Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

MOTION OF THE ECCENTRIC ELLIPSOID: GYROSCOPIC BALANCE CONDITION AND STABILITY

本文研究了摩擦系数 和偏心距离对偏心椭球体回转平衡的影响,得到了椭球极轴与地面法向夹角 的运动方程,导出了两类稳定解.结果表明摩擦力是椭球能否旋转至直立的必要条件,当 偏心距一定, 摩擦系数 越大其运动至直立所需的时间越短.偏心距阻碍直立现象的出现,摩擦系数 一定,偏心距 越大,其运动至直立所需的时间越长.当偏心距值增大到一定程度,其将无法直立而是至一稳定的角度,并且稳定角度正比于偏心距,偏心距继续增大,将不会出现回转平衡.     

Anisotropy Effects and Observational Data on the Constraints of Evolution Dark Energy Models

We investigate cosmological dark energy models where the accelerated expansion of the universe is driven by a field with an anisotropic universe. The constraints on the parameters are obtained by maximum likelihood analysis using observational of 194 Type Ia supernovae(SNIa) and the most recent joint light-curve analysis(JLA) sample. In particular we reconstruct the dark energy equation of state parameter w(z) and the deceleration parameter q(z). We find that the best fit dynamical w(z) obtained from the 194 SNIa dataset does not cross the phantom divide line w(z) =-1 and remains above and close to w(z)≈-0.92 line for the whole redshift range 0 ≤ z ≤ 1.75 showing no evidence for phantom behavior. By applying the anisotropy effect on the ΛCDM model, the joint analysis indicates that ?_(σ0)= 0.0163 ± 0.03,with 194 SNIa, ?_(σ0)=-0.0032 ± 0.032 with 238 the SiFTO sample of JLA and ?_(σ0)= 0.011 ± 0.0117 with 1048 the SALT2 sample of Pantheon at 1σ′confidence interval. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models with JLA SNe datasets. Furthermore, we use two statistical tests such as the usual χ_(min)~2/dof and p-test to compare two dark energy models with ΛCDM model. Finally we show that the presence of anisotropy is confirmed in mentioned models via SNIa dataset.     

基于深度约束的声速估算方法*

高精度的声速剖面数据是提高水下定位精度的关键。在无法精确获得声速剖面数据的情况下，该文提出了一种基于深度约束，同时根据浮标与水下目标的空间几何距离进行有效声速估算的方法。通过仿真模拟，将该文提出的方法与加权平均声速法、泰勒级数展开法和等效声速剖面法的定位结果进行对比分析。结果表明，新方法不需要依靠声速剖面数据，通过深度约束可有效地估算出声速值，其定位精度与等效声速结果相当，极大地提高了无声速剖面数据下的水下定位精度。     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Linear codes associated to skew-symmetric determinantal varieties

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.