Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation

We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method.     

POINTWISE ESTIMATES OF SOLUTIONS TO CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS＊＊＊

This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp pointwise estimates of the solutions on domam under consideration. Specially, the estimate is precise near each characteristic direction.     

Existence and stability of planar diffusion waves for 2-D Euler equations with damping

To study the non-linear stability of a non-trivial profile for a multi-dimensional systems of gas dynamics, the combination of the Green function on estimating the lower order derivatives and the energy method for the higher order derivatives is shown to be not only useful but sometimes maybe also essential. In this paper, we study the stability of a planar diffusion wave for the isentropic Euler equations with damping in two-dimensional space. By introducing an approximate Green function for the linearized equations around the planar diffusion wave and by applying the energy method, we prove the global existence and the L₂ convergence rate of the solution when the initial data is a small perturbation of the planar diffusion wave. The decay rates of the perturbation and its lower order spatial derivatives obtained are optimal in the L₂ norm. Furthermore, the constructed approximate Green function in this paper can be used for the pointwise and the Lp estimates of the solutions concerned. In fact, the approach by combining of the Green function and energy method can be applied to other system especially when the derivatives of the coefficients in the system have certain time decay properties.     

分析保护剂补偿基质效应-气相色谱-质谱法快速测定水果中40种农药残留

建立了水果中40种农药化合物的气相色谱-质谱(GC-MS)多残留检测方法,评价了添加分析保护剂对农药残留分析的补偿基质效应和对定量结果可靠性的影响。采用可以溶于丙酮有机溶剂的聚乙二醇Polyethylene Glycol 400(PEG 400)和橄榄油作为保护剂组合进行定量分析。水果样品采用乙腈提取,微型固相萃取小柱净化,大体积进样,GC-MS选择离子监测(SIM)模式检测。40种农药化合物在1～200 μg/L范围内线性关系良好,线性相关系数在0.99以上,检出限(以信噪比为3计)为0.1～3.0 μg/L。除乐果外,其他化合物的添加回收率为75%～119%,相对标准偏差均小于16.6%。通过对添加分析保护剂的校准曲线与基质匹配校准曲线的定量准确性的比较,发现加入分析保护剂方法可以代替基质匹配校正方法,同时采用大体积进样和微型固相萃取净化相结合的方法,大大减少了样品前处理量。将所建立的分析保护剂方法用于苹果、桃子、橙子、香蕉和葡萄等水果样品的分析,基质补偿效应良好,有效地克服了水溶性分析保护剂对气相色谱分析有影响的缺点。     

Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds*

In this paper, the authors establish a generalized maximum principle for pseudoHermitian manifolds. As corollaries, Omori-Yau type maximum principles for pseudoHermitian manifolds are deduced. Moreover, they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles. Finally, they give some applications of these generalized maximum principles.     

Large-time behavior for the solution to the generalized Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space

In this paper, we consider the global existence as well as the optimal decay estimates of the Cauchy problem for the multi-dimensional Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space. And these results are obtained by Green?s function method, Fourier analysis method, energy estimates method combined with the time-frequency decomposition method.     

An efficient synthesis of 3-arylmethyl-7,8-dihydro-6H-chromene-2,5-diones from Baylis–Hillman adduct acetates under solvent-free conditions

A simple, efficient synthesis of 3-arylmethyl-7,8-dihydro-6H-chromene-2,5-dione 4 from Baylis–Hillman adduct acetates derived from aromatic aldehydes and cyclohexane-1,3-diones under solvent-free conditions is described. Interestingly, when Baylis–Hillman adducts derived from aliphatic aldehydes were tested under the similar conditions, the unexpected stereoisomers 5 and 6 were obtained in moderate yields. A plausible mechanism for the formation of 4–6 is proposed.     

The pointwise estimate of solutions to the parabolic conservation law in multi-dimensions

In this paper we consider the parabolic conservation law with large initial data which has a big perturbation. Using the method of Green function, we first obtain the decay rates of the derivatives of the solutions in L ² and L ^∞ spaces, and then the pointwise estimate of the solutions.