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Hierarchical Interpolative Factorization for Elliptic Operators:Integral Equations
Hierarchical Interpolative Factorization Elliptic Operators Integral Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
Hierarchical Interpolative Factorization for Elliptic Operators:Differential Equations
Hierarchical Interpolative Factorization Elliptic Operators Differential Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an a...
SELF-AVERAGING FROM LATERAL DIVERSITY IN THE ITO-SCHRODINGER EQUATION
Random media Parabolic approximation Stochastic partial differential equations
2015/7/14
We consider the random Schrodinger equation as it arises in the paraxial regime for wave propagation in random media. In the white noise limit it becomes the Ito-Schrodinger stochastic partial differe...
We study the qualitative properties of the generalized transition fronts for the reactiondiffusion equations with the spatially inhomogeneous nonlinearity of the ignition type. We show that transition...
A sharp bound on the L2 norm of the solution of a random elliptic difference equation
sharp bound L2 norm random elliptic difference equation
2015/7/14
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
A differential equations approach to l1-minimization with applications to array imaging
differential equations approach l1-minimization array imaging
2015/7/14
We present an ordinary differential equations approach to the analysis of algorithms for constructing l1 minimizing solutions to underdeter mined linear systems of full rank. It involves a relaxed min...
The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
A natural smooth compactiffcation of the space of elliptic curves in projective space via blowing up the space of stable maps
projective space stable maps
2015/7/14
We nd it interesting that such a natural naive approach as we will describe
actually works, and yields a desingularization with these nice properties.
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model
Traveling wave Wavetrains Nonlocal elliptic equations
2015/7/14
Traveling waves for the nonlocal Fisher Equation can exhibit much more complex behaviours than for the usual Fisher equation. A striking numerical observation is that a traveling wave with minimal spe...
Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity
Traveling Wave Solutions Reaction-Diffusion Model Criminal Activity
2015/7/14
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity, first introduced in [3]. We show that the assumption of a populati...
THE ENUMERATIVE GEOMETRY OF RATIONAL AND ELLIPTIC CURVES IN PROJECTIVE SPACE
ELLIPTIC CURVES PROJECTIVE SPACE
2015/7/14
We study the geometry of moduli spaces of genus 0 and 1 curves in Pn with
speci ed contact with a hyperplane H. We compute intersection numbers on these spaces that
correspond to the number of degre...
TWELVE POINTS ON THE PROJECTIVE LINE, BRANCHED COVERS, AND RATIONAL ELLIPTIC FIBRATIONS
PROJECTIVE LINE BRANCHED COVERS
2015/7/14
The following divisors in the space Sym12 P1 of twelve points on
P1 are actually the same: (A) the possible locus of the twelve nodal bers in
a rational elliptic bration (i.e. a pencil of plane cu...
In the study of the geometry of curves on surfaces, the following
question often arises: given a one-parameter family of divisors over a pointed
curve, what does the central ber look like after sta...
The Technion school lecture notes:the moving plane method,or doing PDEs in a cafe
Technion school lecture notes moving plane method doing PDEs a cafe
2015/7/14
We will have two main characters in these notes: the maximum principle and the sliding method. The latter has a twin, the moving plane method–they are often so indistinguishable that we will count the...
As an application, we show that with boundary conditions corresponding to integer partitions , the six-vertex model is exactly solvable and equal to a Schur
polynomial s times a deformation of the ...