scholarly journals The necessary and sufficient conditions for wavelet frames in Sobolev space over local fields

2021 ◽  
Vol 39 (3) ◽  
pp. 81-92
Author(s):  
Ashish Pathak ◽  
Dileep Kumar ◽  
Guru P. Singh
Keyword(s):  
Sobolev Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Necessary And Sufficient

In this paper we construct wavelet frame on Sobolev space. A necessary condition and sufficient conditions for wavelet frames in Sobolev space are given.

Necessary condition and sufficient conditions for nonuniform wavelet frames in L2(K)

2018 ◽  
Vol 16 (01) ◽  
pp. 1850005 ◽  
Author(s):  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Sufficient Conditions ◽  
Local Fields ◽  
Necessary Condition ◽  
Wavelet Basis ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Constructive Algorithm ◽  
Spectral Pairs ◽  
Funct Anal

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in [Formula: see text] was considered by Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998) 209–241]. In this setting, the associated translation set is a spectrum [Formula: see text] which is not necessarily a group nor a uniform discrete set, given [Formula: see text] where [Formula: see text] (an integer) and [Formula: see text] is an odd integer with [Formula: see text] such that [Formula: see text] and [Formula: see text] are relatively prime and [Formula: see text] is the set of all integers. The objective of this paper is to construct nonuniform wavelet frame on local fields. A necessary condition and four sufficient conditions for nonuniform wavelet frame on local fields are given.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

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 Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fengjuan Zhu ◽  
Qiufu Li ◽  
Yongdong Huang
Keyword(s):  
Scaling Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Numerical Examples ◽  
Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.

scholarly journals Square roots in finite full transformation semigroups

1982 ◽  
Vol 23 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Mary Snowden ◽  
J. M. Howie
Keyword(s):  
Transformation Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Square Root ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Square Roots ◽  
Finite Set ◽  
Necessary And Sufficient

Let X be a finite set and let (X) be the full transformation semigroup on X, i.e. the set of all mappings from X into X, the semigroup operation being composition of mappings. This paper aims to characterize those elements of (X) which have square roots. An easily verifiable necessary condition, that of being quasi-square, is found in Theorem 2, and in Theorems 4 and 5 we find necessary and sufficient conditions for certain special elements of (X). The property of being compatibly amenable is shown in Theorem 7 to be equivalent for all elements of (X) to the possession of a square root.

scholarly journals Buying Supermajorities in Finite Legislatures

2000 ◽  
Vol 94 (3) ◽  
pp. 677-681 ◽  
Author(s):  
Jeffrey S. Banks
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Vote Buying ◽  
Necessary And Sufficient ◽  
Coalition Size

I analyze the finite-voter version of the Groseclose and Snyder vote-buying model. I identify how the optimal coalition size varies with the underlying preference parameters; derive necessary and sufficient conditions for minimal majority and universal coalitions to form; and show that the necessary condition for minimal majorities found in Groseclose and Snyder is incorrect.

scholarly journals Regular formal modules in local fields and irregularly degree

2020 ◽  
Vol 65 (4) ◽  
pp. 588-596
Author(s):  
Natalya K. Vlaskina ◽  
◽  
Sergei V. Vostokov ◽  
Petr N. Pital’ ◽  
Aleksey E. Tsybyshiev ◽  
...  
Keyword(s):  
Positive Integer ◽  
Local Field ◽  
Sufficient Conditions ◽  
Formal Group ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Ramification Index ◽  
Necessary And Sufficient ◽  
Primitive Roots

In this paper we investigate the irregular degree of finite not ramified local field extantions with respect to a polynomial formal group and in the multiplicative case. There was found necessary and sufficient conditions for the existence of primitive roots of ps power from 1 and (endomorphism [ps]Fm) in L-th unramified extension of the local field K (for all positive integer s). These conditions depend only on the ramification index of the maximal abelian subextension of the field K Ka/Qp.

scholarly journals Generalising the Horodecki criterion to nonprojective qubit observables

2021 ◽  
Author(s):  
Michael J W Hall ◽  
Shuming Cheng
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Weak Measurements ◽  
Chsh Inequality ◽  
Bell Nonlocality ◽  
Necessary And Sufficient ◽  
Projective Measurements

Abstract The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that suitable projective measurements can be made on each qubit, and is not sufficient for scenarios in which noisy or weak measurements are either desirable or unavoidable. By characterising two-valued qubit observables in terms of strength, bias, and directional parameters, we address such scenarios by providing necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. In particular, we find the achievable maximal values of the CHSH parameter for unbiased measurements on arbitrary states, and, alternatively, for arbitrary measurements on states with maximally-mixed marginals, and determine the optimal angles in some cases. We also show that for certain ranges of measurement strengths it is only possible to violate the CHSH inequality via biased measurements. Finally, we use the CHSH inequality to obtain a simple necessary condition for the compatibility of two qubit observables.

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