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For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k  D) whose entries are i.i.d. samples of ...
Following the steps of Spanish Mathematical Analysis:From Cauchy to Weierstrass between 1880 and 1914.
We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equati...
Suppose that an $n$-dimensional Cauchy problem \frac{dx}{dt}=f(t,x,\mu) (t \in I, \mu \in M), x(t_0)=x^0 satisfies the conditions that guarantee existence, uniqueness and continuous dependence of solu...
We prove a quantum ergodic restriction theorem for the Cauchy data of a sequence of quantum ergodic eigenfunctions on a hypersurface $H$ of a Riemannian manifold $(M, g)$. The technique of proof is to...
This paper deals with a Cauchy problem for the Helmholtz equa- tion in multiple dimensions.We want to obtain the solution u on the boundary z = 0 from the given function g ontheside z = 1. This proble...
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
本文初步总结了Cauchy不等式的多种形式(有限和、级数、积分形式等),给出了Cauchy不等式与内积空间里的Cauchy-Schwarz不等式的一些关系,最后论述Cauchy不等式的整体性质.
Abstract: The Pareto distribution is a basic probability distribution which shows power-law behaviour and has various kinds of applications. In this paper, we introduce a class of probability measures...
Abstract: In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $(2 + 1)$--dimensional analog of the KdV equation integrable by the method of inver...
Abstract: We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in Comm. Ma...
Abstract: We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface of a smooth manifold, and a symmetric tensor $W$ on this hypersurface, $g$ can be locally extended to a...
Abstract: We discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakov...
针对Helmholtz方程Cauchy问题提出一种数值计算方法。借助于DirichlettoNeumann映射,将Cauchy问题转化为求解散射场初值的紧算子方程。先讨论紧算子奇异值的渐近性质,然后将投影法与Tikhonov正则化方法相结合,提出一种求解相应紧算子方程的带有正则化技巧的投影法,并通过数值实验验证了算法的有效性。

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