高压下层状钙钛矿结构锰氧化物Ca3Mn2O7的结构相变

采用金刚石压砧高压装置(DAC),对Ca₃Mn₂O₇的粉末样品进行了高压能散X射线衍射实验. 实验结果表明,由于岩盐层易被压缩,在压力作用下层状钙钛矿结构锰氧化物Ca₃Mn₂O₇的结构不稳定. 在0~35 GPa压力范围内,Ca₃Mn₂O₇晶体结构发生了两次相变. 在1.3 GPa左右,由原来的四方相变为正交相,在9.5 GPa左右,又由正交相向新的四方相转变.     

ZnAl2O4/α-Al2O3复合衬底的制备和GaN薄膜的生长

利用脉冲激光淀积法(PLD)在α-Al₂O₃衬底上淀积了ZnO薄膜, 通过ZnO和α-Al₂O₃固相反应制备了具有ZnAl₂O₄覆盖层的α-Al₂O₃衬底. X射线衍射谱(XRD)表明ZnAl₂O₄薄膜随反应时间由单一(111)取向转变为多晶取向, 然后变为不完全的(111)择优取向. 同时扫描电子显微镜(SEM)照片表明ZnAl₂O₄表面形貌随反应时间由均匀的岛状结构先变为棒状结构, 然后再变为突起的线状结构. 另外, XRD谱显示低温制备的ZnAl₂O₄在高温下不稳定. 在ZnAl₂O₄覆盖的α-Al₂O₃衬底上利用光加热低压MOCVD法直接生长了GaN薄膜. XRD测量表明随ZnAl₂O₄厚度增加GaN由c轴单晶变为多晶, 单晶GaN的摇摆曲线半高宽为0.4°. 结果表明薄ZnAl₂O₄覆盖层的岛状结构有利于GaN生长初期的成核, 从而提高了GaN的晶体质量.     

Fτ-Coherent 风险度量

该文提出了一个风险度量的新概念,即定义在任意停时 τ上的 F_τ-Coherent 风险度量. 对任一 满足Fatou 性质的F_τ-Coherent 风险调整值度量(即一个F_τCoherent风险度量的负值) ф_т: L^∞ (F) →L^∞ (F_τ) 我们都可以用一个 F_τ-凸概率测度集来给出它的显式表示.同时我们还证明了一个 F_τ-Coherent 风险调整值度量可以用它的可接受头寸集合来表示.     

关于R0 -代数的公理系统

该文给出了R₀ -代数的一些简化公理系统,并证明了R₀ -代数等价于满足某些条件的BCK -代数.     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.     

Gd2SiO5: Eu3+中VUV激发的量子剪裁

在北京同步辐射装置的真空紫外光谱站, 对Gd₂SiO₅: Eu³⁺激发谱、发射谱进行了研究. 基于Gd³⁺-Eu³⁺体系通过能量传递发生可见光量子剪裁的原理, 对实验结果进行了讨论. 当直接激发Gd³⁺的⁶GJ态时, 有2个来自Eu³⁺的可见光光子发射, 粗略的估算表明Gd₂SiO₅: Eu³⁺是一种有效的量子剪裁材料.     

局部域的K2群中的一类挠元素

证明了(K₂Q_p(z_p))_I=G_p(Q_p(z_p)); 还证明若n|w(Q₅ (z₅)), 则(K₅Q₅(z₅))_n=G₅(Q5₅(z₅)), 这说明对于含有p次本原单位根的p局部域, 如果p|n, 则Browkin猜想一般不成立. 由此提出一个一般猜想. 另外, 否定了Urbanowicz的一个猜想.     

氢化非晶硅氧薄膜微结构

以Raman散射、X射线电子能谱和红外吸收光谱细致研究了PECVD法250℃衬底温度下制备的氢化非晶硅氧(a-SiO_x∶∶H)薄膜的微结构及键构型. 研究表明, 在0.52≤x≤1.58的氧含量范围内，a-SiO_x∶∶H薄膜成分和结构不是均一的，依赖于局域键构型氧化程度的不同，大致存在着5种在一定程度上相互分离的结构组分，即Si, Si₂O(∶H), SiO(∶H), Si₂O₃(∶H)和SiO₂. 其中的Si相以非氢化的非晶硅(a-Si)颗粒形式存在，随氧含量x的增加其尺度持续减小但始终存在. 提出一种多壳层模型来描述a-SiO_x∶H薄膜的结构，认为a-SiO_x∶H薄膜中a-Si颗粒依次为Si₂O(∶H), SiO(∶H), Si₂O₃(∶H)和SiO₂壳层所包围. 随薄膜氧含量x的增加，各壳层厚度相应变化但各自的化学构成基本保持不变.     

u0 - 凹算子的不动点定理及其应用

该文利用锥的性质和单调迭代技巧讨论了u₀ - 凹算子正不动点的存在唯一性,所得结论改进并推广了已有的相关结果. 作为应用, 该文研究了一类Hammerstein积分方程正解的存在唯一性.     

弱 (K1, K2) -拟正则映射的正则性

给出空间弱(K₁, K₂) -拟正则映射的定义, 并以Hodge分解及弱逆Hölder不等式为工具, 得到了其正则性结果：对任意满足 的q1, 都存在可积指数 使得对任意弱 (K₁, K₂) -拟正则映射 都有 即f为通常意义下的(K₁, K₂) -拟正则映射.     

Arbitrary-norm hyperplane separation by variable neighbourhood search

^** Email: alejandro.karam{at}hec.ca^*** Email: gilles.caporossi{at}gerad.ca^**** Email: pierre.hansen{at}gerad.ca We consider the problem of separating two sets of points ina Euclidean space with a hyperplane that minimizes the sum ofp-norm distances to the plane of points lying on the ‘wrong’side of the plane. A variable neighbourhood search heuristicis used to determine the plane coefficients. For a set of exampleswith L₁-norm, L₂-norm and L-norm, for which the exact solutioncan be computed, we show that our algorithm finds it in mostcases and gets good approximations in the others. The use ofour heuristic solutions for problems in these norms can dramaticallyaccelerate exact algorithms. Our method can be applied on verylarge instances that are intractable by exact algorithms. Sincethe proposed approach works for truly arbitrary norms (otherthan the traditional 1, 2 and ), we can explore for the firsttime the effects of the choice of p on the generalization propertiesof p-norm hyperplane separation.     

Exponential stability and maximal attractors for a one-dimensional nonlinear thermoviscoelasticity

This paper is concerned with the global existence, exponentialstability of solutions and associated nonlinear C₀-semigroupas well as the existence of maximal attractors in Hⁱ (i = 1,2, 4) for a nonlinear one-dimensional thermoviscoelasticitydescribing a kind of solid-like material. Some new ideas andmore delicated estimates are employed to prove the global existenceand exponential stability of solutions. The important featurefor the existence of maximal attractors in Hⁱ₊ (i = 1, 2, 4)is that the metric spaces H¹₊, H²₊ and H⁴₊ we work with arethree incomplete metric spaces, as can be seen from the physicalconstraints, i.e. > 0 and u > 0, with and u being absolutetemperature and deformation gradient (strain). For any positiveparameters ₁, ₂, ..., ₅ verifying some conditions, a sequenceof closed subspaces Hⁱ Hⁱ+ (i = 1, 2, 4) is found, and theexistence of maximal attractors in Hⁱ (i = 1, 2, 4) is established.     

A Calculation of the Culler-shalen Seminorms Associated to Small Seifert Dehn Fillings

We determine the relationship between the multiplicities ofthe zeros of certain rational functions defined on the SL₂(C)and PSL₂C character varieties of knot exteriors. This leadsto a formula for the Culler–Shalen seminorms associatedto small Seifert Dehn fillings of such manifolds. 2000 MathematicsSubject Classification: 57M05, 57M27, 57R65.     

Observability and reachability for parallel-flow heat exchanger equations

^** Email: sano{at}cc.kagoshima-u.ac.jp This paper is concerned with the dynamical analysis of parallel-flowheat exchanger equations with observation at the outlet of tube/controlat the inlet of tube. The parallel-flow heat exchanger equationis super-stable under zero boundary condition. The system canbe described by an unbounded operator of lower triangular formthrough a variable transformation. By calculating a C₀-semigroupgenerated by the operator, it is shown that the system is observableif both fluid temperatures are measured at the outlet, and thatthe system is observable with respect to the non-negative coneof the state space if either of them is measured at the outlet.Moreover, it is shown that the system is reachable if both fluidtemperatures are controlled at the inlet, and that the systemis reachable with respect to the non-negative cone of the statespace if either of them is controlled at the inlet.     

On O0-boundedness and -stability properties with perturbing Liapunov functional

In this paper we will extend the perturbing Liapunov functionmethod to systems of functional differential equations and discussØ₀-equiboundedness and Ø₀-equistability propertiesvia the concept of perturbing Liapunov functional.     

Finite-dimensional H{infty} control of flexible beam equation systems

In this paper, we consider H control problem with measurementfeedback for flexible beam equation systems. The aim is to constructa finite-dimensional H controller with a given level for theflexible beam equation system. For that purpose, we first formulatethe system as an infinite-dimensional system in l² and derivea finite-dimensional reduced-order system for the infinite-dimensionalsystem. Then, an H controller with level d less than is constructedfor the reduced-order model. The finite-dimensional controllertogether with a residual mode filter plays a role of a finite-dimensionalH controller with level for the original flexible beam equationsystem, if the order of the residual mode filter is chosen sufficientlylarge.     

The group and Riesz basis properties of string systems with time delay and exact controllability with boundary control

^** Email: gqxu{at}tju.edu.cn^*** Email: Jiajg{at}mailst.xjtu.edu.cn The group property of a string system with time delay in boundaryand the Riesz basis property of eigenvectors of the system arediscussed in the present paper. It is proved that, when thefeedback with delay > 0, the system also associates a C₀group, and its eigenvectors (generalized eigenvectors) forma Riesz basis in Hilbert space . This result shows that timedelay may destroy the stability of the system, but the groupand Riesz basis properties are kept. As a consequence, the exactcontrollability of the system with boundary control is given.     

On approximation theorems for controllability of non-linear parabolic problems

^** Email: anil{at}math.iitb.ac.in^*** Email: mcj{at}math.iitb.ac.in^**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u^*,y^*) is then obtained as the limit of the optimal pair sequence{(u_n^*, y_n^*)}, where u_n^* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and y_n^* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result.