We propose a new finite difference MAC scheme based on the staggered mesh for the compressible Navier-Stokes equations. The scheme is designed for both Dirichlet and periodic boundary conditions. The key features are the application of upwind flux and artificial diffusion. We show that the scheme is energy stable and convergent to the dissipative measure-valued solution of the system. Using the argument of weak-strong uniqueness [E.Feireisl, P.Gwiazda, A.Swierczewska-Gwiazda, and E.Wiedemann. Dissipative measure-valued solutions to the compressible Navier-Stokes system.

Fourier restriction estimate is one of the core topics in harmonic analysis. The Fourier restriction conjecture posed by Stein in 1960s is still open today. In this talk I will give a survey on the various types of the restriction estimates and their applications to PDEs.

In this report we study two-sample functional linear regression with a scaling transformation of regression functions. We consider estimation for the intercept, the slope function and the scalar parameter based on the functional principal component analysis. We also establish the rates of convergence for the estimator of the slope function, which is shown to be optimal in a minimax sense under certain smoothness assumptions. We further investigate semiparametric efficiency for the estimation of the scalar parameter and hypothesis testing.

Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of works on SGD, much less is known about the statistical inferential properties of predictions based on SGD solutions. In this talk, we introduce a novel procedure termedHiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with the vanilla SGD. The HiGrad procedure begins by performing SGD iterations for a while and then split the single thread into a few, and this procedure hierarchically operates in this fashion along each thread. With predictions provided by multiple threads in place, a t-based confidence interval is constructed by decorrelating predictions using covariance structures given by the Ruppert–Polyak averaging scheme.

The Mullineux conjecture is about computing the p-regular partition associated with the tensor product of an irreducible representation of a symmetric group with the sign representation. Since being formulated in 1979, the conjecture attracted a lot of attention and was not settled until 1997 when B. Ford and A. Kleshchev first proved it in a paper over a hundred pages. The proof was soon been shorten and, at the same time, its quantum version was also settled. The main ingredient of the proof is the modular branching rules.

In this talk, I will introduce an estimation methodology for a semiparametric quantile factor panel model. I will also talk about our proposed tools for inference that are robust to the existence of moments and to the form of weak cross-sectional dependence in the idiosyncratic error term. Specifically, we use sieve techniques to obtain preliminary estimators of the nonparametric beta functions, and use these to estimate the factor return vector at each time period. We then update the loading functions and factor returns sequentially.

题目：关于弦弧曲线的若干问题报告人：沈玉良 教授（苏州大学必赢国际bwin登录）时间：2018年7月6日（周五）下午14：30-15:30地点：宁静楼104室欢迎广大师生参加

Ramsey theory dates back to the 1930's and computing Ramsey numbers is a notoriously difficult problem in combinatorics. We study Ramsey numbers of graphs in Gallai colorings, where a Gallai coloring is a coloring of the edges of a complete graph such that no triangle has all its edges colored differently. Given an integer $k/ge1$ and ``forbidden" graphs $H_1, /ldots, H_k$, the Gallai-Ramsey number $GR(H_1, /ldots, H_k)$ is the least integer $n$ such that every Gallai coloring of the complete graph $K_n$ using $k$ colors contains a monochromatic copy of $H_i$ in color $i$ for some $i /in /{1, /ldots, k/}$. Gallai-Ramsey numbers are more well-behaved, though computing them is far from trivial.