Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

A New Cohomology Theory of Orbifold

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation     

DIFFUSION-DRIVEN INSTABILITY IN THE GIERER-MEINHARDT MODEL OF MORPHOGENESIS

In this paper, we consider the Gierer-Meinhardt model of morphogenesis. It is shown that the homogeneous equilibrium solution and the homogeneous periodic solution become diffusively unstable if the diffusion coefficients of the two substances are chosen suitably.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

Hamiltonian formulation of generalized quantum dynamics

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations. Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.     

八配位钇(Ⅲ)-反式-1,2-环己二胺四乙酸配合物NH4[Y(trans-CYDTA)(H2O)2]·4.5H2O的合成及分子结构

In this paper, the molecular and crystal structures of the NH₄[Y(trans CYDTA)(H₂O)₂]·4.5 H₂O(trans-CYDTA=trans 1,2-cyclohexanediaminetetraacetic acid) are reported. The crystal data are as follows: Triclinic system, P1space group,a=0.8599(6)nm,b=1.0021(7)nm,c=1.4370(9)nm,α =88.095(13)°,β =75.559(1)°,γ =88.344(12)°,V=1.1981(14)nm³,Z=2, M=708.68,D_c=1.570g· cm^-3, μ =2.506mm^-1 and F(000)=590. The final R₁ and wR₂ are 0.0571 and 0.1350 for 4205 [I >2.0σ (I)] unique reflections and 0.1007 and 0.1615 for all 4981 reflections, respectively. In the title complex, the anion [Y(trans-CYDTA)(H₂O)₂]^- has an eight coordination structure with distorted square antiprism. The trans CYDTA which acts as a hexadentate ligand with four Oatoms and two Natoms and two H₂O molecules directly coordinate to central metal Y(Ⅲ) ion. It can be known that the Y(Ⅲ) ion can form an eight coordinate compound with aminopolycarboxylic acid ligands in addition nine coordination structure.     

Fabrication of highly ordered TiO2 nanotube arrays using an organic electrolyte

Anodization of titanium in a fluorinated dimethyl sulfoxide (DMSO) and ethanol mixture electrolyte is investigated. The prepared anodic film has a highly ordered nanotube-array surface architecture. Using a 20 V anodization potential (vs Pt) nanotube arrays having an inner diameter of 60 nm and 40 nm wall thickness are formed. The overall length of the nanotube arrays is controlled by the duration of the anodization, with nanotubes appearing only after approximately 48 h; a 72 h anodization results in a nanotube array approximately 2.3 mum in length. The photoelectrochemical response of the nanotube-array photoelectrodes is studied using a 1 M KOH solution under both UV and visible (AM 1.5) illumination. Enhanced photocurrent density is observed for samples obtained in the organic electrolyte, with an UV photoconversion efficiency of 10.7%.     

桑蚕丝素蛋白初始结构对其矿化作用的影响

以碱金属离子诱导桑蚕丝素蛋白溶液发生构象转变, 研究了蛋白质初始结构对其矿化作用的影响. FT-IR, XRD和SEM等测试结果显示, 未经任何处理的桑蚕丝素蛋白溶液矿化后形成片状复合物, 其无机相以二水磷酸氢钙(DCPD)为主; 而经过K^＋和Na^＋金属离子处理后, 桑蚕丝素溶液的结构由无规线团/螺旋构象向β-折叠发生转变, 矿化后成纤维状, 并相互结合呈现纳米级的三维多孔结构, 其无机相以热力学稳定的羟基磷灰石(HA)为主. 可以认为, 丝素蛋白结构转化为较伸展的β-折叠后, 使得更多的亲水基团暴露在外面, 在丝素蛋白分子不断凝聚成纤过程中, HA结晶快速生长并附着在这些微纤上, 最终形成纤维状的丝素蛋白/HA复合物. 该结果为阐明蛋白质的生物矿化过程及其调控机理提供了理论依据, 同时可以从矿化复合物的形成来反映这些微量元素可能对骨组织形成的影响, 为临床骨组织的修复提供一定的参考.