High speed liquid chromatography with small bore columns

Using a specially designed column system, we have systematically investigated the effect of mobile phase velocity on column efficiency. The performance of small bore columns operated at different linear velocities of mobile phase was examined for three different types of injection system. Using the value of H^∞/u or n^∞/t${}_{\text{r}}^{\text{º}}$ as a criterion of a high speed separation, we calculated values of n/t${}_{\text{r}}^{\text{º}}$ for different solutes according to the equation \documentclass{article}\pagestyle{empty}\begin{document}$ {{\rm n}\mathord{\left/ {\vphantom {{\rm n} {{\rm t}_{\rm r}^ \circ }}}\right. \kern-\nulldelimiterspace} {{\rm t}_{\rm r}^ \circ }} = {{{\rm n}^\infty } \mathord{\left/ {\vphantom {{{\rm n}^\infty } {{\rm t}_{\rm r}^ \circ }}} \right. \kern-\nulldelimiterspace} {{\rm t}_{\rm r}^ \circ }}\left({\frac{{1 + {\rm k'}}}{{{\rm k' + }\beta }}} \right)^2 $\end{document}; the results obtained are in agreement with the experimentally determined values. These systematic investigations culminated in the separation of seven compounds in less than 10 s; the respective chromatogram is shown.     

Existence analysis of an optimal shape design problem with non coercive state equation

In this paper, a shape optimization problem, modelling a welding process, governed by a second order non coercive PDE is considered. The well posedness of the shape optimal design problem is showed using the degree of Leray–Schauder. Then the existence of an optimal solution is proved.     

Boundary problems for fractional differential equations

In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.     

Existence and boundary behavior of solutions of Hessian equations with singular right-hand sides

In this paper, we establish the existence of viscosity solutions of Hessian equations with singular right-hand sides and obtain the asymptotic boundary behavior of solutions. The asymptotic results generalize those for Poisson equations and Monge-Ampère equations, and are more precise than obtained from Hopf lemma.     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

Well-posedness of an evolution problem with nonlocal diffusion

We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.     

我国渔业企业经济效益分析研究——以2013年我国上市渔业公司数据为例

随着居民收入水平的提高,我国水产品消费数量不断增加.水产品消费需求的增加,一方面导致水产品养殖企业数量增多,水产品养殖产业初具规模;另一方面也导致了市场竞争压力的增大,使得水产品养殖企业经济效益降低.利用2013年我国上市渔业公司财务数据,基于因子分析法研究了我国上市渔业公司经济效益水平.研究结果显示,2013年大湖股份、国联水产各公共因子及综合因子得分都较高,表明其公司盈利能力、偿债能力及运营能力较强,企业后期发展前景较好.而好当家、武昌鱼的综合因子得分较低,需要引起公司重视.最后针对2013年我国上市渔业公司的整体得分情况,提出了提高我国渔业企业经济效益水平的建议.