On scaling functions of non-uniform multiresolution analysis in L2(ℝ)

2019 ◽  
Vol 18 (02) ◽  
pp. 1950055
Author(s):  
Hari Krishan Malhotra ◽  
Lalit Kumar Vashisht
Keyword(s):  
Frequency Domain ◽  
Multiresolution Analysis ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Scaling Functions ◽  
Necessary And Sufficient

The main purpose of this paper is to provide a characterization of scaling functions for non-uniform multiresolution analysis (NUMRA, in short). Some necessary and sufficient conditions for scaling functions of wavelet NUMRA in the frequency domain are also 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 Multiresolution analysis and wavelets on Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 309-325 ◽  
Author(s):  
Yury Farkov
Keyword(s):  
Multiresolution Analysis ◽  
Linear Independence ◽  
Sufficient Conditions ◽  
Partition Of Unity ◽  
Necessary And Sufficient Conditions ◽  
Refinable Functions ◽  
Vilenkin Groups ◽  
Orthogonal Wavelets ◽  
The Stability ◽  
Necessary And Sufficient

This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

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.

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.

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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