Some identities between arithmetic means and the other elementary symmetric functions ofn numbers

1947 ◽  
Vol 120 (1) ◽  
pp. 154-157 ◽  
Author(s):  
Alexander Dinghas
Keyword(s):  
Symmetric Functions ◽  
The Other ◽  
Arithmetic Means ◽  
Elementary Symmetric Functions

scholarly journals On Determinants of Symmetric Functions

1927 ◽  
Vol 1 (1) ◽  
pp. 55-61 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Symmetric Function ◽  
Symmetric Functions ◽  
The Other ◽  
Elementary Symmetric Functions ◽  
The Difference ◽  
Image Position

The result of dividing the alternant |aαbβcγ…| by the simplest alternant |a0b1c2…| (the difference-product of a, b, c, …) is known to be a symmetric function expressible in two distinct ways, (1) as a determinant having for elements the elementary symmetric functions C, of a, b, c, …, (2) as a determinant having for elements the complete homogeneous symmetric functions Hr. For exampleThe formation of the (historically earlier) H-determinant is evident. The suffixes in the first row are the indices of the alternant; those of the other rows decrease by unit steps. This result is due to Jacobi.

scholarly journals Applying Ateb–Gabor Filters to Biometric Imaging Problems

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 717
Author(s):  
Mariia Nazarkevych ◽  
Natalia Kryvinska ◽  
Yaroslav Voznyi
Keyword(s):  
Wavelet Transformation ◽  
Symmetric Functions ◽  
Gabor Filter ◽  
Signal To Noise Ratio ◽  
The Other ◽  
Mean Square ◽  
Image Transformation ◽  
Gabor Filtering ◽  
Signal To Noise ◽  
Filtration Method

This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well.

scholarly journals A note on extrema of linear combinations of elementary symmetric functions

2012 ◽  
Vol 60 (2) ◽  
pp. 219-224 ◽  
Author(s):  
Alexander Kovačec ◽  
Salma Kuhlmann ◽  
Cordian Riener
Keyword(s):  
Symmetric Functions ◽  
Linear Combinations ◽  
Elementary Symmetric Functions

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

scholarly journals A Unified View of Determinantal Expansions for Jack Polynomials

10.37236/1547 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Leigh Roberts
Keyword(s):  
Differential Geometry ◽  
Symmetric Functions ◽  
Jack Polynomials ◽  
Elementary Symmetric Functions ◽  
Fundamental Symmetry ◽  
Unified View

Recently Lapointe et. al. [3] have expressed Jack Polynomials as determinants in monomial symmetric functions $m_\lambda$. We express these polynomials as determinants in elementary symmetric functions $e_\lambda$, showing a fundamental symmetry between these two expansions. Moreover, both expansions are obtained indifferently by applying the Calogero-Sutherland operator in physics or quasi Laplace Beltrami operators arising from differential geometry and statistics. Examples are given, and comments on the sparseness of the determinants so obtained conclude the paper.

scholarly journals On the integrality of the first and second elementary symmetric functions of $1, 1/2^{s_2}, ...,1/n^{s_n}$

2017 ◽  
Vol 2 (4) ◽  
pp. 682-691 ◽  
Author(s):  
Wanxi Yang ◽  
◽  
Mao Li ◽  
Yulu Feng ◽  
Xiao Jiang ◽  
...  
Keyword(s):  
Symmetric Functions ◽  
Elementary Symmetric Functions
Sign in / Sign up

Export Citation Format

Share Document