scholarly journals Weak-basis invariant conditions for CP conservation in SU(2)L X SU(2)R X U(1)B − L models

1986 ◽  
Vol 173 (3) ◽  
pp. 313-318 ◽  
Author(s):  
G.C. Branco ◽  
M.N. Rebelo
Keyword(s):  
Weak Basis ◽  
Basis Invariant

The Weak Basis Theorem Fails in Non-Locally Convex F-Spaces

1977 ◽  
Vol 29 (5) ◽  
pp. 1069-1071 ◽  
Author(s):  
L. Drewnowski
Keyword(s):  
Weak Basis ◽  
Basis Theorem ◽  
Locally Convex

W. J. Stiles showed in [10, Corollary 4.5] that Banach's weak basis theorem fails in the spaces lp, 0 < p < 1. Then, J. H. Shapiro [9] indicated certain general classes of non-locally convex F-spaces with the same property, and asked whether the weak basis theorem fails in every non-locally convex F-space with a weak basis. Our purpose is to answer this question in the affirmative. In [3] we observed that, essentially, the only case that remained open is that of an F-space with irregular basis (en), i.e. such that snen →0 for any scalar sequence (sn).

Mackey duals and almost shrinking bases

1973 ◽  
Vol 74 (1) ◽  
pp. 73-81 ◽  
Author(s):  
N. J. Kalton
Keyword(s):  
Banach Space ◽  
Weak Topology ◽  
Norm Topology ◽  
Weak Basis ◽  
Mackey Topology ◽  
Dual Sequence

Suppose (en) is a basis of a Banach space E, and that (e′n) is the dual sequence in E′. Then if (e′n) is a basis of E′ in the norm topology (i.e. (en) is shrinking) it follows that E′ is norm separable: it is easy to give examples of spaces E for which this is not so. Therefore there are plenty of spaces which cannot have a shrinking basis. This leads one to consider whether it might not be reasonable to replace the norm topology on E′ by one which is always separable (provided E is separable). Of course, the weak*-topology σ(E′, E) is one possibility (Köthe (17), p. 259); then it is trivial that (e′n) is a weak*-basis of E′. However, if the weak*-topology is separable, then so is the Mackey topology τ(E′, E) on E′, and so we may ask whether (e′n) is a basis of (E′,τ(E′, E)).

scholarly journals Ensuring the reliability of pavements in the repair and reconstruction of existing cement-concrete pavements destroyed by vibroresonance on a weak basis

2021 ◽  
Vol 2 (92) ◽  
pp. 17
Author(s):  
Ihor Gameliak ◽  
Vitalii Raikovskyi
Keyword(s):  
Asphalt Concrete ◽  
Modulus Of Elasticity ◽  
Stress Relief ◽  
Concrete Pavements ◽  
Weak Base ◽  
Cement Concrete ◽  
Weak Basis ◽  
Minimum Number ◽  
Modulus Of Deformation ◽  
Number Of Passes

Abstract. Repair and reconstruction of existing ce-ment-concrete pavements of hard pavements should be performed based on the results of the assessment of the condition of the pavement, assessment of their suitability as a basis for new layers and especially when reinforced with asphalt concrete layers. The article presents a method of determining the actual total modulus of elasticity of pavement, using static and dynamic stamping equipment and evaluating the results of measuring the modulus of deformation and elasticity of the concrete base at different passes of the vibrating cavity to decide on the method of re-pair. It is concluded that with a weak base, the vibroresonance method is unsuitable and stress relief should be used with a minimum number of passes of destructive equipment.

scholarly journals Implications of CP invariants for the flavored hybrid neutrino mass matrix

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Madan Singh ◽  
Keyword(s):  
Neutrino Mass ◽  
Mass Matrix ◽  
Majorana Neutrino ◽  
Neutrino Mass Matrix ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Weak Basis ◽  
Low Energies ◽  
Necessary And Sufficient ◽  
Majorana Neutrino Mass

Abstract We re-examine the weak basis invariants at low energies proposed by C. Jarlskog and Branco et al. in their earlier analyses, after confronting them with the assumptions of two zeros and an equality between arbitrary non-zero elements in the Majorana neutrino mass matrix in the flavored basis. This particular conjecture is found to be experimentally feasible, as shown by S. Dev and D. Raj in their recent work. The present analysis attempts to find the necessary and sufficient condition for CP invariance for each experimentally viable ansatz pertaining to the model, along with some important implications.

scholarly journals FLAVOR MIXINGS AND TEXTURES OF THE FERMION MASS MATRICES

2012 ◽  
Vol 27 (31) ◽  
pp. 1230033 ◽  
Author(s):  
MANMOHAN GUPTA ◽  
GULSHEEN AHUJA
Keyword(s):  
Fermion Mass ◽  
Unitarity Triangle ◽  
Specific Mass ◽  
Weak Basis ◽  
New Developments ◽  
Comprehensive Review ◽  
Leptonic Sector ◽  
Mass Matrices ◽  
Relationship Of ◽  
The Relationship

A comprehensive review of several aspects of fermion mixing phenomenon and texture specific mass matrices have been presented. Regarding fermion mixings, implications of unitarity and certain new developments for the CKM paradigm have been discussed. In the leptonic sector, the question of possibility of CP violation has been discussed in detail from the unitarity triangle perspective. In the case of texture specific mass matrices, the issues of viability of Fritzsch-like as well as non-Fritzsch-like mass matrices have been detailed for both the quark and leptonic sectors. The relationship of textures, naturalness and weak basis rotations has also been looked into. The issue of the compatibility of texture specific mass matrices with the SO(10)-based GUT mass matrices has also been discussed.

scholarly journals Clues towards unified textures

2014 ◽  
Vol 29 (21) ◽  
pp. 1444005 ◽  
Author(s):  
Samandeep Sharma ◽  
Priyanka Fakay ◽  
Gulsheen Ahuja ◽  
Manmohan Gupta
Keyword(s):  
Specific Mass ◽  
Weak Basis ◽  
Zero Mass ◽  
Mass Matrices ◽  
General Mass

The issue of texture specific mass matrices has been discussed by incorporating Weak Basis transformations and the concept of "naturalness." Interestingly, we find that starting from the most general mass matrices, one can arrive at texture four zero mass matrices which can fit both quark as well as lepton mixing data and are similar to the original Fritzsch ansatze.

scholarly journals Security evaluation of quantum key distribution with weak basis-choice flaws

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Shi-Hai Sun ◽  
Zhi-Yu Tian ◽  
Mei-Sheng Zhao ◽  
Yan Ma
Keyword(s):  
Quantum Key Distribution ◽  
Single Photon ◽  
Phase Error ◽  
Key Distribution ◽  
Theory And Practice ◽  
Security Evaluation ◽  
Weak Basis ◽  
Definition Of ◽  
Original Approach ◽  
Photon Source

Abstract Quantum key distribution (QKD) can share an unconditional secure key between two remote parties, but the deviation between theory and practice will break the security of the generated key. In this paper, we evaluate the security of QKD with weak basis-choice flaws, in which the random bits used by Alice and Bob are weakly controlled by Eve. Based on the definition of Li et al. (Sci Rep 5:16200, 2015) and GLLP’s analysis, we obtain a tight and analytical bound to estimate the phase error and key rate for both the single photon source and the weak coherent source. Our approach largely increases the key rate from that of the original approach. Finally, we investigate and confirm the security of BB84-QKD with a practical commercial devices.

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