From Affine to Two-Source Extractors via Approximate Duality

2015 ◽  
Vol 44 (6) ◽  
pp. 1670-1697
Author(s):  
Eli Ben-Sasson ◽  
Noga Ron-Zewi
Keyword(s):  
Approximate Duality

On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems

2019 ◽  
Vol 35 (3) ◽  
pp. 417-426 ◽  
Author(s):  
CHANOKSUDA KHANTREE ◽  
RABIAN WANGKEEREE ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Data Uncertainty ◽  
Necessary Condition ◽  
Duality Theorems ◽  
Approximate Form ◽  
Locally Lipschitz ◽  
Approximate Duality

This paper devotes to the quasi ε-solution for robust semi-infinite optimization problems (RSIP) involving a locally Lipschitz objective function and infinitely many locally Lipschitz constraint functions with data uncertainty. Under the fulfillment of robust type Guignard constraint qualification and robust type Kuhn-Tucker constraint qualification, a necessary condition for a quasi ε-solution to problem (RSIP). After introducing the generalized convexity, we give a sufficient optimality for such a quasi ε-solution to problem (RSIP). Finally, we also establish approximate duality theorems in term of Wolfe type which is formulated in approximate form.

Approximate duality for vector quasi-equilibrium problems and applications

2010 ◽  
Vol 72 (11) ◽  
pp. 3994-4004 ◽  
Author(s):  
Pham Huu Sach ◽  
Le Anh Tuan ◽  
Nguyen Ba Minh
Keyword(s):  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Approximate Duality

Duals and multipliers of controlled frames in Hilbert spaces

2018 ◽  
Vol 16 (06) ◽  
pp. 1850057 ◽  
Author(s):  
M. Rashidi-Kouchi ◽  
A. Rahimi ◽  
Firdous A. Shah
Keyword(s):  
Hilbert Spaces ◽  
Dual Frames ◽  
Multiplier Operator ◽  
Mild Conditions ◽  
Multiplier Operators ◽  
Approximate Duality

In this paper, we introduce and characterize controlled dual frames in Hilbert spaces. We also investigate the relation between bounds of controlled frames and their related frames. Then, we define the concept of approximate duality for controlled frames in Hilbert spaces. Next, we introduce multiplier operators of controlled frames in Hilbert spaces and investigate some of their properties. Finally, we show that the inverse of a controlled multiplier operator is also a controlled multiplier operator under some mild conditions.

scholarly journals Baryogenesis, magnetogenesis and the strength of anomalous interactions

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Massimo Giovannini
Keyword(s):  
Power Spectra ◽  
Gauge Coupling ◽  
Late Time ◽  
De Sitter ◽  
Actual Weight ◽  
Duality Symmetry ◽  
Inflationary Phase ◽  
Approximate Duality ◽  
Time Form ◽  
Typical Length

AbstractThe production of the hypermagnetic gyrotropy is investigated under the assumption that the gauge coupling smoothly evolves during a quasi-de Sitter phase and then flattens out in the radiation epoch by always remaining perturbative. In the plane defined by the strength of the anomalous interactions and by the rate of evolution of the gauge coupling the actual weight of the pseudoscalar interactions turns out to be always rather modest if major deviations from the homogeneity are to be avoided during the inflationary phase. Even if the gauge power spectra are related by duality only in the absence of anomalous contributions, an approximate duality symmetry constrains the late-time form of the hypermagnetic power spectra. Since the hypermagnetic gyrotropy associated with the modes reentering prior to the phase transition must be released into fermions later on, the portions of the parameter space where the obtained baryon asymmetry is close to the observed value are the most relevant for the present ends. For the same range of parameters the magnetic power spectra associated with the modes reentering after symmetry breaking may even be of the order of a few hundredths of a nG over typical length scales comparable with the Mpc prior to the collapse of the protogalaxy.

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