DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS

In this paper, we study a differential-difference equation associated with discrete 3 × 3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an application, explicit soliton solutions of the differential-difference equation are given.     

Darboux Transformation of a Differential-Difference Equation and Its Explicit Solutions

The Darboux transformation of a differential-difference equation associated with a 3 × 3 matrix spectral problem is derived. As an application, explicit soliton solutions of the differential-difference equation are presented.     

向量优化的Henig真有效点（解）集的连通性

在局部凸的Hausdorff空间中,首先给出Henig真有效点的等价形式,由此得到了Henig真有效点的纯量化形式.借助纯量化形式,证明了Henig真有效点集的连通性.其次,对集值优化问题,当目标集值映射足锥凸时,给出其象集的Henig真有效点集与其象集凸包的Henig真有效点集是相等的结论,并给出了集值映射象集的Henig真有效点的纯量化形式.最后,证明了集值优化问题的Hcnig真有效解集的连通性.     

Superconductivity in Topological Semimetal θ-TaN at High Pressure

Recently,θ-TaN was proposed to be a topological semimetal with a new type of triply degenerate nodal points.Here,we report studies of pressure dependence of transport,Raman spectroscopy and synchrotron x-ray diffraction on θ-TaN up to 61 GPa.We find that θ-TaN becomes superconductive above 24.6 GPa with T_c at 3.1 K.The θ-TaN is of n-type carrier nature with carrier density about 1.1 × 10~(20)/cm~3 at 1.2 GPa and 20 K, while the carrier density increases with the pressure and saturates at about 40 GPa in the measured range.However,there is no crystal structure transition with pressure up to 39 GPa,suggesting the topological nature of the pressure induced superconductivity.     

焦煤裂解反应研究

本文研究了我国河北峰峰焦煤裂解反应,根据总包一级反应动力学模型对实验数据进行处理,结果表明温度低于700℃时满足阿仑尼乌斯方程,活化能为E=46kJmol~(-1)。 如果把煤裂解按一系列并行的不可逆一级反应步骤进行模拟,连续分布函数f(E)对活化能E的曲线遵从高斯正态分布,从而得到最可几活化能为E=259kJmol~(-1)。 测定了气相中碳氢化合物和氢的含量。结果表明气相中主要成分是甲烷,其来源,一来自煤裂解本身,二来自气相产物的二次反应。     

CrB_2的高温高压合成与物性研究

采用高温高压手段,以单质硼粉和铬粉为原料,在压力为6GPa、温度为1 200℃的条件下成功制备出CrB2化合物。利用X射线衍射仪、X射线能谱仪、硬度检测仪和扫描电子显微镜,对合成产物进行了物性表征。结果表明:合成的CrB2固体为六方结构,空间群为P6/mmm,晶格常数a=0.297nm,b=0.307nm;合成样品的晶粒直径为5~40μm,结晶质量良好。硬度测试结果显示,高温高压合成的CrB2具有很高的硬度。对比实验条件和实验结果发现,温度和原料配比均影响CrB2的合成,提高原料中硼的比例有助于目标产物CrB2的形成。     

Synthesis,structure, and properties of Ba9Co3Se(15) with one-dimensional spin chains

A new compound with one-dimensional spin chains, Ba9Co3Se(15), was synthesized under high pressure and high temperature conditions and systematically characterized via structural, transport and magnetic measurements. Ba9Co3Se(15) crystallizes in a hexagonal structure with the space group P-6c2(No. 188) and lattice constants of a = b = 9.6765 ? and c = 18.9562 ?. The structure consists of trimeric face-sharing octahedral CoSe6 chains, which are arranged in a triangular lattice in the ab-plane and separated by Ba atoms. The distance of the nearest neighbor of CoSe6 chains is very large, given by the lattice constant a = 9.6765 ?. The Weiss temperature Tθ associated with the intra-chain coupling strength is about -346 K. However, no long-range magnetic order but a spin glass transition at ~ 3 K has been observed. Our results indicate that the spin glass behavior in Ba9Co3Se(15) mainly arises from the magnetic frustration due to the geometrically frustrated triangular lattice.     

集值优化问题在Henig真有效解意义下的导数型最优性条件

给出实的赋范空间中集值映射的Henig真有效解集的一些性质,并利用集值映射的相依上图导数和集值映射的次微分给出了集值优化问题Henig真有效解的最优性条件的充要条件.