Geometric character of domain and the Harnack inequality of solution of a singular parabolic equation

The geometric character of domains of solutions of a singular parabolic equation with the Neumann boundary condition are discussed in this work. We prove a gradient estimate and a Harnack type inequality and then, show that the domains of the solutions are exactly columns in the space-time. Specially, the altitudes of the columns are calculated accurately.     

拟线性退化抛物方程Cauchy问题的解

对来自金融数学领域的方程_xxu+u_yu-_tu=c（x,y,t,u）,（x,y,t）∈Q_T=R²×[0,T)的Cauchy问题,给出了一种新的熵解的定义,得到了其适定性结果.可以证明所得到的解还是强解,即方程中所出现的各阶偏导数几乎处处连续.最后讨论了解的爆破性质以及与解的间断点相关的几何性质.     

一类抛物方程组解的存在唯一性及关于耦合函数的连续依赖性

利用上、下解方法讨论了抛物方程组解的存在唯一性,并证明了解关于耦合函数的连续依赖性,同时给出了误差估计．     

A new extended dispersionless mKP hierarchy and hodograph solution

In this article, a new extended dispersionless mKP hierarchy (exdmKPH) is constructed to obtain two types of dispersionless mKP equations with self-consistent sources (dmKPSCS) and their associated conservation equations. Two reductions of this hierarchy are used to get two types of the corresponding dispersionless mKdV equations with self-consistent sources (dmKdVSCS). A hodograph solution for the first type of dmKdVSCS and Bäcklund transformation between the extended dispersionless KP hierarchy (exdKPH) and exdmKPH are also given.     

锥度量空间的若干拓扑性质

讨论锥度量空间的一些拓扑性质．主要讨论锥度量空间的邻域,开集和拓扑结构,以及锥度量空间中序列的收敛性．     

具脉冲效应的非自治随机干扰的捕食-食饵系统的研究

建立一个具有脉冲效应的非自治随机的比例依赖的捕食-食饵模型,通过研究具有脉冲效应的非自治随机系统与无脉冲效应的非自治随机系统的等价性,证明该模型的有界性,均值一致有界和灭绝性等动力学性质.     

Tunable multiwavelength erbium-doped fiber laser based on intensity-dependent loss and intra-cavity loss modulation

A tunable multiwavelength erbium-doped fiber laser is proposed and experimentally studied. The intensity-dependent loss (IDL) in a nonlinear optical loop mirror is utilized for stable multiwavelength lasing output. The accurate switch operation, i.e., the lasing lines emerge/disappear one by one at the longer wavelength side of the initial one, is achieved by adjusting the intra-cavity loss using a variable attenuator. The effect of the intra-cavity loss on the lasing characteristics is theoretically analyzed. Numerical results confirm the experiment measurements and suggest that both the IDL and the gain spectrum, which vary with the intra-cavity loss, lead to the observed tunable lasing behavior.     

高速逆流色谱法分离制备中药诃子中的没食子酸

利用高速逆流色谱法从100 mg诃子醇提物中一次性分离制备得到8.6 mg没食子酸。通过分析型高速逆流色谱对5种溶剂系统进行筛选,确定以正己烷-乙酸乙酯-甲醇-水(体积比为1:5:1:5)为两相溶剂体系并放大到制备型上,以上相为固定相,下相为流动相,在主机转速850 r/min、流动相流速2 mL/min、检测波长254 nm的条件下进行分离制备,获得4个分离峰(组分Ⅰ、Ⅱ、Ⅲ、Ⅳ)。经高效液相色谱检测,按照面积归一法计算,其中组分Ⅲ的纯度达96.40%。经电喷雾电离质谱分析,并结合与没食子酸标准品的高效液相色谱测定结果的对比,确定组分Ⅲ为没食子酸。该方法简便、快速、重复性好,适合于诃子中没食子酸的分离制备。     

Inhibition of α/β-K6P2W18O62·10H2O on the Activity of Mushroom Tyrosinase and Its Antimicrobial Effects

Dawson-type phosphotungstic polyoxometalate α/β-K₆P₂W₁₈O₆₂·10H₂O(P₂W₁₈) was synthesized and its inhibitory effect on the mushroom tyrosinase was investigated. It could inhibit diphenolase activity of mushroom tyrosinase as an irreversible inhibitor. When the concentration of the enzyme reached 0.0176 mg/mL, the concentration of P₂W₁₈ leading to 50% activity lost(IC₅₀) was 0.05 mmol/L for monophenolase and 0.64 mmol/L for diphenolase. In addition, the antimicrobial activity of P₂W₁₈ was evaluated by zone of inhibition test. The results show that P₂W₁₈ possesses effective antimicrobial ability against Escherichia coli, Bacillus subtilis, yeast, especially Escherichia coli and yeast.     

Electric potential distribution near nanocone arrays on metal substrates

Based on the nanostructured surface model,where conical nanoparticle arrays grow out symmetrically from a plane metal substrate,a theoretical model of the local electric potential near nanocones is built when a uniform external electric field is applied.In terms of this model,the electric potential distribution near the nanocone arrays is obtained and given by a curved surface using a numerical computation method.The computational results show that the electric potential distribution near the nanocone arrays exhibit an obvious geometrical symmetry.These results could serve as a basis for explaining many abnormal phenomena,such as the abnormal infrared effects(AIREs) which are found on nanostructured metal surfaces,as well as a reference for investigating the applications of nanomaterials,such as nanoelectrodes and nanosensors.