scholarly journals Calculating Infinitesimal Generators

2020 ◽  
Author(s):  
Majnu John ◽  
Yihren Wu
Keyword(s):  
Infinitesimal Generators

scholarly journals Optimal transport over nonlinear systems via infinitesimal generators on graphs

2018 ◽  
Vol 0 (0) ◽  
pp. 1-32 ◽  
Author(s):  
Karthik Elamvazhuthi ◽  
◽  
Piyush Grover ◽  
Keyword(s):  
Nonlinear Systems ◽  
Optimal Transport ◽  
Infinitesimal Generators

Lie symmetry analysis and invariant solutions of (3+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

2022 ◽  
Author(s):  
Hengchun Hu ◽  
Runlan Sun
Keyword(s):  
Vector Fields ◽  
Periodic Wave ◽  
Lie Symmetry ◽  
Periodic Wave Solution ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
Infinitesimal Generators ◽  
New Exact Solutions ◽  
Trigonometric Function Solutions ◽  
Function Selection

In this paper, the (3+1)-dimensional constant coefficient of Date–Jimbo–Kashiwara–Miwa (CCDJKM) equation is studied. All of the vector fields, infinitesimal generators, Lie symmetry reductions and different similarity reduction solutions are constructed. Due to the arbitrary functions in the infinitesimal generators, the (3+1)-dimensional CCDJKM equation can further be reduced to many (2+1)-dimensional partial differential equations. The explicit solutions of the similarity reduction equations, which include the quasi-periodic wave solution, the interaction solution between the periodic wave and a kink soliton and the trigonometric function solutions, are constructed with proper arbitrary function selection, and these new exact solutions are given out analytically and graphically.

scholarly journals One-parameter Groups of Operators and Discrete Hilbert Transforms

2016 ◽  
Vol 59 (3) ◽  
pp. 497-507 ◽  
Author(s):  
Laura De Carli ◽  
Gohin Shaikh Samad
Keyword(s):  
Hilbert Transform ◽  
Hilbert Transforms ◽  
Discrete Hilbert Transform ◽  
Infinitesimal Generators

AbstractWe show that the discrete Hilbert transform and the discrete Kak–Hilbert transform are infinitesimal generators of one-parameter groups of operators in ℓ2.

scholarly journals On a Comparison Result for Markov Processes

2008 ◽  
Vol 45 (01) ◽  
pp. 279-286
Author(s):  
Ludger Rüschendorf
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
General Class ◽  
Stochastic Monotonicity ◽  
Comparison Result ◽  
State Spaces ◽  
Stochastic Orderings ◽  
Infinitesimal Generators ◽  
Real Functions

A comparison theorem is stated for Markov processes in Polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In particular, Liggett's theorem on the association of Markov processes is a consequence of this comparison result.

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