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A Polytope Combinatorics for Semisimple Groups
Algebraic cross homology of the cycle cycle the image
2014/12/29
Mirkovi and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties ar...
We show that for n 3 there are 3 · 2n−1 complex common tangent lines to 2n−2 general spheres in Rn and that there is a choice of spheres with all common tangents real.
Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real ...
Elementary Transversailty in the Schubert Calculus in any Characteristic
Characteristic - free schubert varieties cross data transversality theory algebraic geometry
2014/12/29
We give a characteristic-free proof that general codimension-1 Schubert varieties meet transversally in a Grassmannian and in some related varieties. Thus the corresponding intersection numbers are en...
Focusing Revisited: an MN-dynamics Approach
Nonlinear Schr odinger equation the dispersion system focusing on NLS equation
2014/12/29
The nonlinear Schr¨odinger (NLS) equation is a ubiquitous example of an envelope wave equation for conservative, dispersive systems. We revisit here the problem of self-similar focusing of waves in th...
Common Transversals and Tangents to Two Lines and Two Quadrics in P^3
Geometry 3 d application infinitely many line projective quadratic projective space quadratic curve
2014/12/29
We solve the following geometric problem, which arises in several threedimensional applications in computational geometry: For which arrangements of two lines and two spheres in R3 are there infinitel...
Skew Schubert Polynomials
Oblique schubert polynomial bloom the symmetry group oblique schubert polynomials non-negative integer coefficient
2014/12/29
We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction o...
Using the Continuous Spectrum to “Feel” Integrability: the Effect of Boundary Conditions
Test model integrability partial differential differential difference equations of continuous spectrum
2014/12/29
The scope of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE). For monoparametric families of PDE/DDE’...
Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity
Stability in two-dimensional discrete nonlinear schrodinger equation lattice discrete soliton
2014/12/29
We study the existence and stability of localized states in the discrete nonlinear Schrödinger equation on two-dimensional nonsquare lattices. The model includes both the nearest-neighbor and lon...
Scattering of a Solitary Pulse on a Local Defect or Breather
Model of nonlinear impulsive nonlinear defect optical pulse long fiber nonlinear optical fiber
2014/12/29
A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one. The model with the st...
Analogues of Weyl’s Formula for Reduced Enveloping Algebras
Module reduce enveloping algebra dimension formula the hyperplane affine cells
2014/12/29
In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions o...
Units, polyhedra, and a conjecture of Satake
Real number field degree polyhedral cone circular resolution
2014/12/29
Let F/Q be a totally real number field of degree n. We explicitly evaluate a certain sum of rational functions over a infinite fan of F-rational polyhedral cones in terms of the norm map N: F ¨ ...
Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows
Two-dimensional correlation structure of equilibrium model the model of energy balance ratio model water resources
2014/12/29
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or...
Binomial residues
Binomial residue rational function definitions singular binomial hypergeometric integral factor Lawrence type
2014/12/29
A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solut...
Intersection cohomology of Drinfeld‚s compactifications
Smooth complete curve parabola double algebras
2014/12/29
Let X be a smooth complete curve, G be a reductive group and a parabolic. Following Drinfeld, one defines a (relative) compactification of the moduli stack of P-bundles on X. The present paper is conc...