Time-dependent solution for non-circular tunnels considering the elasto-viscoplastic rockmass

2020 ◽  
Vol 133 ◽  
pp. 104395 ◽  
Author(s):  
Eugie Kabwe ◽  
Murat Karakus ◽  
Emmanuel K. Chanda
Keyword(s):  
Time Dependent ◽  
Time Dependent Solution

A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows

1971 ◽  
Vol 8 (04) ◽  
pp. 708-715 ◽  
Author(s):  
Emlyn H. Lloyd
Keyword(s):  
Functional Equation ◽  
Explicit Formula ◽  
Generating Function ◽  
Present Theory ◽  
The Other ◽  
Time Dependent ◽  
Independent Sequence ◽  
Time Dependent Solution ◽  
Infinite Reservoir ◽  
Stationary Behaviour

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).

Hybrid heuristic time dependent solution of the radiative transfer equation for the slab

2009 ◽  
Author(s):  
Fabrizio Martelli ◽  
Samuele Del Bianco ◽  
Antonio Pifferi ◽  
Lorenzo Spinelli ◽  
Alessandro Torricelli ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Time Dependent ◽  
Hybrid Heuristic ◽  
Time Dependent Solution

scholarly journals Semigroup Methods for the M/G/1 Queueing Model with Working Vacation and Vacation Interruption

2016 ◽  
Vol 8 (5) ◽  
pp. 56 ◽  
Author(s):  
Ehmet Kasim
Keyword(s):  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Queueing Model ◽  
Working Vacation ◽  
Positive Time ◽  
Vacation Interruption ◽  
Vacation Period ◽  
Time Dependent Solution

By using the strong continuous semigroup theory of linear operators we prove that the M/G/1 queueing model with working vacation and vacation interruption has a unique positive time dependent solution which satisfies probability conditions. When the both service completion rate in a working vacation period and in a regular busy period are constant, by investigating the spectral properties of an operator corresponding to the model we obtain that the time-dependent solution of the model strongly converges to its steady-state solution.

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