Journal ArticleDOI
Gamma Function Derivation of n-Sphere Volumes
TLDR
In this article, the Gamma Function Derivation of n-Sphere Volumes (GFDF) is used to derive the n-sphere volumes of a n-dimensional volume.Abstract:
(1982). Gamma Function Derivation of n-Sphere Volumes. The American Mathematical Monthly: Vol. 89, No. 5, pp. 301-302.read more
Citations
More filters
Book
Nonlocal Diffusion and Applications
Claudia Bucur,Enrico Valdinoci +1 more
TL;DR: In this article, a probabilistic motivation was proposed for the random walk with arbitrarily long jumps. But this motivation was based on the assumption that all functions are locally s-harmonic up to a small error.
Journal ArticleDOI
Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space
TL;DR: A novel approach to constructing the same SDE based on spectral decomposition of the sample covariance is proposed, by which the SDE concept is naturally generalized into higher dimensional Euclidean space, named standard deviational hyper-ellipsoid (SDHE).
Journal ArticleDOI
An exploration of the equivalent weights particle filter
Melanie Ades,P. J. van Leeuwen +1 more
TL;DR: In this article, a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function, which gives rise to the possibility of nonlinear data assimilation in large-dimensional systems.
Journal ArticleDOI
Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem
TL;DR: It is demonstrated that the resulting algorithm is a general-purpose TRS solver, effective both for dense and large-sparse problems, including the so-called hard case, and obtaining approximate solutions efficiently when high accuracy is unnecessary.
Journal ArticleDOI
Granular Data Description: Designing Ellipsoidal Information Granules
TL;DR: This paper is concerned with a design of a collection of meaningful, easily interpretable ellipsoidal information granules with the use of the principle of justifiable granularity by taking into consideration reconstruction abilities of the designed information Granules.