Single-molecule photon emission statistics for systems with explicit time dependence: Generating function approach

2009 ◽  
Vol 131 (21) ◽  
pp. 214107 ◽  
Author(s):  
Yonggang Peng ◽  
Shijie Xie ◽  
Yujun Zheng ◽  
Frank L. H. Brown
Keyword(s):  
Time Dependence ◽  
Generating Function ◽  
Single Molecule ◽  
Photon Emission ◽  
Function Approach ◽  
Explicit Time Dependence

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.

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.

scholarly journals New Results on the Coagulation Equation

1987 ◽  
Vol 115 ◽  
pp. 547-547
Author(s):  
Pierre Bastien ◽  
Claude Lejeune
Keyword(s):  
Mass Spectrum ◽  
Time Dependence ◽  
Star Clusters ◽  
Mass Function ◽  
Mass Dependence ◽  
Coagulation Rate ◽  
Precise Form ◽  
Explicit Time Dependence ◽  
Coagulation Equation ◽  
Free Parameters

In attempting to reproduce the initial stellar mass function, we solved analytically the coagulation equation with an explicit time dependence in the coagulation rate in order to simulate the gravitational collapse of the fragments upon themselves as they move within the progenitor cloud. Two separate cases have been studied, with and without a mass dependence in the coagulation rate. The solution show that (1) inclusion of self-gravitation is very important and can change the results to the point of preventing coalescence to work altogether, depending on the values of the two free parameters, (2) the precise form of the mass dependence of the coagulation rate is not of prime importance in most situations of astrophysical interest, and (3) coagulation alone is not sufficient to yield a realistic mass spectrum and fragmentation must also be taken into account. Coagulation is more efficient for massive fragments and fragmentation for the smaller ones. These results are applied to different regions: star clusters, associations, and starburst regions.

Single molecule photon emission statistics in the slow modulation limit

2004 ◽  
Vol 121 (16) ◽  
pp. 7914 ◽  
Author(s):  
Yujun Zheng ◽  
Frank L. H. Brown
Keyword(s):  
Single Molecule ◽  
Photon Emission ◽  
Slow Modulation
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