57 research outputs found
Higher order duality and toric embeddings
The notion of higher order dual varieties of a projective variety is a
natural generalization of the classical notion of projective duality,
introduced by Piene in 1983. In this paper we study higher order dual varieties
of projective toric embeddings. We compute the degree of the second dual
variety of a smooth toric threefold in geometric and combinatorial terms, and
we classify smooth 2-jet spanned projective embeddings of smooth threefolds
whose second dual variety has dimension less than expected. We also describe
the tropicalization of the k-th dual variety of an equivariantly embedded (not
necessarily normal) toric variety.Comment: Final version to appear in Annales de l'Institut Fourier. Deleted an
unnecessary wrong statemen
On Higher-order Duality in Nondifferentiable Minimax Fractional Programming
In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulated two types of higher-order dual models for such optimization problem.Weak, strong and strict converse duality theorems are derived under higherorder generalized invexity
Higher order duality in multiobjective fractional programming with support functions
AbstractIn this paper a new class of higher order (F,Ï,Ï)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order MondâWeir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,Ï,Ï)-type I. A number of previously studied problems appear as special cases
Higher Order Duality for Vector Optimization Problem over Cones Involving Support Functions
In this paper, we consider a vector optimization problem over cones involving support functions in objective as well as constraints and associate a unified higher order dual to it. Duality result have been established under the conditions of higher order cone convex and related functions. A number of previously studied problems appear as special cases. Keywords: Vector optimization, Cones, Support Functions, Higher Order Duality
Higher order wave-particle duality
The complementarity of single-photon's particle-like and wave-like behaviors
can be described by the inequality , with being the path
distinguishability and being the fringe visibility. In this paper, we
generalize this duality relation to multi-photon case, where two new concepts,
higher order distinguishability and higher order fringe visibility, are
introduced to quantify the higher order particle-like and wave-like behaviors
of multi-photons.Comment: 5 pages, 1 figur
Linear Toric Fibrations
These notes are based on three lectures given at the 2013 CIME/CIRM summer
school. The purpose of this series of lectures is to introduce the notion of a
toric fibration and to give its geometrical and combinatorial
characterizations. Polarized toric varieties which are birationally equivalent
to projective toric bundles are associated to a class of polytopes called
Cayley polytopes. Their geometry and combinatorics have a fruitful interplay
leading to fundamental insight in both directions. These notes will illustrate
geometrical phenomena, in algebraic geometry and neighboring fields, which are
characterized by a Cayley structure. Examples are projective duality of toric
varieties and polyhedral adjunction theory
Special Geometry and Twisted Moduli in Orbifold Theories with Continuous Wilson Lines
Target space duality symmetries, which acts on K\"ahler and continuous Wilson
line moduli, of a () 2-dimensional subspace of the moduli
space of orbifold compactification are modified to include twisted moduli.
These spaces described by the cosets are
K\"ahler, a fact which is exploited in deriving the extension of tree
level duality transformation to include higher orders of the twisted moduli.
Also, restrictions on these higher order terms are derived.Comment: 13 page
BFKL at Next-to-Next-to-Leading Order
We determine an approximate expression for the O(alpha_s^3) contribution
chi_2 to the kernel of the BFKL equation, which includes all collinear and
anticollinear singular contributions. This is derived using recent results on
the relation between the GLAP and BFKL kernels (including running-coupling
effects to all orders) and on small-x factorization schemes. We present the
result in various schemes, relevant both for applications to the BFKL equation
and to small-x evolution of parton distributions.Comment: 34 pages, 6 figures, TeX with harvmac. Various small typos corrects,
in particular first term in eq D.3. Final version to be published in Nucl.
Phys.
- âŠ