The Gaussian formula and the elusive fourth principal ray

1992 ◽  
Vol 60 (2) ◽  
pp. 160-163 ◽  
Author(s):  
Sue Allen
Keyword(s):  
Gaussian Formula

DIVERGENCE RESULTS FOR SELF-INTERSECTION LOCAL TIMES OF GAUSSIAN ${\mathscr S}' ({\mathbb R}^d)$-PROCESSES

2001 ◽  
Vol 04 (04) ◽  
pp. 417-488 ◽  
Author(s):  
ANNA TALARCZYK
Keyword(s):  
Local Time ◽  
Necessary Conditions ◽  
Particle Systems ◽  
The Self ◽  
Local Times ◽  
Intersection Local Time ◽  
Convergence In Law ◽  
Stable Particle ◽  
Gaussian Formula ◽  
Intersection Local Times

For various types of Gaussian [Formula: see text]-processes we consider the case when the self-intersection local time (SILT) does not exist. We study the rate of divergence of the corresponding approximating processes obtaining, after suitable normalizations convergence in law to some [Formula: see text]-valued processes (not necessarily Gaussian). We also obtain some new necessary conditions for the existence of SILT. We give examples associated with fluctuation limits of α-stable particle systems.

scholarly journals A generalization of the Gaussian formula and a q -analog of Fleckʼs congruence

2013 ◽  
Vol 133 (11) ◽  
pp. 3717-3738 ◽  
Author(s):  
Andrew Schultz ◽  
Robert Walker
Keyword(s):  
Gaussian Formula

Gaussian Formula for Ray Tracing in Lenses and Mirrors

2022 ◽  
Vol 60 (1) ◽  
pp. 56-57
Author(s):  
Nuri Balta
Keyword(s):  
Ray Tracing ◽  
Gaussian Formula

scholarly journals Uniform point variance bounds in classical beta ensembles

2020 ◽  
pp. 2150033
Author(s):  
Joseph Najnudel ◽  
Bálint Virág
Keyword(s):  
Unit Circle ◽  
Real Line ◽  
Variance Bounds ◽  
Multiplicative Constant ◽  
The Real ◽  
Beta Ensembles ◽  
Gaussian Formula

In this paper, we give bounds on the variance of the number of points of the Circular and the Gaussian [Formula: see text] Ensemble in arcs of the unit circle or intervals of the real line. These bounds are logarithmic with respect to the renormalized length of these sets, which is expected to be optimal up to a multiplicative constant depending only on [Formula: see text].

Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions

2016 ◽  
Vol 12 (02) ◽  
pp. 495-504 ◽  
Author(s):  
Emrah Kiliç ◽  
Helmut Prodinger
Keyword(s):  
Weight Function ◽  
Binomial Coefficients ◽  
Weight Functions ◽  
Partial Fraction ◽  
Decomposition Technique ◽  
Lucas Numbers ◽  
Finite Products ◽  
Partial Fraction Decomposition ◽  
Gaussian Formula

We consider sums of the Gaussian [Formula: see text]-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications of our results to certain generalized Fibonomial sums weighted with finite products of reciprocal Fibonacci or Lucas numbers.

Remarks on the Gaussian formula for refraction at a single spherical interface

1992 ◽  
Vol 60 (2) ◽  
pp. 131-135 ◽  
Author(s):  
V. Greco ◽  
G. Molesini ◽  
F. Quercioli
Keyword(s):  
Spherical Interface ◽  
Gaussian Formula
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