Discussion of measurement of surge impedance of a horizontal grounding conductor using approximate expression

2010 ◽  
Author(s):  
Shozo Sekioka
Keyword(s):  
Approximate Expression

scholarly journals The genetic variability of polygenic characters under optimizing selection, mutation and drift

1972 ◽  
Vol 19 (1) ◽  
pp. 17-25 ◽  
Author(s):  
M. G. Bulmer
Keyword(s):  
Genetic Variability ◽  
Stable Equilibrium ◽  
Finite Size ◽  
Approximate Expression ◽  
Average Amount

SUMMARYThe effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci with equal effects without dominance was investigated theoretically. Conditions for a stable equilibrium under selection and mutation, in the absence of drift, have been obtained, and hence the amount of genetic variability which can be maintained by mutation has been determined. An approximate expression for the average amount of genetic variability to be expected in the presence of drift in a population of finite size has also been obtained and evaluated.

Approximate Expression for the Mutual Information of Dense PAM

2018 ◽  
Vol 22 (11) ◽  
pp. 2182-2185
Author(s):  
Chen Ji ◽  
Jue Wang ◽  
Guoan Zhang
Keyword(s):  
Mutual Information ◽  
Approximate Expression

scholarly journals A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

2021 ◽  
Vol 8 (1) ◽  
pp. 33-44
Author(s):  
Toufik Chaayra ◽  
Hussain Ben-azza ◽  
Faissal El Bouanani
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Performance Metrics ◽  
Approximate Expression ◽  
Maximal Ratio Combining ◽  
Generalized Gamma ◽  
The Moment ◽  
Probability Density Function Pdf ◽  
Closed Form Approximation ◽  
Fox’S H Function

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

Convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks

2018 ◽  
Vol 32 (15) ◽  
pp. 1850159
Author(s):  
Yin Long ◽  
Xiao-Jun Zhang ◽  
Kui Wang
Keyword(s):  
Analytical Solution ◽  
Numerical Method ◽  
Power Law ◽  
Approximate Calculation ◽  
Approximate Expression ◽  
Network Size ◽  
Average Degree ◽  
Large Network ◽  
Network Link ◽  
Theoretical Results

In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.

Nuclear Scattering

2020 ◽  
pp. 127-184
Author(s):  
Andrew T. Boothroyd
Keyword(s):  
Cross Sections ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Spin Echo ◽  
Harmonic Approximation ◽  
Approximate Expression ◽  
Neutron Spin ◽  
Response Functions ◽  
Nuclear Scattering ◽  
Scattering Cross

This chapter contains an overview of the different types of structural dynamics found in condensed matter, and the associated neutron scattering cross-sections. The scattering dynamics of the harmonic oscillator is discussed, and an expression for the Debye-Waller factor is obtained. In the case of crystalline solids, the vibrational spectrum in the harmonic approximation is described, including the phonon dispersion and the cross-sections for one-phonon coherent and incoherent scattering. Multi-phonon scattering is discussed briefly. For non-crystalline matter, the time-dependent van Hove correlation and response functions are introduced, and their relation to the scattering cross-section established. An approximate expression for the correlation function is obtained from the classical form. Partial correlation and response functions are defined for multicomponent systems. The technique of neutron Compton scattering as a probe of single-particle recoil dynamics is described. Quasielastic and neutron spin-echo spectroscopy are introduced, as well as examples of relaxational dynamics which these techniques can measure.

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