含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*

在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|²dx) Δu + λV (x)u = μf(x)|u|^q?2u + |u|^p?2u, x ∈ R³,u ∈ H¹(R³),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到.     

The structure characteristics of photoproducts of indolinospirooxazines

Photochromic reactions of four indolinospirooxazine derivatives have been studied using nanosecond laser flash photolysis techniques. Photolysis of the four compounds in acetonitrile and in cyclohexane all leads to the formation of the short-lived CT intermediates as the predominant photoproducts. In certain circumstances few photomerocyanines (PMC) can be observed. From the absorption bands and the lifetimes of CT intermediates, it has been speculated that the substituents at the nitrogen atom of the indole ring influence the structural characteristics of CT intermediates mainly through steric hindrance effects, whereas the substituents at the 5 position of the indoline ring influence mainly through electron effects. A potential energy surface model is established to explain the results.     

“限时服务规则”下的复线船闸多目标调度优化

针对现有船舶过闸排队规则的欠缺,基于“限时服务规则”,构建复线船闸多目标双层优化调度模型:上层模型用于获得两个闸室安全区域的船舶排布可行方案;下层模型用于获得不同船舶排布可行方案的优化闸次数。下层模型分两个阶段完成:对符合“限时服务规则”的船舶,构建以闸次最少为目标的0-1规划模型,获得此类船舶安排的闸次;对其余船舶按照“先到先服务规则”,构建以闸次最少、闸室利用率最大为目标的多目标决策模型,获得不同船舶排布可行方案应该安排的频次。以位于江苏省干线航道上的某复线船闸某日24小时内过闸船舶的数据为例,计算结果表明:采用本文优化模型获得的优化方案与“经验编排方式”相比,两座船闸各节约2个闸次,两个船闸的平均闸室利用率分别提高了3.66和4.72个百分点。     

On bandwidth sums of graphs

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Electropolymerized m-phenylenediamine as a means to immobilize active protein on thickness-shear-mode quartz crystal

Electropolymerized m-phenylenediamine was used as an active coating for immobilizing urease and lectin on a gold-plated thickness-shear-mode (TSM) crystal. To enhance effectiveness of immobilization. a bilayer polymer film composed of polyaniline and poly-m-phenylenediamine was proposed. Compared with single poly-m-phenylenediamine film, the bilayer polymer film gave better results in terms of immobilizing capacity, stability and reproductivity. On this bilayer-film-coated TSM quartz crystal, the amount of immobilized lectin was estimated about 1.8 mug/cm(2). Detection of purified human erythrocytes is demonstrated as an example of potential application of this lectin-modified TSM biosensor in clinic.     

Local error estimates for radial basis function interpolation of scattered data

Introducing a suitable variational formulation for the localerror of scattered data interpolation by radial basis functions(r), the error can be bounded by a term depending on the Fouriertransform of the interpolated function f and a certain ‘Krigingfunction’, which allows a formulation as an integral involvingthe Fourier transform of . The explicit construction of locallywell-behaving admissible coefficient vectors makes the Krigingfunction bounded by some power of the local density h of datapoints. This leads to error estimates for interpolation of functionsf whose Fourier transform f is ‘dominated’ by thenonnegative Fourier transform of (x) = (||x||) in the sense . Approximation orders are arbitrarily high for interpolationwith Hardy multiquadrics, inverse multiquadrics and Gaussiankernels. This was also proven in recent papers by Madych andNelson, using a reproducing kernel Hilbert space approach andrequiring the same hypothesis as above on f, which limits thepractical applicability of the results. This work uses a differentand simpler analytic technique and allows to handle the casesof interpolation with (r) = r^s for s R, s > 1, s 2N, and(r) = r^s log r for s 2N, which are shown to have accuracy O(h^s/2)     

含吲哚核端基多甲川菁染料的合成及性能

我们曾合成了具有桥环的硫三碳菁及多甲川苯乙烯菁,并测定了光学性能。本文报道吲哚环为端基的桥链三碳菁和四甲川苯乙烯菁的合成及在有机溶剂中电子吸收光谱及溶解性能的测定。所用仪器同前,7种多甲川菁染料的合成反应如下:     

Self-assembly of highly oriented one-dimensional h-WO3 nanostructures

A new self-assembled and highly oriented one-dimensional single-crystal nanostructure of WO3 with hexagonal form was successfully prepared by a mild, solution-based colloidal approach.