Uniqueness of singular solution of semilinear elliptic equation

In this paper, we study asymptotic behavior of solution near 0 for a class of elliptic problem. The uniqueness of singular solution is established.     

纳米晶粒TiO2多孔微球的合成与表征

 钛酸四丁酯经酸性水解得到TiO2溶胶，将溶胶与苯酚混合后加入到正庚烷分散介质中，再滴加甲醛水溶液，通过反相悬浮聚合和溶胶－凝胶过程制备了聚合物与TiO2的复合微球．对复合微球进行焙烧处理，使聚合物分解，从而得到由纳米TiO2晶粒组成的多孔微球．以示差扫描量热法、热重分析、X射线衍射、扫描电子显微镜和氮吸附等方法对TiO2多孔微球的物理性质进行了表征．结果表明，所得TiO2多孔微球主要由锐钛型TiO2纳米晶粒组成，晶粒尺寸为20～30nm；TiO2多孔微球的直径为200～500μm，比表面积为87．40m2／g，平均孔径为8．65nm，孔径的分布具有单分散特征．     

Singularity of the Extremal Solution for Supercritical Biharmonic Equations with Power-Type Nonlinearity

Let B  R~n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ* 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r~(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .     

微波水解-液相色谱-原子荧光光谱法测定硒蛋白中的硒代氨基酸

针对酶解法测定硒代氨基酸操作复杂,时间长,水解不完全且水解产物不稳定等问题,建立一种微波水解-液相色谱-原子荧光光谱仪测定硒蛋白中硒代氨基酸的方法。样品经HCl(6 mol/L)微波水解后,调节pH值至7.5,采用阴离子色谱柱,pH=6.0的(NH_(4))_(2)HPO_(4)(40 mmol/L)溶液为流动相,流速0.6 mL/min,等度洗脱12 min的条件对硒代胱氨酸(SeCys_(2))、甲基-硒代半胱氨酸(MeSeCys)和硒代蛋氨酸(SeMet)进行分离,用原子荧光光谱仪测定其含量。微波水解条件采用星点设计-响应面法进行优化,优选最佳水解条件为:称样量20 mg,水解温度150℃,水解时间40 min。SeCys_(2)、MeSeCys和SeMet均在0~100 ng浓度范围内呈线性关系,相关系数均大于0.999,检出限分别为0.07、0.03和0.14 mg/kg,RSD分别为5.6%、4.6%、3.7%(n=6)。用来测定硒代氨基酸,耗时短,成本低,水解完全,操作简单,水解产物稳定,能够科学评价硒蛋白中硒代氨基酸的组成,对硒蛋白产品的质量控制和溯源提供了科学方法,值得推广应用。     

一个模拟趋化现象的广义双曲-抛物系统的光滑解的全局分析

考虑一个模拟趋化现象的广义双曲-抛物系统的Cauchy问题,当动能函数为非线性函数且初始值具有小的L~2能量但其H~2能量可能任意大时,得到了全局光滑解的存在性和渐近行为.这些结果推广了以前的关于动能函数为线性函数或初始值具有小的H~2能量情形下的相关结果,首次获得了关于全局光滑大解方面的结果.这些结果的证明基于构造一个新的非负凸熵和做精细的能量估计.     

Local L2 theory of the fractional Navier-Stokes equations and the self-similar solution

This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L² theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time as well as global-in-time local energy weak solutions to the hypo-dissipative Navier-Stokes system is proved.In particular, in order to construct a pressure with an explicit representation, some technical innovations are required due to the lack of known results on the loc...     

Saddle solutions of nonlinear elliptic equations involving the p-Laplacian

We prove the existence of saddle solutions of nonlinear elliptic equation involving the p-Laplacian