Method of Laurent series expansion for internal crack problems

1973 ◽  
pp. 56-130 ◽  
Author(s):  
M. Isida
Keyword(s):  
Series Expansion ◽  
Laurent Series ◽  
Internal Crack ◽  
Crack Problems

scholarly journals Complex blow-up in Burgers' equation: an iterative approach

1996 ◽  
Vol 54 (3) ◽  
pp. 353-362 ◽  
Author(s):  
Nalini Joshi ◽  
Johannes A. Petersen
Keyword(s):  
Holomorphic Function ◽  
Series Expansion ◽  
Laurent Series ◽  
Burgers Equation ◽  
Blow Up ◽  
Meromorphic Solution ◽  
Iterative Approach ◽  
Painlevé Test ◽  
Formal Laurent Series

We show that for a given holomorphic noncharacteristic surface S ∈ ℂ2, and a given holomorphic function on S1 there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.

Transfer Function Reduction

1976 ◽  
Vol 190 (1) ◽  
pp. 643-651 ◽  
Author(s):  
R. Whalley
Keyword(s):  
Transfer Function ◽  
Series Expansion ◽  
Laurent Series ◽  
Hankel Matrix ◽  
Rational Functions ◽  
Reduced Form ◽  
Reduced Order Models ◽  
Minimum Phase ◽  
Reduced Order

SYNOPSIS A method of generating reduced order models from the Laurent series expansion of a transfer function is examined by means of the Hankel Matrix and its correspondence to the field of rational functions. The approach enables particularly simple results to be derived regarding the composition of the reduced form and the avoidance of non minimum phase characteristics therein.

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