhulst type) equation. Its solution is shown to be a regular generalized process with martingale property.

Terrain LOD algorithm is a dynamic and local dough sheet subduction algorithm. On the basis of the research on traditional quadtree algorithm, this paper proposed a new terrain LOD algorithm using quadtree. On deviation computing standard, besides static deviation and view distance, motion vector and observation vector are introduced, which made the result of deviation computing close to the ac...

A simple but powerful modification of the standard Gaussian distribution is studied. The variables of the rectified Gaussian are constrained to be nonnegative, enabling the use of nonconvex energy functions. Two multimodal examples, the competitive and cooperative distributions, illustrate the representational power of the rectified Gaussian. Since the cooperative distribution can represent the...

We present new complexity results on the class of All constraints The central idea involves func tional elimination a general method of elimination whose focus is on the subclass of functional constraints One result is that for the subclass of All constraints strong n consistency and minimality is achievable in O en time where e n are the number of constraints and variables The main result is t...

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time’s spending. Further, both of them can be used efficiently not only for positive (semi-) definite, but for any non-singular symmetric matrix inversion. We use simulation to verify results, ...