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Landau-Lifshitz-Gilbert equation (LLG) describes magnetization of ferromagnets. In this paper, we consider the singularity formation of LLG from R^2 to S^2. For any prescribed N distinct points q^{j} ...
The Ricci flow is a powerful tool in geometry to construct the canonical metric on a given manifold. It can be viewed as a nonlinear heat flow of the Riemannian metric and may develop finite time sing...
The aim of the symposium is to bring together specialists of various do- mains of singularity theory and mathematical foundation of complex systems representing very classical aspects of the Fields. W...
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
In a previous paper, there was defined a multi-index filtration on the ring of functions on a hypersurface singularity corresponding to its Newton diagram generalizing (for a curve singularity) the di...
Abstract: We show a new path to {\epsilon}~0 materials without resorting to metal-based metamaterial composites. A medium that can be modeled using Lorentz oscillators usually displays {\epsilon}=0 cr...
Abstract: It was shown, in our previous works, that periodic points of $d$ dimensional rational integrable maps form varieties if the number of invariants $p$ is greater than $d/2$. In the case of 3 d...
Abstract: This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta functio...
In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the corresponding...
Abstract: In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the cor...
Singularity invariants related to Milnor fibers: survey      Singularity invariants  Milnor fibers  survey        font style='font-size:12px;'> 2011/1/21
This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicali...
We show that a homology plane of general type has at worst a single cyclic quotient singular point. An example of such a surface with a singular point does exist [MS, Theorem 3.1]. We also show that ...
Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.
Singularity of Random Matrices over Finite Fields     Singularity of Random Matrices  Finite Fields       font style='font-size:12px;'> 2011/1/20
Let A be an n×n random matrix with iid entries over a finite field of order q. Suppose that the entries do not take values in any additive coset of the field with probability greater than 1 − ...
In this article we study the 2-distributions in Rn satisfying everywhere the Goursat condition. We give the normal form at a neighborhood of a point where the small growth vector has a singularity of ...

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