Proportional difference operator method and its application to studying the saturation characteristics of MOSFETs

1998 ◽  
Vol 34 (21) ◽  
pp. 2067 ◽  
Author(s):  
Changhua Tan ◽  
Mingzhen Xu ◽  
Jinyan Wang ◽  
Bing Xie ◽  
Yandong He
Keyword(s):  
Difference Operator ◽  
Operator Method

scholarly journals Synchronized abandonment in discrete-time renewal input queues with vacations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Veena Goswami ◽  
Gopinath Panda
Keyword(s):  
Discrete Time ◽  
Difference Operator ◽  
Operator Method ◽  
Stochastic Decomposition ◽  
Variable Technique ◽  
Input Queue ◽  
Decomposition Structure ◽  
Heavy Tailed ◽  
System Length ◽  
Number Of Customers

<p style='text-indent:20px;'>We consider a discrete-time infinite buffer renewal input queue with multiple vacations and synchronized abandonment. Waiting customers get impatient during the server's vacation and decide whether to take service or abandon simultaneously at the vacation completion instants. Using the supplementary variable technique and difference operator method, we obtain an explicit expression to find the steady-state system-length distributions at pre-arrival, random, and outside observer's observation epochs. We provide the stochastic decomposition structure for the number of customers and discuss the various performance measures. With the help of numerical experiments, we show that the method formulated in this work is analytically elegant and computationally tractable. The results are appropriate for light-tailed inter-arrival distributions and can also be leveraged to find heavy-tailed inter-arrival distributions.</p>

scholarly journals A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

2021 ◽  
Author(s):  
Yasuhisa Abe ◽  
David Boilley ◽  
Quentin Hourdillé ◽  
Caiwan Shen
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Operator Method ◽  
Initial Distribution ◽  
Physical Parameters ◽  
Relaxation Processes ◽  
Fast Variable ◽  
Dynamical Study ◽  
Injection Point ◽  
Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

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