Erratum: “Higher Order Correction to Screening Constant”

1962 ◽  
Vol 17 (8) ◽  
pp. 1322-1322
Author(s):  
Yukio Ôsaka
Keyword(s):  
Higher Order ◽  
Order Correction ◽  
Screening Constant

Higher Order Correction to Screening Constant

1962 ◽  
Vol 17 (3) ◽  
pp. 547-565 ◽  
Author(s):  
Yukio Ôsaka
Keyword(s):  
Higher Order ◽  
Order Correction ◽  
Screening Constant

A Continuous Compact Model Incorporating Higher-Order Correction for Junctionless Nanowire Transistors With Arbitrary Doping Profiles

2016 ◽  
Vol 15 (4) ◽  
pp. 657-665 ◽  
Author(s):  
Chuyang Hong ◽  
Libo Yang ◽  
Qi Cheng ◽  
Ting Han ◽  
James B. Kuo ◽  
...  
Keyword(s):  
Higher Order ◽  
Compact Model ◽  
Order Correction ◽  
Nanowire Transistors ◽  
Doping Profiles

scholarly journals Uniform renewal theory with applications to expansions of random geometric sums

2007 ◽  
Vol 39 (4) ◽  
pp. 1070-1097 ◽  
Author(s):  
J. Blanchet ◽  
P. Glynn
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Renewal Theory ◽  
Random Variable ◽  
Higher Order ◽  
Order Correction ◽  
Diffusion Approximations ◽  
Geometric Sums ◽  
Correction Terms

Consider a sequence X = (Xn: n ≥ 1) of independent and identically distributed random variables, and an independent geometrically distributed random variable M with parameter p. The random variable SM = X1 + ∙ ∙ ∙ + XM is called a geometric sum. In this paper we obtain asymptotic expansions for the distribution of SM as p ↘ 0. If EX1 > 0, the asymptotic expansion is developed in powers of p and it provides higher-order correction terms to Renyi's theorem, which states that P(pSM > x) ≈ exp(-x/EX1). Conversely, if EX1 = 0 then the expansion is given in powers of √p. We apply the results to obtain corrected diffusion approximations for the M/G/1 queue. These expansions follow in a unified way as a consequence of new uniform renewal theory results that are also developed in this paper.

scholarly journals Uniform renewal theory with applications to expansions of random geometric sums

2007 ◽  
Vol 39 (04) ◽  
pp. 1070-1097 ◽  
Author(s):  
J. Blanchet ◽  
P. Glynn
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Renewal Theory ◽  
Random Variable ◽  
Higher Order ◽  
Order Correction ◽  
Diffusion Approximations ◽  
Geometric Sums ◽  
Correction Terms

Consider a sequenceX= (Xn:n≥ 1) of independent and identically distributed random variables, and an independent geometrically distributed random variableMwith parameterp. The random variableSM=X1+ ∙ ∙ ∙ +XMis called a geometric sum. In this paper we obtain asymptotic expansions for the distribution ofSMasp↘ 0. If EX1> 0, the asymptotic expansion is developed in powers ofpand it provides higher-order correction terms to Renyi's theorem, which states that P(pSM>x) ≈ exp(-x/EX1). Conversely, if EX1= 0 then the expansion is given in powers of √p. We apply the results to obtain corrected diffusion approximations for the M/G/1 queue. These expansions follow in a unified way as a consequence of new uniform renewal theory results that are also developed in this paper.

A higher order correction to NM0 for improved AVO and imaging

1996 ◽  
Author(s):  
Robert N. Shurtleff ◽  
William A. Schneider ◽  
Dwight A. Mackie ◽  
David B. Hays
Keyword(s):  
Higher Order ◽  
Order Correction

Development of High-Order Scheme in Unstructured Mesh for Direct Numerical Simulations

2013 ◽  
Author(s):  
H. Q. Yang ◽  
Z. J. Chen ◽  
Jonathan G. Dudley
Keyword(s):  
Degrees Of Freedom ◽  
Unstructured Grids ◽  
Correction Method ◽  
Higher Order ◽  
High Order ◽  
Order Correction ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
High Order Scheme ◽  
Upwind Schemes

There has been a growing interest in higher-order spatial discretization methods due to their potential for delivering high accuracy at reasonable computational overhead for the Direct Numerical Simulation (DNS) of vortex-dominated flows. Many of the existing high-order schemes for unstructured grids use more degrees-of-freedom (DOF) in each cell to achieve high-order accuracy. This paper formulates and demonstrates a high-order correction method for unstructured grids. Using this approach, there is no increase in DOF within each cell. By adding higher order correction terms, higher order accuracy can be achieved. The present technique is innovative in that it can be readily added to existing lower order solvers, it can achieve very high-order accuracy, it is stable, and it can make use of either central or upwind schemes. Many examples are presented and used to demonstrate the high-order accuracy.

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