Uniform surface-to-line integral reduction of physical optics for curved surfaces by modified edge representation with higher-order correction

Radio Science ◽  
2017 ◽  
Vol 52 (9) ◽  
pp. 1106-1116
Author(s):  
Pengfei Lyu ◽  
Makoto Ando
Keyword(s):  
Higher Order ◽  
Order Correction ◽  
Physical Optics ◽  
Curved Surfaces ◽  
Line Integral

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.

Sign in / Sign up

Export Citation Format

Share Document