Polynomial Representation

2013 ◽  
pp. 191-226
Author(s):  
Brigitte d’Andréa-Novel ◽  
Michel De Lara
Keyword(s):  
Polynomial Representation

The Hilbert series of the irreducible quotient of the polynomial representation of the rational Cherednik algebra of type An−1 in characteristic p for p|n − 1

2021 ◽  
pp. 2250191
Author(s):  
Merrick Cai ◽  
Daniil Kalinov
Keyword(s):  
Hilbert Series ◽  
Positive Characteristic ◽  
Closed Field ◽  
Simple Criterion ◽  
Characteristic P ◽  
Polynomial Representation ◽  
Cherednik Algebra ◽  
Rational Cherednik Algebra ◽  
Polynomial Formula ◽  
Field Of Positive Characteristic

In this paper, we study the irreducible quotient [Formula: see text] of the polynomial representation of the rational Cherednik algebra [Formula: see text] of type [Formula: see text] over an algebraically closed field of positive characteristic [Formula: see text] where [Formula: see text]. In the [Formula: see text] case, for all [Formula: see text] we give a complete description of the polynomials in the maximal proper graded submodule [Formula: see text], the kernel of the contravariant form [Formula: see text], and subsequently find the Hilbert series of the irreducible quotient [Formula: see text]. In the [Formula: see text] case, we give a complete description of the polynomials in [Formula: see text] when the characteristic [Formula: see text] and [Formula: see text] is transcendental over [Formula: see text], and compute the Hilbert series of the irreducible quotient [Formula: see text]. In doing so, we prove a conjecture due to Etingof and Rains completely for [Formula: see text], and also for any [Formula: see text] and [Formula: see text]. Furthermore, for [Formula: see text], we prove a simple criterion to determine whether a given polynomial [Formula: see text] lies in [Formula: see text] for all [Formula: see text] with [Formula: see text] and [Formula: see text] fixed.

Seismic calibration using the simplex algorithm

1989 ◽  
Vol 79 (5) ◽  
pp. 1618-1628
Author(s):  
Lee Steck ◽  
William A. Prothero
Keyword(s):  
Response Function ◽  
Degrees Of Freedom ◽  
Simplex Algorithm ◽  
Complex Polynomial ◽  
High Signal ◽  
Polynomial Representation ◽  
Important Improvement ◽  
The Time Domain ◽  
Calibration Program ◽  
Starting Model

Abstract We have modified the software of Sauter and Dorman (1986) to produce a robust and flexible calibration program that works in the frequency domain for longer and noisy calibration signals, as well as in the time domain when shorter, high signal-to-noise calibration signals may be used. The most important improvement was to replace the least squares fitting of the complex polynomial representation of the response function with the simplex fitting of the pole-zero representation of the response function. The simplex algorithm always converges to a minimum, regardless of starting model, and by fitting the poles and zeroes directly, we minimize the degrees of freedom of the solution. Typical VAX 11/750 CPU requirements are on the order of 2 to 3 minutes for both codes, with average errors less than 1 per cent in amplitude and 1° in phase.

scholarly journals On the polynomial representation for the number of partitions with fixed length

2007 ◽  
Vol 77 (262) ◽  
pp. 1135-1152
Author(s):  
So Ryoung Park ◽  
Jinsoo Bae ◽  
Hyun Gu Kang ◽  
Iickho Song
Keyword(s):  
Polynomial Representation ◽  
Fixed Length

Polynomial Representation of Steam Tables

Nature ◽  
1959 ◽  
Vol 183 (4661) ◽  
pp. 598-599 ◽  
Author(s):  
W. G. BERRY ◽  
G. BLACK ◽  
J. A. ENDERBY
Keyword(s):  
Polynomial Representation

scholarly journals Chebyshev polynomial representation of imaginary-time response functions

2018 ◽  
Vol 98 (7) ◽  
Author(s):  
Emanuel Gull ◽  
Sergei Iskakov ◽  
Igor Krivenko ◽  
Alexander A. Rusakov ◽  
Dominika Zgid
Keyword(s):  
Chebyshev Polynomial ◽  
Time Response ◽  
Response Functions ◽  
Imaginary Time ◽  
Polynomial Representation
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