1,928 research outputs found
Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory
The soft wall model in holographic QCD has Regge trajectories but wrong
operator product expansion (OPE) for the two-point vectorial QCD Green
function. We modify the dilaton potential to comply OPE. We study also the
axial two-point function using the same modified dilaton field and an
additional scalar field to address chiral symmetry breaking. OPE is recovered
adding a boundary term and low energy chiral parameters, and ,
are well described analytically by the model in terms of Regge spacing and QCD
condensates. The model nicely supports and extends previous theoretical
analyses advocating Digamma function to study QCD two-point functions in
different momentum regions.Comment: Major changes to improve the presentation of the paper but main
results unchanged. Added appendix on Regge progressio
About least-squares type approach to address direct and controllability problems
- We discuss the approximation of distributed null controls for partial
differential equations. The main purpose is to determine an approximation of
controls that drives the solution from a prescribed initial state at the
initial time to the zero target at a prescribed final time. As a non trivial
example, we mainly focus on the Stokes system for which the existence of
square-integrable controls have been obtained in [Fursikov \& Imanuvilov,
Controllability of Evolution Equations, 1996]) via Carleman type estimates. We
introduce a least-squares formulation of the controllability problem, and we
show that it allows the construction of strong convergent sequences of
functions toward null controls for the Stokes system. The approach consists
first in introducing a class of functions satisfying a priori the boundary
conditions in space and time-in particular the null controllability condition
at time T-, and then finding among this class one element satisfying the
system. This second step is done by minimizing a quadratic functional, among
the admissible corrector functions of the Stokes system. We also discuss
briefly the direct problem for the steady Navier-Stokes system. The method does
not make use of any duality arguments and therefore avoid the ill-posedness of
dual methods, when parabolic type equation are considered
Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems
In this paper, a new class of generalized of nonconvex multitime multiobjective variational problems is considered. We prove the sufficient optimality conditions for efficiency and proper efficiency in the considered multitime multiobjective variational problems with univex functionals. Further, for such vector variational problems, various duality results in the sense of Mond-Weir and in the sense of Wolfe are established under univexity. The results established in the paper extend and generalize results existing in the literature for such vector variational problems
Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems
Two approximation algorithms for solving convex vector optimization problems
(CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual
problem simultaneously. The first algorithm is an extension of Benson's outer
approximation algorithm, and the second one is a dual variant of it. Both
algorithms provide an inner as well as an outer approximation of the (upper and
lower) images. Only one scalar convex program has to be solved in each
iteration. We allow objective and constraint functions that are not necessarily
differentiable, allow solid pointed polyhedral ordering cones, and relate the
approximations to an appropriate \epsilon-solution concept. Numerical examples
are provided
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