Vanishing of linear forms without complex multiplication

1975 ◽  
pp. 16-35
Author(s):  
D. W. Masser
Keyword(s):  
Complex Multiplication ◽  
Linear Forms

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 Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

2018 ◽  
Vol 2020 (13) ◽  
pp. 3902-3926
Author(s):  
Réda Boumasmoud ◽  
Ernest Hunter Brooks ◽  
Dimitar P Jetchev
Keyword(s):  
Vertical Distribution ◽  
Three Dimensional ◽  
Complex Multiplication ◽  
Horizontal Distribution ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Heegner Points ◽  
Universal Norm

Abstract We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.

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.

scholarly journals Primitive divisors of sequences associated to elliptic curves with complex multiplication

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Matteo Verzobio
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Number Field ◽  
Complex Multiplication ◽  
Dedekind Domain ◽  
Torsion Point ◽  
Integral Ideal ◽  
Primitive Divisors ◽  
Primitive Divisor ◽  
The Ideal

AbstractLet P and Q be two points on an elliptic curve defined over a number field K. For $$\alpha \in {\text {End}}(E)$$ α ∈ End ( E ) , define $$B_\alpha $$ B α to be the $$\mathcal {O}_K$$ O K -integral ideal generated by the denominator of $$x(\alpha (P)+Q)$$ x ( α ( P ) + Q ) . Let $$\mathcal {O}$$ O be a subring of $${\text {End}}(E)$$ End ( E ) , that is a Dedekind domain. We will study the sequence $$\{B_\alpha \}_{\alpha \in \mathcal {O}}$$ { B α } α ∈ O . We will show that, for all but finitely many $$\alpha \in \mathcal {O}$$ α ∈ O , the ideal $$B_\alpha $$ B α has a primitive divisor when P is a non-torsion point and there exist two endomorphisms $$g\ne 0$$ g ≠ 0 and f so that $$f(P)= g(Q)$$ f ( P ) = g ( Q ) . This is a generalization of previous results on elliptic divisibility sequences.

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
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