Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

ON THE EXISTENCE WITH EXPONENTIAL DECAY AND THE BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF SEMI-LINEAR CORNER-DEGENERATE PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.     

Comprehensive profiling and evaluation of the alteration of RNA modifications in thyroid carcinoma by liquid chromatography-tandem mass spectrometry

RNA molecules contain diverse modifications that display important functions in a variety of physiological and pathological processes. So far over 150 chemical modifications have been characterized to be present in various RNA species, such as in messenger RNA (mRNA), ribosomal RNA (rRNA), and transfer RNA (tRNA). Previous studies revealed that certain RNA modifications were correlated to specific human diseases, indicating RNA modifications could serve as the potential indicator of human diseases. However, systemic investigation of the alteration of RNA modifications in different RNA species of carcinoma tissues are still lacked. Herein, we carried out the comprehensive profiling and evaluation of the alteration of RNA modifications in thyroid carcinoma by liquid chromatography-tandem mass spectrometry (LC-ESI-MS/MS) analysis. The developed method allowed us to simultaneously detect 48 different types of RNA modifications. Using this method, we detected 10, 15, 14, and 25 modifications in mRNA, 18S rRNA, 28S rRNA and small RNA (< 200 nt), respectively. Compared to the normal tissues, we revealed a total of 14 RNA modification exhibited significant increase and 2 RNA modifications showed significant decrease in thyroid carcinoma tissues. Our study provided the first comprehensive profile as well as the alteration of modifications in different RNA species in thyroid carcinoma and matched tumor-adjacent normal tissues. The altered pattern RNA modifications may serve as the indicator of thyroid carcinoma. Moreover, this study may promote the in-depth understanding of the regulatory roles of RNA modifications in thyroid carcinoma.     

Portfolio Selection and Risk Control for an Insurer With Uncertain Time Horizon and Partial Information in an Anticipating Environment

Methodology and Computing in Applied Probability - This paper is devoted to the study of an optimal investment and risk control problem for an insurer. The risky asset process and the insurance...     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

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