scholarly journals Generating-function approach for double freeform lens design

2021 ◽  
Vol 38 (3) ◽  
pp. 356
Author(s):  
L. B. Romijn ◽  
M. J. H. Anthonissen ◽  
J. H. M. ten Thije Boonkkamp ◽  
W. L. IJzerman
Keyword(s):  
Generating Function ◽  
Function Approach ◽  
Lens Design ◽  
Freeform Lens

Freeform lens design for complicated optical field tailoring

2021 ◽  
Author(s):  
ZeXin Feng ◽  
Dewen Cheng ◽  
Yongtian Wang
Keyword(s):  
Optical Field ◽  
Lens Design ◽  
Freeform Lens

scholarly journals Labels distance in bucket recursive trees with variable capacities of buckets

2021 ◽  
Vol 13 (2) ◽  
pp. 413-426
Author(s):  
S. Naderi ◽  
R. Kazemi ◽  
M. H. Behzadi
Keyword(s):  
Partial Differential Equations ◽  
Probability Distribution ◽  
Differential Equations ◽  
Generating Function ◽  
Generating Functions ◽  
Function Approach ◽  
Closed Formula ◽  
Tree Model ◽  
Partial Differential ◽  
Recursive Trees

Abstract The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.

scholarly journals Freeform lens design for LED collimating illumination

2012 ◽  
Vol 20 (10) ◽  
pp. 10984 ◽  
Author(s):  
Jin-Jia Chen ◽  
Te-Yuan Wang ◽  
Kuang-Lung Huang ◽  
Te-Shu Liu ◽  
Ming-Da Tsai ◽  
...  
Keyword(s):  
Lens Design ◽  
Freeform Lens

Theoretical solutions for degree distribution of decreasing random birth-and-death networks

2017 ◽  
Vol 31 (14) ◽  
pp. 1750161 ◽  
Author(s):  
Yin Long ◽  
Xiao-Jun Zhang ◽  
Kui Wang
Keyword(s):  
Steady State ◽  
Computer Simulations ◽  
Generating Function ◽  
Degree Distribution ◽  
Probability Generating Function ◽  
Function Approach ◽  
Poisson Summation

In this paper, theoretical solutions for degree distribution of decreasing random birth-and-death networks [Formula: see text] are provided. First, we prove that the degree distribution has the form of Poisson summation, for which degree distribution equations under steady state and probability generating function approach are employed. Then, based on the form of Poisson summation, we further confirm the tail characteristic of degree distribution is Poisson tail. Finally, simulations are carried out to verify these results by comparing the theoretical solutions with computer simulations.

Sign in / Sign up

Export Citation Format

Share Document