Behavior of the homogeneous symmetric polynomial in an angular region

1995 ◽  
Vol 35 (4) ◽  
pp. 373-387
Author(s):  
È. G. Kir'yatskii
Keyword(s):  
Symmetric Polynomial ◽  
Angular Region ◽  
Homogeneous Symmetric Polynomial

scholarly journals An Orthosymplectic Pieri Rule

10.37236/7387 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Anna Stokke
Keyword(s):  
Linear Combination ◽  
Schur Functions ◽  
Symmetric Polynomial ◽  
Schur Function ◽  
Product Rule ◽  
Integer Coefficients ◽  
Pieri Formula ◽  
Symplectic Characters ◽  
Homogeneous Symmetric Polynomial

The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for describing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundaram's Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule. 

scholarly journals Enumerations for Compositions and Complete Homogeneous Symmetric Polynomial

2015 ◽  
Vol 7 (2) ◽  
pp. 1
Author(s):  
Soumendra Bera
Keyword(s):  
Positive Integer ◽  
Symmetric Polynomial ◽  
Enumeration Problems ◽  
Homogeneous Symmetric Polynomial

<p class="abstract">We count the number of occurrences of <em>t </em>as the summands<em> </em>(i) in the compositions of a positive integer <em>n</em> into <em>r</em> parts; and (ii) in all compositions of <em>n</em>; and subsequently obtain other results involving compositions. The initial counting further helps to solve the enumeration problems for complete homogeneous symmetric polynomial.</p>

scholarly journals Pairs of Comparable Relations for Complete Homogeneous Symmetric Polynomial

2015 ◽  
Vol 7 (4) ◽  
pp. 26
Author(s):  
Soumendra Bera
Keyword(s):  
Exponential Function ◽  
Stirling Numbers ◽  
Binomial Coefficient ◽  
Symmetric Polynomial ◽  
Elementary Symmetric Polynomial ◽  
Generating Series ◽  
Homogeneous Symmetric Polynomial

<p>Complete homogeneous symmetric polynomial has connections with binomial coefficient, composition, elementary symmetric polynomial, exponential function, falling factorial, generating series, odd prime and Stirling numbers of the second kind by different summations. Surprisingly the relations in the context are comparable in pairs. </p>

Measurement of the spin correlation parameter Aoonn(pp) in a large angular region between 0.88 and 2.7 GeV

1987 ◽  
Vol 294 ◽  
pp. 1013-1021 ◽  
Author(s):  
F. Lehar ◽  
A. De Lesquen ◽  
J.P. Meyer ◽  
L. Van Rossum ◽  
P. Chaumette ◽  
...  
Keyword(s):  
Spin Correlation ◽  
Angular Region ◽  
Correlation Parameter

scholarly journals Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

2007 ◽  
Vol 79 (4) ◽  
pp. 563-575 ◽  
Author(s):  
Jaume Llibre ◽  
Marcelo Messias
Keyword(s):  
Large Amplitude ◽  
Symmetric Polynomial ◽  
The Other ◽  
Poincaré Compactification ◽  
Heteroclinic Loop ◽  
Differential Systems ◽  
Heteroclinic Cycles ◽  
Polynomial Differential Systems ◽  
Global Study ◽  
Straight Lines

In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n <FONT FACE=Symbol>Î</FONT> N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.

Note on roots location of a symmetric polynomial with respect to the imaginary axis

2012 ◽  
Vol 60 (4) ◽  
pp. 499-510
Author(s):  
Hui-Feng Hao ◽  
Yong-Jian Hu ◽  
Gong-Ning Chen
Keyword(s):  
Imaginary Axis ◽  
Symmetric Polynomial

scholarly journals A method for measuring angular bearing errors in the “antenna - radome” system in the phased-array beam scanning region

2019 ◽  
pp. 7-24
Author(s):  
I. E. Makushkin ◽  
A. E. Dorofeev ◽  
A. N. Gribanov ◽  
S. E. Gavrilova ◽  
A. I. Sinani
Keyword(s):  
Phased Array ◽  
Array Antenna ◽  
Two Dimensional ◽  
Phased Array Antenna ◽  
Angular Region ◽  
Mathematical Expressions ◽  
Initial Stage ◽  
Steerable Antenna ◽  
Release Model ◽  
Scanning Region

The paper introduces a method for measuring angular bearing errors in an antenna-radome system in a two-dimensional angular region of scanning of electronically steerable antenna, i.e. phased array antenna, active phased array antenna. The measurements were based on an antenna measuring collimator system - “compact testing ground”. The mathematical expressions used in processing the obtained data are given. To make a matrix of angular bearing errors, measurements are carried out at different angles of the heel of the antenna - radome system when the phased array antenna beam is deflected in oblique planes. To perfect the method at the initial stage, we used a quick-release model of the radome, which has the ability to introduce angular bearing errors

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