The destabilizing effect of boundary slip on Bénard convection

We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev‐tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Ⅱ型三角剖分上二次双周期样条

本文用B-网方法确定了△_(nm)~((2))剖分上二次双周期样条函数空间的维数,给出了插值条件的几种提法,证明了解的存在唯一性.     

Hydrogen peroxide promoted hydroxylation of haloarenes and heteroarenes

Addition of aqueous hydrogen peroxide significantly accelerates the substitution reactions of hydroxide salts with haloarenes bearing electron withdrawing substituents. A similar effect is observed in the reactions of hydroxide salts with halogenated heteroarenes. Reactions are carried out in water or water-THF at ambient temperature or at 50-60 °C.     

A note on minimum degree conditions for supereulerian graphs

A graph is called supereulerian if it has a spanning closed trail. Let G be a 2-edge-connected graph of order n such that each minimal edge cut SE(G) with |S|3 satisfies the property that each component of G−S has order at least (n−2)/5. We prove that either G is supereulerian or G belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore, our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree δ4: If G is a 2-edge-connected graph of order n with δ(G)4 such that for every edge xyE(G) , we have max{d(x),d(y)}(n−2)/5−1, then either G is supereulerian or G belongs to one of two classes of exceptional graphs. We show that the condition δ(G)4 cannot be relaxed.     

非光滑非凸多目标规划解的充分条件

Kuhn-Tucker型条件的充分性一直是最优化理论中引人注意的一个问题.本文对非光滑函数提出了几个非凸概念,然后,讨论了非光滑非凸多目标规划中Kuhn-Tucker型条件和Fritz John型条件的充分性,在很弱的条件下,建立了一系列充分条件.     

Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions

In this paper we consider an initial boundary value problem for a reaction-diffusion equation under nonlinear and nonlocal Robin type boundary condition. Assuming the existence of an ordered pair of upper and lower solutions we establish a generalized quasilinearization method for the problem under consideration whose characteristic feature consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic. Thus this method provides an efficient iteration technique that produces not only improved approximations due to the monotonicity of its iterates, but yields also a measure of the convergence rate.     

满足Solow条件的矩阵的性质

讨论了满足 Solow条件矩阵的几个性质 ,并给出了与此相关的经济意义 .     

具P-Laplacian算子型周期边值问题解的存在性

本文利用拓扑度理论和一些分析技巧讨论了具p—Laplacian算子型周期边值问题(φp(χ’))’+d/dt gradF(χ)+gradG(χ)=e(t),χ(0)=χ(T),χ’(0)=χ’(T)解的存在性,在对阻尼项d/dtgradF(χ)没有任何限制的前提下,给出了解存在的充分条件.     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

Lithium heptadecafluorooctanesulfonate catalyzed Mannich-type and aza-Diels-Alder reactions in supercritical carbon dioxide

The Mannich-type reaction of imines with (1-methoxy-2-methylpropenyloxy)trimethylsilane and aza-Diels-Alder reaction of imines with Danishefsky's diene can be carried out in scCO₂ in the presence of lithium heptadecafluorooctanesulfonate which offer a way to synthesize β-amino carbonyl compounds and nitrogen-containing six-membered ring compounds under environmentally benign conditions.