scholarly journals A note on induced central extensions

1979 ◽  
Vol 20 (3) ◽  
pp. 411-420 ◽  
Author(s):  
L.R. Vermani
Keyword(s):  
Abelian Group ◽  
Nilpotent Group ◽  
Central Extension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Central Extensions ◽  
Baer Sum ◽  
Necessary And Sufficient

A characterization of induced central extensions which gives an explicit relationship between induced central extensions and n-stem extensions is obtained. Using the characterization, necessary and sufficient conditions for a central extension of an abelian group by a nilpotent group of class n to be a Baer sum of an induced central extension and an extension of class n are obtained.

scholarly journals On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

2020 ◽  
Vol 15 (1) ◽  
pp. 258-265
Author(s):  
Yu Zhou ◽  
Daoguang Mu ◽  
Xinfeng Dong
Keyword(s):  
Sufficient Conditions ◽  
Sum Of Squares ◽  
Basic Component ◽  
Necessary And Sufficient Conditions ◽  
Autocorrelation Functions ◽  
Walsh Spectrum ◽  
Cryptographic Algorithms ◽  
Necessary And Sufficient ◽  
Relationship Of

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

scholarly journals Multigenerator Gabor Frames on Local Fields

2018 ◽  
Vol 33 (2) ◽  
pp. 307
Author(s):  
Owais Ahmad ◽  
Neyaz Ahmad Sheikh
Keyword(s):  
Sufficient Conditions ◽  
Complete Characterization ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Gabor Frames ◽  
Gabor System ◽  
Necessary And Sufficient

The main objective of this paper is to provide complete characterization of multigenerator Gabor frames on a periodic set $\Omega$ in $K$. In particular, we provide some necessary and sufficient conditions for the multigenerator Gabor system to be a frame for $L^2(\Omega)$. Furthermore, we establish the complete characterizations of multigenerator Parseval Gabor frames.

scholarly journals Cheap Talk and Editorial Control

2014 ◽  
Vol 14 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Jonathan Newton
Keyword(s):  
Information Transmission ◽  
Sufficient Conditions ◽  
Cheap Talk ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Simple Models

AbstractThis paper analyzes simple models of editorial control. Starting from the framework developed by Krishna and Morgan (2001a), we analyze two-sender models of cheap talk where one or more of the senders has the power to veto messages before they reach the receiver. A characterization of the most informative equilibria of such models is given. It is shown that editorial control never aids communication and that for small biases in the senders’ preferences relative to those of the receiver, necessary and sufficient conditions for information transmission to be adversely affected are (i) that the senders have opposed preferences relative to the receiver and (ii) that both senders have powers of editorial control. It is shown that the addition of further senders beyond two weakly decreases information transmission when senders exercising editorial control are anonymous, and weakly increases information transmission when senders exercising editorial control are observed.

scholarly journals On the equivalence of cancellative extensions of commutative cancellative semigroups by groups

1971 ◽  
Vol 12 (2) ◽  
pp. 187-192
Author(s):  
Charles V. Heuer
Keyword(s):  
Abelian Group ◽  
Cyclic Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ideal Extension ◽  
Cancellative Semigroup ◽  
Finitely Generated ◽  
Necessary And Sufficient

In [1] D. W. Miller and the author established necessary and sufficient conditions for the existence of a cancellative (ideal) extension of a commutative cancellative semigroup by a cyclic group with zero. The purpose of this paper is to extend these results to cancellative extensions by any finitely generated Abelian group with zero and to establish in this general case conditions under which two such extensions are equivalent.

Stochastic Orders in Terms of Laplace Transforms

1995 ◽  
Vol 45 (3-4) ◽  
pp. 195-202 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Laplace Transform ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Orders ◽  
Partial Orderings ◽  
Life Distributions ◽  
Necessary And Sufficient

Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.

scholarly journals A characterization of recurrent motions

1983 ◽  
Vol 28 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Ronald A. Knight
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Stable Flow

Necessary and sufficient conditions for a Poisson stable flow to be recurrent are given.

scholarly journals A characterization of point semiuniformities

1996 ◽  
Vol 19 (2) ◽  
pp. 311-316
Author(s):  
Jennifer P. Montgomery
Keyword(s):  
Topological Group ◽  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Groups ◽  
Necessary And Sufficient

The concept of a uniformity was developed by A. Well and there have been several generalizations. This paper defines a point semiuniformity and gives necessary and sufficient conditions for a topological space to be point semiuniformizable. In addition, just as uniformities are associated with topological groups, a point semiuniformity is naturally associated with a semicontinuous group. This paper shows that a point semiuniformity associated with a semicontinuous group is a uniformity if and only if the group is a topological group.

scholarly journals Pairs of rings with a bijective correspondence between the prime spectra

1993 ◽  
Vol 55 (2) ◽  
pp. 238-245
Author(s):  
E. Jespers ◽  
P. Wauters
Keyword(s):  
Abelian Group ◽  
Commutative Ring ◽  
Free Abelian Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Polynomial Rings ◽  
Prime Spectrum ◽  
Bijective Correspondence ◽  
Natural Mapping ◽  
Necessary And Sufficient

AbstractLet A be a subring of a commutative ring B. If the natural mapping from the prime spectrum of B to the prime spectrum of A is injective (respectively bijective) then the pair (A, B) is said to have the injective (respectively bijective) Spec-map. We give necessary and sufficient conditions for a pair of rings A and B graded by a free abelian group to have the injective (respectively bijective) Spec-map. For this we first deal with the polynomial case. Let l be a field and k a subfield. Then the pair of polynomial rings (k[X], l[X]) has the injective Spec-map if and only if l is a purely inseparable extension of k.

Characterization of primes dividing the index of a trinomial

2017 ◽  
Vol 13 (10) ◽  
pp. 2505-2514 ◽  
Author(s):  
Anuj Jakhar ◽  
Sudesh K. Khanduja ◽  
Neeraj Sangwan
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Sufficient Conditions ◽  
Algebraic Number Field ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Integers ◽  
Ring Of Algebraic Integers ◽  
Necessary And Sufficient

Let [Formula: see text] denote the ring of algebraic integers of an algebraic number field [Formula: see text], where [Formula: see text] is a root of an irreducible trinomial [Formula: see text] belonging to [Formula: see text]. In this paper, we give necessary and sufficient conditions involving only [Formula: see text] for a given prime [Formula: see text] to divide the index of the subgroup [Formula: see text] in [Formula: see text]. In particular, we deduce necessary and sufficient conditions for [Formula: see text] to be equal to [Formula: see text].

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