Comment on "Optimized matrix inversion technique for the T-matrix method"

The matrix inversion technique for the T-matrix method recently suggested by Petrov et al. [Opt. Lett.32, 1168 (2007)] is not new. Their way of implementing the technique, in which Strassen's matrix multiplication algorithm is not adopted, does not save computation time when the LU factorization technique of matrix computation theory is used.     

一维无序系统本征矢的解法

本文提出了一种直接求解五对角厄米特矩阵本征矢的方法,即通过代数运算求出本征矢,而不是用三对角块矩阵来解。该方法对计算一维无序系统的本征矢特别适用。计算结果表明,此方法的存储量小,计算精度高,速度快,并可计算上十万个点阵的无序系统本征矢。     

Density matrix in technique of polarized ion sources

The use of the density matrix is the most direct way to work with polarization parameters. The solutions of the equation for the density matrix are obtained for hydrogen and deuterium. The magnetic moments of nuclei are explicitly incorporated into the equations, even though numerically it does not make a big difference. It is shown that in the general case the density matrix can not be reduced to the one with the only spin variables of the nucleus in contradiction with the statement of K. Blum [K. Blum, Density Matrix Theory and Applications].     

On the decoupling of interacting systems

It is shown that the one electron energy matrix of a system composed of similar interacting subsystems does not, in general, provide a unique determination of the energy matrix of the subsystems. A criterion for making this separation is proposed.     

Optical ray paths in a quasi-periodic waveguide or a multipass cavity with smoothly varying properties

Ray paths in a quasi-periodic optical system (waveguide of cavity) with smoothly varying properties have been constructed along the ray path. The ray-transfer matrix is constructed for a large number of ray paths; it has been shown that the conventional stability condition (the modulus of the ray-transfer matrix trace for a ray path is smaller than two) does not ensure the boundedness of the beam path after a large number of paths.     

Fluorescence in a Quantum System with Violated Symmetry

The model of a single multilevel one-electron atom with violated symmetry such that its transition dipole-moment operator has constant diagonal matrix elements, among which not all are pairwise equal to each other, has been studied. It has been shown that the expression for the far electromagnetic field of such an atom does not contain any appreciable contributions from the diagonal matrix elements of the transition dipole moment in an explicit form; thus, these matrix elements have an effect on fluorescence via the time dependence of non-diagonal matrix elements due to quantum non-linear processes of higher orders. It has also been demonstrated that a two-level quantum system, whose transition dipole operator has constant unequal diagonal matrix elements, can continuously fluoresce under excitation with monochromatic laser radiation at a much lower frequency than the frequency of the exciting radiation. The possibility of the experimental detection and practical application of this effect are discussed.     

Auto-Bäcklund transformations for a matrix partial differential equation

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.     

No-relationship Between Impossibility of Faster-Than-Light Quantum Communication and Distinction of Ensembles with the Same Density Matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related.We argue that even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.     

水平层状介质并矢Green函数的递推矩阵方法

采用递推矩阵方法计算任意数目水平层状介质的并矢Green函数.根据层界面处电场和磁场的连续性条件得到3个确定Sommerfeld积分待定系数的矩阵方程组,分别对应于垂向单位电偶极子产生的TM波、水平方向单位电偶极子产生的TE波和TM波,这些方程组均可通过递推方法快速求解.只需改变3个方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的并矢Green函数.本文给出的并矢Green函数表达式形式简洁且不含指数增加项,计算时不会出现溢出现象.     

No-relationship Between Impossibility of Faster-Than-Light Quantum Communication and Distinction of Ensembles with the Same Density Matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related. We argue that even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.     

An energy criterion for the initiation of interface failure ahead of a matrix crack in brittle matrix composites

The mechanism of interfacial failure occurring as a consequence of the stress concentration induced by a matrix crack located in the vicinity of the interface is analysed. For this purpose, an asymptotic analysis is carried out to assess the competition between the propagation of the matrix crack towards the interface and the nucleation of an interfacial debond. An energetic approach provides a necessary condition comparing the ratio of the interfacial toughness over the matrix toughness to a critical value depending on the elastic mismatch between the fibre and the matrix and the ratio of the interfacial nucleation length over the width of the matrix ligament. Presented results show that the interfacial debonding is enhanced if the matrix is softer than the fibre. Further, a modified condition which does not involve the crack increment ratio is established if the matrix crack lies in the stiffest material.     

局域规范群C~∞(M,G)上不存在有限不变正测度(英文)

研究了对 Faddeev- Popov方法有关键意义的局域规范群上不变测度的存在性问题 .证明了局域规范群 C∞ (M,G) (M为一紧致流形 ,G为一矩阵李群 )上不存在有限的平移不变的正测度. In is proved that on the local gauge group C ∞ (M,G) ( M a compact manifold and G a matrix Lie group) there does not exist a finite positive invariant measure.     

纳米碳管复合凝胶玻璃结构及谱学性能研究

用物理掺杂工艺将纳米碳管引入二氧化硅凝胶玻璃基质,成功制备了纳米碳管复合凝胶玻璃,采用X射线衍射、透射电子显微镜、紫外-可见吸收光谱、红外光谱、拉曼光谱等测试方法对其结构和谱学性能进行了表征。结果表明,通过优化掺杂工艺能够实现纳米碳管与基质的均匀复合,纳米碳管本身的结构在掺杂过程中并未发生改变。纳米碳管的引入对二氧化硅凝胶玻璃基质的紫外-可见吸收光谱和红外光谱未产生显著影响。     

Three-spin interaction Ising model with a nondegenerate ground state at zero applied field

The field-temperature phase diagram of a two-dimensional, three-spin interaction Ising model is studied using two different methods: mean field approximation and numerical transfer matrix techniques. The former leads to a rather rich phase diagram in which two separate phases with different symmetries can be found, and which presents first-order transition lines, a triple point, and a critical end point, like the solid-liquid-gas phase diagram of a pure compound. The numerical transfer matrix study confirms part of these results, but does not clearly evidence the existence of the less symmetric phase.     

Luminescent Hybrid Materials Based on Polymers of Poly(Alpha-Fluoroacrylates) Doped with Tb(III) Complex

This study is devoted to the development of efficient luminescent hybrid materials excited by UV radiation and featuring narrow luminescence lines as well as light, humidity, and temperature resistance. As a luminescent material, a terbium ion coordination compound introduced into the matrix of an organofluorine polymer is used. It has been shown that efficient excitation transfer to electronic levels of the terbium ion can be achieved by proper ligand selection. The polymer matrix material does not affect the luminescence properties of the Tb(III) coordination compound.     

Thermochemical reactions with powderized carbon in emission spectral analysis

The thermochemical reactions occurring during diluting of samples with carbon powder are discussed. Isobaric potentials of possible reactions are presented. It is shown that fractional distillation of the vapors of admixtures and matrix does not always occur.     

Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting

In this work, we formulate the image in-painting as a matrix completion problem. Traditional matrix completion methods are generally based on linear models, assuming that the matrix is low rank. When the original matrix is large scale and the observed elements are few, they will easily lead to over-fitting and their performance will also decrease significantly. Recently, researchers have tried to apply deep learning and nonlinear techniques to solve matrix completion. However, most of the existing deep learning-based methods restore each column or row of the matrix independently, which loses the global structure information of the matrix and therefore does not achieve the expected results in the image in-painting. In this paper, we propose a deep matrix factorization completion network (DMFCNet) for image in-painting by combining deep learning and a traditional matrix completion model. The main idea of DMFCNet is to map iterative updates of variables from a traditional matrix completion model into a fixed depth neural network. The potential relationships between observed matrix data are learned in a trainable end-to-end manner, which leads to a high-performance and easy-to-deploy nonlinear solution. Experimental results show that DMFCNet can provide higher matrix completion accuracy than the state-of-the-art matrix completion methods in a shorter running time.     

Dynamics of quantum correlations

The density matrix describing the state of a sybsystem of a physical system whose time dependence is assumed to follow a Schrödinger equation does not itself obey a von Neumann equation. The behavior of the eigenvalues and eigenfunctions of this density matrix is studied. An expression for the rate at which initially separating systems are de-separated is derived in perturbation theory. Indications are given that coherent photon states are more stable in the presence of charged particles than photon number eigenstates. The possible dynamical origin of super selection rules is discussed. A simple model is solved analytically.     

Thermotropic phase transitions in model membranes of the outer skin layer based on ceramide 6

The lipid intercellular matrix stratum corneum of the outer skin layer is a multilayer membrane consisting of a complex mixture of different lipids: ceramides, fatty acids, cholesterol, and its derivatives. The basis of the multilayer membrane is the lipid bilayer, i.e., a two-dimensional liquid crystal. Currently, it is known that the main way of substance penetration through the skin is the lipid matrix. The complexity of the actual biological system does not allow reliable direct study of its properties; therefore, system modeling is often used. Phase transitions in the lipid system whose composition simulates the native lipid matrix are studied by the X-ray synchrotron radiation diffraction method.