A Rational Function Approach to Multilayer Synthesis

1967 ◽  
Vol 6 (2) ◽  
pp. 331 ◽  
Author(s):  
Zdeněk Knittl
Keyword(s):  
Rational Function ◽  
Function Approach

scholarly journals A rational function approach for estimating mean annual evapotranspiration

2004 ◽  
Vol 40 (2) ◽  
Author(s):  
L. Zhang ◽  
K. Hickel ◽  
W. R. Dawes ◽  
F. H. S. Chiew ◽  
A. W. Western ◽  
...  
Keyword(s):  
Rational Function ◽  
Function Approach

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 $n\geq4$.

Sign in / Sign up

Export Citation Format

Share Document