An approach combining the Ritz-Galerkin and finite difference methods

The nonconforming combination of Ritz-Galerkin and finite difference methods is presented for solving elliptic boundary value problems with singularities. The Ritz-Galerkin method is used in the subdomains including singularities, the finite difference method is used in the rest of the solution domain. Moreover, on the common boundary of two regions where two different methods are used, the continuity conditions are constrained only on the nodes of difference grids. Theoretical analysis and numerical experiments have shown that average errors of numerical solutions and their generalized derivatives can reach the convergence rate O(h^2-δ), where h is the mesh spacing of uniform difference grids, and δ is an arbitrarily small, positive number. This convergence rate is better than O(h), obtained by the nonconforming combination of the Ritz-Galerkin and finite element methods.     

大学物理课程网络辅助教学系统的构建与应用

本文介绍了上海交通大学大学物理课程网络辅助教学系统的设计思想、整体结构和主要的功能模块，概述了运用网络辅助教学系统实施“课堂教学＋网络辅助教学”：这种教学模式的应用情况．     

C2(×)Cn量子系统的最大纠缠混合态

讨论了C2(×)Cn量子系统的最大纠缠混合态,得到了Negativity纠缠度下的最大纠缠混合态的解析结果,并计算了该态在非满秩情形下的量子相对熵纠缠度.     

Theoretical Research on a Kind of Quantum Left-handed Metamaterial

Recently, research on left-handed materials （LHMs） has attracted considerable attentions. The LHMs are a kind of metameterial which have negative permittivity and negative permeability, which lead to negative refractive index in a frequency range. The LHMs that have been available so far are in the microwave range and are usually composed of classical particles, such as split-ring resonators. Some quantum phenomena such as spontaneous emission of atoms in the LHMs which are considered to be ＇classical background＇ have also been investigated. Many potential applications of LHMs have been proposed, such as superlenses which, in principle, can achieve arbitrary subwavelength resolution.     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

SiOx纳米管的制备及其发光特性

以液态金属镓为媒介,利用热蒸发法合成大量非晶SiOx纳米管,这些纳米管管径均匀分布,平均约80 nm,长度大于10μm,且管内外径比例较小．分析发现,在实验过程中,熔入金属镓液滴中的硅元素和氧元素结合并从液滴的表面饱和析出,形成以镓为中心的非晶SiOx纳米管状结构．在室温中,利用260 nm的激发光源激发SiOx纳米管,发现在蓝光波段附近发出强而稳定的PL谱线,这可能与样品中的氧缺陷和空位有关．     

High-throughput screening of fuel cell electrocatalysts

The drawbacks of our earlier report of preparing fuel cell catalyst arrays by borohydride reduction of inkjet prepared arrays of metal salts are discussed along with the need for inclusion of state-of-the-art metrics in all array screening. An alternative method for screening of hydrogen/air cathode catalysts, direct methanol fuel cell (DMFC) anode catalysts, and catalyst loading studies is provided. State-of-the-art Johnson Matthey catalysts were used in control experiments to demonstrate the utility of the array fuel cell for high throughput screening of fuel cell catalysts in the 3-4 mg/cm² range. This report lays out hard learned rules for high throughput screening and demonstrates that the array fuel cell can be used for very precise screening of libraries of membrane electrode assembly (MEA) components without the pitfalls discussed in the introduction.     

Spectral line suppression and sideband narrowing via quantum interference

We reveal that for a realistic system, interference effects are obtained such as the suppression of central line and inner sidebands and the narrowing of the outer fluorescence sidebands. For this purpose, we consider a spontaneous decay from an excited state to a metastable state when the excited and metastable states are resonantly coupled to an auxiliary metastable state by a laser field and a microwave field, respectively. The fluorescence spectrum evolves from a five-peaked structure into a doublet of ultrasharp lines as the ratio of the laser field Rabi frequency to the microwave Rabi frequency is decreased. The physical origin is presented in terms of dressed states.     

On completely irreducible operators

Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more. The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section 2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties of completely irreducible operators are different from properties of unicellular operators. __________ Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29     

Soliton interaction under the influence of higher-order effects

In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schrödinger (HNLS) equation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically.