scholarly journals Representations of multivariate polynomials by sums of univariate polynomials in linear forms

2008 ◽  
Vol 112 (2) ◽  
pp. 201-233 ◽  
Author(s):  
A. Białynicki-Birula ◽  
A. Schinzel
Keyword(s):  
Multivariate Polynomials ◽  
Linear Forms ◽  
Univariate Polynomials

scholarly journals Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros

2021 ◽  
Author(s):  
Xialiang Li ◽  
Wei Niu
Keyword(s):  
Theoretical Result ◽  
Finite Number ◽  
Dual Space ◽  
Multivariate Polynomials ◽  
Real Solution ◽  
The Real ◽  
Simple Set ◽  
Univariate Polynomials ◽  
Simple Sets

In this paper, we are concerned with the problem of counting the multiplicities of a zero-dimensional regular set’s zeros. We generalize the squarefree decomposition of univariate polynomials to the so-called pseudo squarefree decomposition of multivariate polynomials, and then propose an algorithm for decomposing a regular set into a finite number of simple sets. From the output of this algorithm, the multiplicities of zeros could be directly read out, and the real solution isolation with multiplicity can also be easily produced. As a main theoretical result of this paper, we analyze the structure of dual space of the saturated ideal generated by a simple set as well as a regular set. Experiments with a preliminary implementation show the efficiency of our method.

Impact of Training and Development Programmes on the Productivity of Employees in the Banks

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Jaspreet Kaur
Keyword(s):  
Regression Analysis ◽  
Banking Sector ◽  
Human Resources Management ◽  
Training And Development ◽  
Linear Forms ◽  
Knowledge And Skills ◽  
Resources Management ◽  
Level Of Satisfaction ◽  
Log Linear ◽  
The Impact

Manpower training and development is an important aspect of human resources management which must be embarked upon either proactively or reactively to meet any change brought about in the course of time. Training is a continuous and perennial activity. It provides employees with the knowledge and skills to perform more effectively. The study examines the opinions of trainees regarding the impact of training and development programmes on the productivity of employees in the selected banks. To evaluate the impact of training and development programmes on productivity of banking sector, multiple regression analysis was employed in both log as well as log-linear forms. Also the impact of three sets of training i.e. objectives, methods and basics on level of satisfaction of respondents with the training was also examined through employing the regression analysis in the similar manner.

scholarly journals On the Condition of Independence of Linear Forms with a Random Number of Summands

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1516
Author(s):  
Abram M. Kagan ◽  
Lev B. Klebanov
Keyword(s):  
Random Number ◽  
Linear Forms

The property of independence of two random forms with a non-degenerate random number of summands contradicts the Gaussianity of the summands.

scholarly journals True complexity of polynomial progressions in finite fields

2021 ◽  
pp. 1-53
Author(s):  
Borys Kuca
Keyword(s):  
Finite Fields ◽  
Linear Forms ◽  
Gowers Norm ◽  
Counting Lemma

Abstract The true complexity of a polynomial progression in finite fields corresponds to the smallest-degree Gowers norm that controls the counting operator of the progression over finite fields of large characteristic. We give a conjecture that relates true complexity to algebraic relations between the terms of the progression, and we prove it for a number of progressions, including $x, x+y, x+y^{2}, x+y+y^{2}$ and $x, x+y, x+2y, x+y^{2}$ . As a corollary, we prove an asymptotic for the count of certain progressions of complexity 1 in subsets of finite fields. In the process, we obtain an equidistribution result for certain polynomial progressions, analogous to the counting lemma for systems of linear forms proved by Green and Tao.

Linear forms of plasmid DNA are superior to supercoiled structures as active templates for gene expression in plant protoplasts

1988 ◽  
Vol 11 (4) ◽  
pp. 517-527 ◽  
Author(s):  
Nurit Ballas ◽  
Nehama Zakai ◽  
Devorah Friedberg ◽  
Abraham Loyter
Keyword(s):  
Gene Expression ◽  
Plasmid Dna ◽  
Plant Protoplasts ◽  
Linear Forms

scholarly journals A NOTE ON WEIGHTED BADLY APPROXIMABLE LINEAR FORMS

2016 ◽  
Vol 59 (2) ◽  
pp. 349-357 ◽  
Author(s):  
STEPHEN HARRAP ◽  
NIKOLAY MOSHCHEVITIN
Keyword(s):  
Diophantine Approximation ◽  
Affirmative Answer ◽  
Famous Conjecture ◽  
Linear Forms ◽  
Badly Approximable

AbstractWe prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give an affirmative answer to the analogue in this setting of a famous conjecture of Schmidt from Diophantine approximation.

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