一类具p-Laplacian算子三阶m点边值问题的三个正解

考察了一类具p-Laplacian算子三阶m点边值问题的三个正解.首先利用二阶m点边值问题的Green函数把该类问题转化为一个等价的积分方程,在适当的锥上应用Avery-Peteron不动点定理讨论该类积分方程的正解存在性,从而得到了正解存在的充分条件.     

Novel β-cyclodextrin chiral stationary phases with different length spacers for normal-phase high performance liquid chromatography enantioseparation

Cyclodextrin and its derivatives are widely used as selectors of chiral stationary phases (CSPs) for high performance liquid chromatography (HPLC) due to their unique molecular structure and resolution capability. Three mono(6(A)-N-(ω-alkenylamino)-6(A)-deoxy)perphenylcarbamoylated β-cyclodextrin (PICD) based CSPs with different length spacers have been prepared, with their enantioseparation abilities evaluated with 10 model racemates including aromatic alcohols, flavanone compounds, amine and non-protolytic compounds under normal-phase conditions. The effect of spacer length and surface loading on the enantioseparation performance of CSPs is investigated herewith. The results indicate that higher surface loading 6C-PICD displays the best enantioselectivities towards selected racemates under normal-phase conditions.     

Unusual multi-step sequential Au(III)/Au(II) processes of gold(III) quinoxalinoporphyrins in acidic non-aqueous media

The electrochemistry of gold(III) mono- and bis-quinoxalinoporphyrins was examined in CH(2)Cl(2) or PhCN containing 0.1 M tetra-n-butylammonium perchlorate (TBAP) before and after the addition of trifluoroacetic acid to solution. The investigated porphyrins are represented as Au(PQ)PF(6) and Au(QPQ)PF(6), where P is the dianion of the 5,10,15,20-tetrakis(3,5-di-tert-butylphenyl)porphyrin and Q is a quinoxaline group fused to a β,β'-pyrrolic position of the porphyrin macrocycle; in Au(QPQ)PF(6) there is a linear arrangement where the quinoxalines are fused to pyrrolic positions that are opposite each other. The porphyrin without the fused quinoxaline groups, Au(P)PF(6), was also investigated under the same solution conditions. In the absence of acid, all three gold(III) porphyrins undergo a single reversible Au(III)/Au(II) process leading to the formation of a Au(II) porphyrin which can be further reduced at more negative potentials to give stepwise the Au(II) porphyrin π-anion radical and dianion, respectively. However, in the presence of acid, the initial Au(III)/Au(II) processes of Au(PQ)PF(6) and Au(QPQ)PF(6) are followed by an internal electron transfer and protonation to regenerate new Au(III) porphyrins assigned as Au(III)(PQH)(+) and Au(III)(QPQH)(+). Both protonated gold(III) quinoxalinoporphyrins then undergo a second Au(III)/Au(II) process at more negative potentials. The electrogenerated monoprotonated monoquinoxalinoporphyrin, Au(II)(PQH), is then further reduced to its π-anion radical and dianion forms, but this is not the case for the monoprotonated bis-quinoxalinoporphyrin, Au(II)(QPQH), which accepts a second proton and is rapidly converted to Au(III)(HQPQH)(+) before undergoing a third Au(III)/Au(II) process to produce Au(II)(HQPQH) as a final product. Thus, Au(P)PF(6) undergoes one metal-centered reduction while Au(PQ)PF(6) and Au(QPQ)PF(6) exhibit two and three Au(III)/Au(II) processes, respectively. These unusual multistep sequential Au(III)/Au(II) processes were monitored by thin-layer spectroelectrochemistry and a reduction/oxidation mechanism for Au(PQ)PF(6) and Au(QPQ)PF(6) in acidic media is proposed.     

Dithienothiophene (DTT)-based dyes for dye-sensitized solar cells: synthesis of 2,6-dibromo-DTT

A one-pot synthesis of 2,6-dibromodithieno[3,2-b;2',3'-d]thiophene (dibromo-DTT, 4) was developed. A key step was bromodecarboxylation of DTT-2,6-dicarboxylic acid, obtained by saponification of the diester 1. The donor-acceptor dye DAHTDTT (13), based on a central 2,6-bis[2'-(3'-hexylthienyl)]dithieno[3,2-b;2',3'-d]thiophene core (9), was prepared and incorporated in a dye-sensitized solar cell (DSC), which exhibited an energy conversion efficiency of 7.3% with V(oc) of 697 mV, J(sc) of 14.4 mA/cm(2), and ff of 0.73 at 1 sun.     

Selective supramolecular assembly of multifunctional ligands on a Cu(111) surface: metallacycles, propeller trimers and linear chains

We studied the supramolecular assembly of a multifunctional ligand, cis-bis-terpyridine tetraphenyl ethylene, on a Cu(111) surface by low-temperature scanning tunneling microscopy (STM). Three distinctive supramolecular structures, metallacycles, propeller-shaped clusters and extended linear chains, are formed under specific assembly conditions owing to different inter-molecular binding modes of Cu-coordination, van der Waals interaction and hydrogen bonding, respectively.     

Hopf and Bogdanov�CTakens bifurcations in a coupled FitzHugh�CNagumo neural system with delay

In this paper, Hopf bifurcation and Bogdanov?CTakens bifurcation with codimension 2 in a coupled FitzHugh?CNagumo neural system with gap junction are investigated. At first, a general bifurcation diagram on the plane of coupling strength and delay is derived. Then, explicit algorithms due to Hassard and Faria are applied to determine the normal forms of Hopf and Bogdanov?CTakens bifurcations, respectively. Next, we analyze the codimension-2 unfolding for Bogdanov?CTakens bifurcation, and give complete bifurcation diagrams and phase portraits. Furthermore, we also consider the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. By the results of theoretical analysis, we obtain that the values of coupled strength, which make the transmission and received signals be synchronous and anti-phase, are opposite. And universal unfolding of Bogdanov?CTakens bifurcation indicates that the neuron signals can transit between resting and spiking.     

Bifurcations and spatiotemporal patterns in a ratio‐dependent diffusive Holling‐Tanner system with time delay

In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics.     

基于超疏水高黏附结构的痕量农药分子现场检测SERS基底研究

多种农药,包括孔雀石绿（MG）作为禁用兽药,存在食用致癌的风险。由于MG低廉的价格和极好的药效,在渔业养殖中一直被不法商贩非法使用,使得鱼类生鲜中时有MG残留检出。针对MG分子痕量残留的检测,目前一般是抽取少量养殖水样,再利用高效液相色谱柱、液相色谱-光谱等方法来评估其是否超标。这类传统的检测方法一般需要依赖价格昂贵的大型设备,且检测过程操作繁琐复杂,单次检测耗时长、价格高,因而与农贸市场中商品流通量大、速度快、价格需亲民低廉等特点和要求不相符合。近年来,表面增强拉曼散射（SERS）检测技术以及便携式拉曼光谱仪的出现,有望实现对痕量农药分子的现场快速检测,进而很好地解决这一问题。SERS检测技术利用金属纳米结构的表面等离激元效应感应位于其结构表面附近的分子,得到分子种类和浓度信息。为了降低可检测的浓度极限,一般会在SERS基底上利用咖啡环效应或其他手段将待测分子蒸发富集,以获得足够高的信号强度。针对亲水基底,液滴与基底相接触后,会在基底表面摊开,使其分布面积扩大,导致其咖啡环周长变长,分子分布浓度随之降低。而当采用疏水基底富集时,由于常规的疏水基底表面黏附性小,液滴在其表面处于随处滚动无法抓取的状态,极大增加了操作的难度。以MG分子痕量残留的检测为例,由于农贸市场人员众多、无专业实验平台,磕碰撞击时有发生,在此环境下采用疏水SERS基底对农药分子进行检测显然是不可取的。该研究提出一种基于超疏水高黏附纳米森林结构的SERS基底用于痕量MG分子的快速现场检测。相比于超疏水SERS基底,所提出的超疏水高黏附基底利用其高黏附性可牢固抓取待测液滴,解决了以往超疏水基底在实际现场检测中存在液滴滚动无法操作的问题。此外,与亲水基底相比,超疏水高黏附基底由于接触角大,可将咖啡环面积缩小5.73倍,继而使分子的富集浓度提高5.73倍,最终使检测极限浓度降低了至少两个数量级。研究所提出的超疏水高黏附SERS基底有望在痕量农药分子快速现场检测中得到应用。     

1.06μm连续激光辐照TiO_2/SiO_2/K_9薄膜元件温升规律研究

利用1.06μm连续激光在不同强度下辐照TiO2/SiO2/K9薄膜元件,实验中用红外热像仪测量激光辐照在TiO2/SiO2/K9元件表面引起的温升随时间的变化,通过数据处理,获得激光辐照区域最高温度随辐照时间的增加而增加。同时,给出材料温升随材料发射率的变化关系。并用程序模拟不同激光强度下薄膜温度场的分布,通过实验测量数据校正数值模拟计算结果,给出TiO2/SiO2/K9薄膜元件温度随激光辐照强度和辐照时间的变化规律。并且获得在薄膜厚度方向:薄膜表面温度最高,基底与薄膜接触处温度最低;沿径向:激光辐照中心温度最高,边沿温度最低。     

T—S模糊控制器中各类算子对系统输出的影响

模糊控制系统的核心是模糊控制算法，对Takagi-Sugeno（以下简称T—S）模糊控制器，由于其合取算子与汇总算子选取的不同，使其算法区别很大。文中对几种常用T-S模糊控制算法的输出曲面及误差曲面进行比较，以确定这些算子变化对系统输出的影响。