Abstract The present paper describes the first part of an investigation into the possibility of finding a set of simple functions for the construction of molecular wave functions which satisfies two essential requirements: that the number of basis functions required to produce a given accuracy be comparable to the number of Slater functions required to give the same accuracy, and that the molecular multicentre integrals should be considerably easier to evaluate than those over Slater functions. It is shown that a basis made up of 1s gaussians supplemented by a single ‘cusp function’ of the form may be expected to satisfy the requirements for the s-orbitals in atoms other than hydrogen. Calculations of the ground-state orbital approximations of the helium and beryllium atoms show that an inner-shell 1s orbital can be satisfactorily described by the cusp function and two gaussians, whilst subsequent s-orbitals should require not more than two or three gaussians per orbital to produce better than ‘double-zeta’ accuracy.

Cited by 26

Complex-variable-function–Gaussian solitons

Dongmei Deng, Qi Guo, Wei Hu · Optics Letters · 2008

We have introduced a novel (to our knowledge) class of complex-variable-function (CVF)-Gaussian solitons that constitute the exact soliton solutions of the Snyder-Mitchell model. The CVF-Gaussian solitons whose transverse structure has an inherent rotation are the product of an arbitrary analytic CVF and a Gaussian function. A distribution factor that is the parameter for the description of the transverse distribution of the CVF-Gaussian solitons is discussed.

Cited by 54

A = Amplitude of Gaussian function

Dennis K. Mclaughlin, Ching-wen Kuo, Dimitri Papamoschou · 2015

The influence of ground reflections on the measurement of aircraft engine exhaust noise is examined in this paper. A series of experiments were performed in the UCI aeroacoustic facility of supersonic jet noise with and without a ground plane in close proximity to the jet. Thus the effect of the ground plane on the radiated noise was isolated. Additionally, a computational model for the phenomenon was developed, which included the determination of a distribution of noise sources within the jet column. This distribution was developed from phased microphone array measurements incorporating an advanced beamforming algorithm. The developed model did a reasonably good job of predicting the effect of the reflecting ground surface. The most important exception is in the additional noise source caused by aerodynamic “scrubbing ” of the turbulent jet on the surface far downstream of the jet exit. Guidance on how to alter the proposed model to account for porosity of the ground in field experiments over grassy or sandy terrain, is also given.

Cited by 0

Anisotropic Gaussian Vacuum Potential and Gaussian Lagrangian Derivation using Anisotropic Gaussian Vacuum Potential Function

한, 재준 · Zenodo (CERN European Organization for Nuclear Research) · 2025

Cited by 0Open access

Anisotropic Gaussian Vacuum Potential and Gaussian Lagrangian Derivation using Anisotropic Gaussian Vacuum Potential Function

한, 재준 · Zenodo (CERN European Organization for Nuclear Research) · 2025

Cited by 0Open access

Gaussian function surface with different σs.

JianWu Long (10731271), ZeRan Yan (10731274), HongFa Chen (10731277) et al. · Figshare · 2021

Cited by 0Open access

Abstract. Consider a Gaussian Entire Function

F. Nazarov, M. Sodin, A. Volberg · 2012

∞ ∑ z f(z) = k k! k=0 where ζ0, ζ1,... are Gaussian i.i.d. complex random variables. The zero set of this function is distribution invariant with respect to the isometries of the complex plane. Let n(R) be the number of zeroes of f in the disk of radius R. It is easy to see that En(R) = R 2, and it is known that the variance of n(R) grows linearly with R (Forrester and Honner). We prove that, for every α&gt; 1/2, the tail probability P { |n(R)−R 2 |&gt; R α} behaves as exp [ −R ϕ(α)] with some explicit piecewise linear function ϕ(α). For some special values of the parameter α, this law was found earlier by Sodin and Tsirelson, and by Krishnapur. In the context of charge fluctuations of a one-component Coulomb system of particles of one sign embedded into a uniform background of another sign, a similar law was discovered some time ago by Jancovici, Lebowitz and Magnificat. ζk

Cited by 0

On Gaussian Radial Basis Function Approximations

Mário A. T. Figueiredo · 2000

In this paper we focus on an interpretation of Gaussian radial basis functions (GRBF) which motivates extensions and learning strategies. Specifically, we show that GRBF regression equations naturally result from representing the input-output joint probability density function by a finite mixture of Gaussians. Corollaries of this interpretation are: some special forms of GRBF representations can be traced back to the type of Gaussian mixture used; previously proposed learning methods based on input-output clustering have a new meaning; finally, estimation techniques for finite mixtures (namely the EM algorithm, and model selection criteria) can be invoked to learn GRBF regression equations. 1.

Cited by 0

Gaussian Transfer Function Based on Boundary

Ying Zhao, Fang Zhou, Xiaoping Fan · 2006

In direct volume rendering, transfer functions map data points to optical properties such as color and opacity. This paper advances the use of boundary information in transfer functions with a methodology for computing high-quality boundary measurements. An efficient approach for the extraction of boundary from volume datasets was describes. First, boundary voxels are defined by gradient magnitude threshold to refine the dataset. And then an objective function to detect the good boundary can be defined as the surface integral of the mean gradient magnitude. The boundaries are detected as maxima in cumulative Laplacian-weighted gray value histograms divided by boundary area values, with a computationally efficient method that requires only a single pass through the boundary volume. Last, a Gaussian transfer function is designed by the boundaries for high-quality rendering, and the transfer function can be analytically integrated over a line segment under the assumption that data values vary linearly between two sampled points. Analytically integrated segment can then be composed using standard techniques.

Cited by 1

Airy complex variable function Gaussian beams

Dongmei Deng, Qi Guo · New Journal of Physics · 2009

We have presented a novel family of paraxial laser beams, which are called Airy complex variable function Gaussian (ACVF–Gaussian) beams. The ACVF–Gaussian beams are formed by the product of an Airy complex variable function and a Gaussian function. Unlike Airy–Gaussian beams, which are nondiffracting, the ACVF–Gaussian beams, which have a rotating phase term are diffracting and rotating. The rotating velocity decreases when the propagation distance increases. We have analyzed the evolution of the Poynting vector and angular momentum density of the ACVF–Gaussian beams as they propagate in free space.

Cited by 49Open access