The q-Gamma White Noise

Abstract

ABSTRACT. For 0 < q < 1 and 0 < α < 1, we construct the infinite dimensional q-Gamma white noise measure γ α,q by using the Bochner-Minlos theorem. Then we give the chaos decomposition of an L 2 space with respect to the measure γ α,q via an isomorphism with the 1-mode type interacting Fock space associated to the q-Gamma measure.

The Geometrical Formulation of Variational Principle under the Theory of Fiber Bundle

“…( 1) is the Euler-Lagrange equation in classical case, and ( 35) is the Euler-Lagrange equation in particle feld; the new formula is simple and comprehensive in particle felds. We expect to study the nanoparticle and quantum white noise [19][20][21][22][23] case which is now attractive in mathematical physics.…”

Phase Congruential White Noise Generator

“…Formula ( 6) formally coincides with the Pythagorean Theorem in a multidimensional linear geometric space. From analytical geometry it is known (or it could be counted directly) that cosine of the angle between two linear vectors is determined by the scalar multiplication (5) between them and their norms (6). So, using Expressions (5) and ( 6), the following Formula (7) for the angle between the autovectors Z i and Z k can be obtained:…”

“…An analysis of the literature shows that most of the articles describe different applications of white noise, as well as its recognition in transmitted signals. This includes the areas such as theoretical and applied mathematics [5][6][7][8][9], physical research [3,4,[10][11][12][13], electronic and radio engineering [14][15][16][17][18][19][20][21][22][23], acoustics and noise phenomena [1][2][3][4]24,25], computer algorithms [26,27], geological prospecting and exploration [28,29], medical and biological research [30][31][32][33][34][35][36], psychology and psychiatry [37,38], and others. It is worth noting that significant results have been achieved in those fields.…”