光子扫描隧道显微镜球形样品二维近场强度分析

采用时域有限差分方法计算全内反射和光子扫描隧道显微镜系统。光子扫描隧道显微镜的基本工作原理是隐失波的产生和探测，当入射光在两种介质的分界面上发生全内反射，并在界面处产生非辐射的电磁波——隐失波时，采取对两界面入射光进行分别设置的方法即“三波法”设置入射激励元。分别计算一个球和两个球形样品的近场分布，并计算散射小球为探针，一个球为样品的扫描图像。结果表明：采用二维时域有限差分方法计算能较直观地显示样品表面的近场分布。表明时域有限差分方法在光子扫描隧道显微镜理论研究中具有很大潜力。     

Shortcuts in Cosmological Branes

We aim at gathering information from gravitational interaction in the Universe, at energies where quantum gravity is required. In such a setup a dynamical membrane world in a space-time with scalar bulk matter described by domain walls, as well as a dynamical membrane world in empty Anti de Sitter space-time, is analyzed. We later investigate the possibility of having shortcuts for gravitons leaving the membrane and returning subsequently. In comparison with photons following a geodesic inside the brane, we verify that shortcuts exist. For late time universes they are small, but for some primordial universes they can be quite effective. In the case of matter branes, we argue that at times just before nucleosynthesis the effect is sufficiently large to provide corrections to the inflationary scenario, especially as concerning the horizon problem and the Cosmological Background Radiation.     

任意三角形区域中一组完备正交基的构造与分类

1.引言 正交函数基底在函数逼近、图像压缩和模式识别等领域中起着重要的作用.在二维区域中,通常采用分离变量法构造张量积形式的基底.然而,这种方法本质上只适用于规则的矩形区域.如何构造非规则区域,如三角形上的正交基底,是一个值得研究的课题[1][2][3][4][5].在一维情形下,通过求解Sturm—Liouville特征方程可以得到一组完备的正交基底.通过求解相应区域的特征方程,我们可以将这种方法推广到高维的基底构造.以三角区域为例,我们可以通过求解形式如下的特征方程来构造正交基底函数:     

爆炸荷载作用下封堵立柱运动参数的近似计算

本文以平战两用人防工程口部典型封堵方案缩尺模型试验为背景,运用结构动力学等效体系的基本方法,导出一般爆炸荷载作用下典型封堵结构立柱弹性响应的解析计算公式,计算结果与实验数据符合较好。     

DOMAIN AVERAGE SCM AND CONSTITUTIVE MODELLING OF POLYCRYSTALLINE AGGREGATES

A theoretical framework for the approximate constitutive assembly of polycrystals,termed henceforth domain average self consistent method, is developed to extend to SCM ofHill to adhered or sliding aggregates of arbitrary grain shape. The legitimacy and usefulnessof the current theory are justified by the polycrystals composed of cubic grains and slidingspherical grains.     

对具有从属关系的社会选择函数进一步的探讨

分析了Hattori给出的三个条件的合理性，并建立了一个仅满足非限制域条件而不满足存在一个独裁与无关个人影响力独立性条件的具有从属关系的社会选择函数，使具有从属关系的社会选择函数族更加完备。     

Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces

For holomorphic noncontractive maps on (not necessarily bounded) domains in complex Banach spaces, we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations. In particular, we show that the problem, concerning the existence of the horospheres determined by Carathéodory-Reiffen-Finsler pseudometrics defined on unbounded domains, has the solution and we prove new results of type of Julia's lemma and Wolff's theorem.     

两个非紧致齐性复解析流形

本文给出两个非紧致的齐性复解析流形．用它的齐性子流形构造出两个例外对称典型域的扩充空间，并由复流形上的运动群在超圆上的限制得到了两个例外对称典型域的仿射自同胚群，它们是闭的辛子群．     

Spatial organization in two-species annihilation

The spatial structure of reactants in the two-species annihilation reaction A+B0 is described. In one dimension, we investigate the distribution of domain sizes and the distributions of nearest-neighbor distances between particles of the same and of opposite species. The latter two quantities are characterized by a new length scale which is intermediate to the domain size t^1/2 and the typical interparticle spacing t^1/4. A scaling argument suggests that the typical distance between particles of opposite species, or equivalently the gaps between domains, grows ast , with = 3/8 and 1/3, respectively, in spatial dimensiond=1 and 2. The average density profile of a single domain is spatially nonuniform, with the density decaying to zero linearly as the domain edge is approached. This behavior permits a determination of the distribution of nearest-neighbor distances of same-species reactants. The corresponding moments of this distribution exhibit multiscaling which involves geometric averages of different powers of the domain size and the interparticle spacing.     

Canonical conjugate momentum of discrete label operators in quantum mechanics I: formalism

We discuss the inadequacy of the standard definition of canonical conjugation for a quantum operator having adiscrete spectrum. A different definition is proposed, based on the analogy betweencontinuous anddiscrete translations (or rotations). This definition can be applied to special operators which we calllabel operators. The general form of the conjugate momentum of a label operator is found and the resulting canonical commutation rules are discussed. It is shown that the canonical commutator acts like ac number in itsdomain _I , but the domain does not coincide with the whole Hilbert space. The properties of the subspace _I are also discussed.