光纤光栅的局域耦合模分析

本文运用矢量局域耦合理论分析了平均扰动折射率随Z轴变化的单模光纤光栅的纤芯模场分布、包层模场分布以及耦合系数,得到更为精确的光栅光谱特性.并分别计算了布喇格光栅和长周期光纤光栅在平均扰动折射率在Z轴有扰动时的光谱特性图.从而得出平均折射率随Z轴变化对光谱特性的危害性,并提出了解决方法.     

Temperature dependent properties of metallic clusters containing magnetic impurities

The properties of magnetic impurities in small metallic clusters are investigated in the framework of the Anderson model by using exact diagonalization methods. Parameters representative of the Kondo limit are considered. The spin gap ΔE = E(S=1, 3/2) - E(S=0, 1/2) shows a remarkable band-filling dependence that can be interpreted in terms of the cluster-specific conduction-electron spectrum. Finite-temperature properties such as the magnetic susceptibility and specific heat are calculated exactly in the canonical and grand canonical ensembles. The structural dependence is illustrated. Received 30 November 2000     

有理B样条曲线的光顺拟合法

研究了用三次均匀有理Ｂ样条样曲线光顺拟合一组平面点列的问题,其中光顺性由曲线的能量积分与扰动的权平均来确定。     

Global,local and unique decompositions in OnPLS for multiblock data analysis

OnPLS is an extension of O2PLS that decomposes a set of matrices, in either multiblock or path model analysis, such that each matrix consists of two parts: a globally joint part containing variation shared with all other connected matrices, and a part that contains locally joint and unique variation, i.e. variation that is shared with some, but not all, other connected matrices or that is unique in a single matrix.     

Combining multiset resolution and segmentation for hyperspectral image analysis of biological tissues

Hyperspectral images can provide useful biochemical information about tissue samples. Often, Fourier transform infrared (FTIR) images have been used to distinguish different tissue elements and changes caused by pathological causes. The spectral variation between tissue types and pathological states is very small and multivariate analysis methods are required to describe adequately these subtle changes.     

A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.     

Minimum distance of linear codes and the α-invariant

The simple interpretation of the minimum distance of a linear code obtained by De Boer and Pellikaan, and later refined by the second author, is further developed through the study of various finitely generated graded modules. We use the methods of commutative/homological algebra to find connections between the minimum distance and the α-invariant of such modules.     

Nonlinear growth in weighted networks with neighborhood preferential attachment

We propose a nonlinear growing model for weighted networks with two significant characteristics: (i) the new weights triggered by new edges at each time step grow nonlinearly with time; and (ii) a neighborhood local-world exists for local preferential attachment, which is defined as one selected node and its neighbors. Global strength-driven and local weight-driven preferential attachment mechanisms are involved in our model. We study the evolution process through both mathematical analysis and numerical simulation, and find that the model exhibits a wide-range power-law distribution for node degree, strength, and weight. In particular, a nonlinear degree–strength relationship is obtained. This nonlinearity implies that accelerating growth of new weights plays a nontrivial role compared with accelerating growth of edges. Because of the specific local-world model, a small-world property emerges, and a significant hierarchical organization, independent of the parameters, is observed.     

Theoretical studies of the EPR parameters and local structures for the two Cu2+ centers in Cd(HCOO)2·2H2O

Based on the studies of the electron paramagnetic resonance parameters for two types of the Cu²⁺ centers in Cd(HCOO)₂·2H₂O by using the high‐order perturbation formulas for a 3d⁹ ion in a rhombically elongated octahedron, local structure of the doped copper ion is determined. Research suggests that the impurity Cu²⁺ replaces the host Cd²⁺ and undergoes the local rhombic elongation distortion, characterized by the axial elongation ratios of 4.1%, and 3.8% along the z‐axis and the planar bond length variation ratios of 3.8%, and 3.1% along the x‐axis and y‐axis, for Cu²⁺ Centers, I and II, respectively. The above slightly different axial elongation ratios and planar bond length variation ratios may suitably account for the slightly dissimilar axial g anisotropies Δg (≈0.351 and 0.339) and perpendicular g anisotropies δg (≈0.028 and 0.022) of the two centers, respectively.     

Local and global solutions for some parabolic nonlocal problems

We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a “Newtonian” nonlocal term.