Partial derivatives of travel-time curves of reflected waves in a layered medium

1980 ◽  
Vol 24 (4) ◽  
pp. 355-364 ◽  
Author(s):  
Oldřich Novotný ◽  
I. Pšenčik
Keyword(s):  
Travel Time ◽  
Layered Medium ◽  
Reflected Waves ◽  
Partial Derivatives ◽  
Derivatives Of

Derivatives of travel time curves in a horizontally layered medium

1983 ◽  
Vol 27 (3) ◽  
pp. 233-240
Author(s):  
Jaromír Janský ◽  
Oldřich Novotný ◽  
J. Vaněk
Keyword(s):  
Travel Time ◽  
Layered Medium ◽  
Derivatives Of

Partial Derivatives of the Lambert Problem

2014 ◽  
Author(s):  
Nitin Arora ◽  
Ryan P. Russell ◽  
Nathan J. Strange
Keyword(s):  
Partial Derivatives ◽  
Lambert Problem ◽  
Derivatives Of

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

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