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The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
Recent Progress on de Finetti's Notions of Exchangeability.
In this paper we describe our current research in the theory of partial di erential equations in conformal geometry. We introduce a bubble tree structure to study the degeneration of a class of Yamabe...
Abstract: Let $N(5,D_5,X)$ be the number of quintic number fields whose Galois closure has Galois group $D_5$ and whose discriminant is bounded by $X$. By a conjecture of Malle, we expect that $N(5,D_...
We survey some of the state of the art regarding singu-larities in Lagrangian mean curvature ow. Some open problems are suggested at the end.
In this paper, the TOPSIS method is used for two times t and t + 1. In order to calculate the progress or regress via Malmquist index, the positive and negative ideal and negative ideals at time t and...
In this short survey paper, we discuss certain recent results in classical gravity. Our main attention is restricted to two topics: the positive mass conjecture and its extensions to the case with ho...

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