物理实验教学与中学生辩证逻辑思维能力的培养

阐述了如何在辩证逻辑基本规律——对立统一规律指导下，通过挖掘物理实验中蕴涵的辩证逻辑思维素材，在物理实验教学中有意识地培养学生的辩证逻辑思维能力。     

LIGHT-SCATTERING STUDY OF POLYELECTROLYTE HOLLOW CAPSULES

Silver halide (AgX) microcrystal was used as template to synthesize hollow polyelectrolyte capsules. These hollow capsules were characterized by laser light scattering (LLS) used to measure the size of the capsules in solution. The ratio of hydrodynamic radius (Rh) from dynamic LLS to the radius of gyration (Rg) from static LLS is almost unity, revealing that the entities are hollow in solution. The results suggest that the LLS method can be regarded as a good complement to the confocal laser scanning microscopy (CLSM) method for the characterization of small hollow capsules, and it possesses the advantage of not needing fluorescence labeling.     

On Solutions of the q-Hypergeometric Equation with q N = 1

We consider the q-hypergeometric equation with q ^N = 1 and , , . We solve this equation on the space of functions given by a power series multiplied by a power of the logarithmic function. We prove that the subspace of solutions is two-dimensional over the field of quasi-constants. We get a basis for this space explicitly. In terms of this basis, we represent the q-hypergeometric function of the Barnes type constructed by Nishizawa and Ueno. Then we see that this function has logarithmic singularity at the origin. This is a difference between the q-hypergeometric functions with 0 < |q| < 1 and at |q| = 1.     

Group Representation of Waves in Gyrotropic Crystals

A new group (linear) representation of the propagation of waves in properly and naturally gyrotropic crystals in the general case where the nonreciprocity effect takes place has been developed. Simple expressions of the dependence of ray (group) velocities and polarization vectors of isonormal waves on the complex vector of principal velocities dual to the unitary tensor by which the optical properties of crystals are directly characterized have been obtained. The relationship between gyrotropy and anisotropy and the dipole moment and displacement current induced by the radiation in the crystal has been established. It is shown that the presence of gyrotropy and nonlinear polarization of radiation together with the elimination of conical points entails a phase ambiguity of the ray velocity of the quantummechanical type and a smearing and layering of the wave surface, as well as a discreteness of the spectrum of velocity values of isonormal waves.     

The Two-Step Nilpotent Representations of the Extended Affine Hecke Algebra of Type A

We define a set of cell modules for the extended affine Hecke algebra of type A which are parametrised by SL_n()-conjugacy classes of pairs (s, N), where s SL_n() is semisimple and N is a nilpotent element of the Lie algebra which has at most two Jordan blocks and satisfies Ad(s)·N=q ² N. When q ²–1, each of these has irreducible head, and the irreducible representations of the affine Hecke algebra so obtained are precisely those which factor through its Temperley–Lieb quotient. When q ²=–1, the above remarks apply to a subset of the cell modules. Using our work on the cellular nature of those quotients, we are able to obtain complete information on the decomposition of the cell modules in all cases, even when q is a root of unity. They turn out to be multiplicity free, and the composition factors may be precisely described in terms of a partial order on the pairs (s, N). These results give explicit formulae for the dimensions of the irreducibles. Assuming our modules are identified with the standard modules earlier defined by Bernstein–Zelevinski, Kazhdan–Lusztig and others, our results may be interpreted as the determination of certain Kazhdan–Lusztig polynomials. [This has now been proved and will appear in a subsequent work of the authors.]The second author thanks the Australian Research Council and the Alexander von Humboldt Stiftung for support and the Universität Bielefeld for hospitality during the preparation of this work.     

爱因斯坦坚持场纲领的原因

探讨了爱因斯坦坚持场纲领的物理学认识基础和思想发展过程，分析了其坚持场纲领的目的及未获成功的原因。     

Finite Hopf Algebras and Bidifferential Structures

In this Letter we show the existence of bidifferential structures on finite Hopf algebras, which arise from quantum groups at roots of unity.     

The intrinsic XFEM for two‐fluid flows

In two‐fluid flows, jumps and/or kinks along the interfaces are present in the resulting velocity and pressure fields. Standard methods require mesh manipulations with the aim that either element edges align with the interfaces or that the mesh is sufficiently refined near the interfaces. In contrast, enriched methods, such as the extended finite element method (XFEM), enable the representation of arbitrary jumps and kinks inside elements. Thereby, optimal convergence can be achieved for two‐fluid flows with meshes that remain fixed throughout the simulation. In the intrinsic XFEM, in contrast to other enriched methods, no more unknowns are present in the approximation than in a standard finite element approximation. In this work, the intrinsic XFEM is employed for the simulation of incompressible two‐fluid flows. Numerical results are shown for a number of test cases and prove the success of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

A stabilized formulation for the advection–diffusion equation using the Generalized Finite Element Method

This paper presents a stable formulation for the advection–diffusion equation based on the Generalized (or eXtended) Finite Element Method, GFEM (or X‐FEM). Using enrichment functions that represent the exponential character of the exact solution, smooth numerical solutions are obtained for problems with steep gradients and high Péclet numbers in one‐ and two‐dimensions. In contrast with traditional stabilized methods that require the construction of stability parameters and stabilization terms, the present work avoids numerical instabilities by improving the classical Galerkin solution with enrichment functions (that need not be polynomials) using GFEM, which is an instance of the partition of unity framework. This work also presents a strategy for constructing enrichment functions for problems involving complex geometries by employing a global–local‐type approach. Representative numerical results are presented to illustrate the performance of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.