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Mathematical tools are developed for describing low-dimensional projec- tions of high-dimensional data. Theorems are given to show that under suitable conditions, most projections are approximatel...
Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plaus...
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christ...
Let $\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\R^d$. We study the Markov chain $\{X_n^x\}_{n=0}^\8$ on $\R^d$ defined by the recursion $X_n^x = \Phi_n(X^x_{n-1})$, $n\ge 0$, $X_0=x\in\...
In this note we give a derivation of the asymptotic main term for the q-Gamma function as q approaching 1. This formula is valid on all the complex plan except at the poles of the Euler Gamma function...
We construct a family of measures on $\bbR$ that are purely singular with respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics in the bulk. The measures are best described v...
Starting from microscopic interaction rules we derive kinetic models of Fokker–Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the correspondin...

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