实Clifford分析中一类高阶奇异积分的计算公式

讨论了实Clifford分析中的一类高阶奇异积分,给出了这类高阶奇异积分的递推公式,计算公式.从而使实Clifford分析理论得以拓展.     

EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.     

Synthesis and structure of anhydrous complexes of magnesium(II) with β-ketoesters of higher alcohols

Methods for the synthesis of anhydrous complexes of magnesium(II) with β-ketoesters of higher alcohols have been developed. A number of novel magnesium complexes of the general formula MgL₂ (where HL is hexyl-, dodecyl-, tert-butyl-, cyclohexyl-, bornyl- and 1-adamantyl acetoacetate), which are readily soluble in organic media, have been synthesized. It has been found by X-ray crystallography that bis(1-adamantyl acetoacetato)magnesium(II) has a trimeric structure. The structure of the complexes in solutions is discussed.     

High throughput study of phase inversion parameters for polyimide-based SRNF membranes

High throughput (HT) techniques were applied for the first time for a detailed study of parameters involved in a phase inversion process. The synthesis of integrally skinned asymmetric polyimide (Matrimid^®) membranes was investigated. In spite of being one of the most important materials of reference in solvent resistant nanofiltration (SRNF), a detailed study of the phase inversion parameters for this system is still missing. Phase inversion parameters were selected both on the level of the composition of the casting solution (polymer concentration, solvent type, co-solvent/solvent weight ratio, non-solvent content) as on the level of the post-casting (evaporation time) and immersion (composition coagulation medium) conditions. The study of this extensive parameter space was conducted in a HT-fashion, in which the entire membrane preparation and testing process was miniaturized, parallellized and automated. Thanks to the availability of reliable HT techniques at all levels (i.e. preparation of polymer solutions, membrane casting and membrane testing), 145 membranes were prepared and tested (in triplicate) in the separation of the dye rose Bengal from 2-propanol within a time frame of a few months, meaning a dramatic improvement in time- and cost-efficiency. An attempt was made to link the SRNF performances of the prepared membranes and their SEM-observed morphologies more fundamentally to the phase inversion parameters through the use of Hansen solubility parameters and viscosity measurements.     

Higher order duality for a new class of nonconvex semi-infinite multiobjective fractional programming with support functions

In the paper, a new class of semi-infinite multiobjective fractional programming problems with support functions in the objective and constraint functions is considered. For such vector optimization problems, higher order dual problems in the sense of Mond-Weir and Schaible are defined. Then, various duality results between the considered multiobjective fractional semi-infinite programming problem and its higher order dual problems mentioned above are established under assumptions that the involved functions are higher order $\left(\Phi,\rho,\sigma^{\alpha}\right)$-type I functions. The results established in the paper generalize several similar results previously established in the literature.     

一类收敛的线性Hermite重心权有理插值

众所周知, Hermite有理插值比Hermite多项式插值具有更好的逼近性, 特别是对于插值点序列较大时, 但很难解决收敛性问题和控制实极点的出现. 本文建立了一类线性Hermite重心有理插值函数$r(x)$,并证明其具有以下优良性质: 第一, 在实数范围内无极点; 第二, 当$k=0,1,2$时,无论插值节点如何分布, 函数$r^{(k)}(x)$具有$O(h^{3d+3-k})$的收敛速度; 第三, 插值函数$r(x)$仅仅线性依赖于插值数据.     

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Let p_M(t,x,y) be the minimal heat kernel of a d-dimenional compact Riemannian manifold M for any time t\in(0,1] and x,y\in M. Using the horizontal Brown bridge on M, we prove that, for any nonnegative integers n and m, there is a constant C depending on n,m and the manifold M, such that |\nabla^n_x\nabla^m_y\ln p_M(t,x,y)|\leq C[d(x,y)/t+1/\sqrt{t}\,]^{n+m}$, which generalizes the conclusion of the higher derivatives of the logarithmic heat kernel \ln p_M(t,x,y) about single variable in \ncite{1}.     

New lower bounds for t‐coverings

Fisher proved in 1940 that any 2‐ design with has at least v blocks. In 1975, Ray‐Chaudhuri and Wilson generalized this result by showing that every t‐ design with has at least blocks. By combining methods used by Bose and Wilson in proofs of these results, we obtain new lower bounds on the size of t‐ coverings. Our results generalize lower bounds on the size of 2‐ coverings recently obtained by the first author.