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We will report our recent work on weak multisymplectic spectral integrators for a wide range of nonsmooth Hamiltonian partial differential equations, which appear in quite a few physical applications ...
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar generalization of the nonlinear steepest descent method to compute the leading order approximatio...
Resolution and sidelobe are mutual restrict for SAR image. Usually sidelobe suppression is based on resolution reduction. This paper provide a method for resolution enchancement using sidelobe opposit...
We discuss a Continuous Curvelet Transform (CCT), a transform f → Γf(a, b, θ) of functions f(x1, x2) on R2, into a transform domain with continuous scale a > 0, location b ∈ R2, and orientation θ ∈...
We discuss a Continuous Curvelet Transform (CCT), a transform f → Γf(a, b, θ) of functions f(x1, x2) on R2, into a transform domain with continuous scale a > 0, location b ∈ R2, and orientation θ ∈ [...
We introduce a new approach to image super-resolution. The idea is to use a simple wavelet-based linear interpolation scheme as our initial estimate of high-resolution image; and to intensify geometri...
Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli pro...
Abstract: In this sequel to Resolution except for minimal singularities I, we find the smallest class of singularities in four variables with which we necessarily end up if we resolve singularities ex...
Abstract: The philosophy of the article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of singularities. The idea is used...
Abstract: The global nilpotent cone N is a singular stack associated to the choice of an algebraic group G, a smooth projective curve X, and a line bundle L on X, which is of fundamental importance to...
Abstract: The purpose of this paper is to extend the notions of generalised Poincar\'e series and divisorial generalised Poincar\'e series (of motivic nature) introduced by Campillo, Delgado and Gusei...
A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established in [1] in the context ...
A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds ...
Let k be a field. For each pair of positive integers (n,N), we resolve Q = R/(xN, yN, zN) as a module over the ring R = k[x, y, z]/(xn +yn + zn). Write N in the form N = an + r for integers a and r.
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the...

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