scholarly journals Rational Function Representation of Flap Noise Spectra including Correction for Reflection Effects

1975 ◽  
Vol 12 (11) ◽  
pp. 899-905
Author(s):  
J. H. Miles
Keyword(s):  
Rational Function ◽  
Function Representation ◽  
Noise Spectra

scholarly journals Network modelling with Brune's synthesis

2011 ◽  
Vol 9 ◽  
pp. 91-94 ◽  
Author(s):  
F. Mukhtar ◽  
Y. Kuznetsov ◽  
P. Russer
Keyword(s):  
Rational Function ◽  
Numerical Data ◽  
Circuit Synthesis ◽  
Network Modelling ◽  
Function Representation ◽  
Vector Fitting ◽  
Lumped Element ◽  
Fitting Procedure ◽  
Systematic Strategy

Abstract. Network modelling of general, lossy or lossless, one-port and symmetric two-port passive electromagnetic structures in systematic manner is presented. Rational function representation of the numerical data of Z- or Y-parameters is obtained with the use of Vector Fitting procedure. A systematic strategy for obtaining equivalent lumped element circuit from the rational function, applying Brune's circuit synthesis, is also presented.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals The differential Galois group of the rational function field

2021 ◽  
Vol 381 ◽  
pp. 107605
Author(s):  
Annette Bachmayr ◽  
David Harbater ◽  
Julia Hartmann ◽  
Michael Wibmer
Keyword(s):  
Galois Group ◽  
Rational Function ◽  
Function Field ◽  
Differential Galois Group ◽  
Rational Function Field

scholarly journals The bifurcation set of a rational function via Newton polytopes

2021 ◽  
Author(s):  
Tat Thang Nguyen ◽  
Takahiro Saito ◽  
Kiyoshi Takeuchi
Keyword(s):  
Rational Function ◽  
Newton Polytopes ◽  
Bifurcation Set
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