Eigensolution of specially structured matrices with hyper‐symmetry

Recently, four canonical forms have been developed and applied to the dynamics and stability analysis of symmetric frames. In this paper, hyper‐symmetric matrices and specially structured matrices are defined and efficient methods are proposed for the eigensolution of such matrices. Applications are extended to hyper‐graphs and specially structured graphs. Simple methods are developed for calculating the eigenvalues of the Laplacian matrices of such graphs. The developments presented in this paper can also be considered as generalization of Form II and Form III symmetry, previously defined by the authors. Copyright © 2006 John Wiley & Sons, Ltd.     

Eigensolution of augmented graph products using shifted inverse iteration method

Two important matrices associated with graphs are adjacency and Laplacian matrices. In this paper efficient methods are presented for eigensolution of graph products augmented by other graphs. For augmentations that do not destroy the symmetry of the graph products, a method is proposed for decomposition of matrices resulting in considerable simplification of their eigensolution. For graphs composed of two non‐overlapping graph products joined through a small number of link members, a method based on shifted inverse iteration is proposed which utilizes all eigenvalues and eigenvectors of each individual graph products. Owing to the availability of fast methods for eigensolution of graph products, this method simplifies the eigensolution of a variety of graph models and proves to be very efficient in determining the few smallest eigenpairs of these models with high levels of accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

复杂二维契合图形研究及应用展望

目的补充与完善现有契合图形设计方法,并对其实际应用提出构想。方法首先采用程序的穷举法推导出正十二边形以下正多边形的所有契合解,并以此为基础从几何变换的角度进行复杂契合图形的创新设计。结论给出了简单契合图形转化成旋转对称图形与轴对称图形的通用方法,以及正四边形通过变换形成契合图形的特殊规律,提出了"布尔契合"的思想,形成一种新的契合图形。最后阐述了此理论在当代设计领域与设计思潮下的应用价值。     

Ti基DSA阳极在三价铬硫酸盐镀液中的电化学行为

为了获得满足三价铬硫酸盐镀液镀铬要求的阳极,采用热分解法制备了具有Pt-Ir-Ta-Sn氧化物涂层的Ti基DSA阳极,并研究了3种Ti基DSA阳极在三价铬硫酸盐镀液中的电化学行为.结果表明:具有Pt-Ir-Ta-Sn氧化物涂层的Ti基DSA阳极表面结构致密、稳定性好;在三价铬硫酸盐镀液中的析氧电位较低、对阳极析氧反应具有较好的催化活性;不发生Cr3 被氧化成Cr6 的反应;金属Ta-Sn氧化物的引入可以增加Ti基DSA阳极的活性表面面积,提高催化活性和增强其稳定性.     

Synthese et etude structurale du tellurate (VI) de thallium (III) Tl2TeO6

Tl₂TeO₆ is the last reported member of the trivalent metal tellurate family with general formula M₂TeO₆. It was prepared by oxydation of intimate mixture of thallous carbonate and tellurium dioxyde. Its thermal stability was studied. Tl₂TeO₆ crystallizes with trigonal symmetry and hexagonal unit-cell parameters: a = 9,070 Å, c = 4,984 Å, Z = 3. The space group is P321. After single crystal analysis the structure was solved and refined to a final R = 0,057 for 1505 independent reflexions. Like Lu₂TeO₆ and In₂TeO₆, Tl₂TeO₆ is isostructural with sodium fluosilicate Na₂SiF₆. Each metallic-ion is octahedrally coordinated to a slightly distorded anionic hexagonal close packed array.     

三价、四价铱盐的应用研究

通过对掺杂（NH4）3IrCl6、（NH4）2IrCl6的氯化银乳剂进行性能应用对比，主要在普通灯光曝光性能、高照度曝光性能、潜影稳定性三个方面进行研究。结果表明：铱盐的化合价位越低，对提高乳剂的高照度曝光性能与潜影稳定性，有较大优势，并从机理上解释了价位低的铱盐，做为浅电子陷阱掺杂剂有较大优势的原因。     

三价铬电沉积研究状况

阐述了目前三价铬电沉积研究的主要内容,包括镀层增厚问题、镀液稳定性的探讨和机理研究,指出了当前三价铬电沉积存在的主要问题,并简单介绍了有关三价铬最近几年的发展趋势,指出三价铬非晶态合金及复合镀层的研究是今后一段时间电镀行业研究的主要走向。     

Improved group theoretic method using graph products for the analysis of symmetric-regular structures

In this paper, a new combined graph-group method is proposed for eigensolution of special graphs. Symmetric regular graphs are the subject of this study. Many structural models can be viewed as the product of two or three simple graphs. Such models are called regular, and usually have symmetric configurations. The proposed method of this paper performs the symmetry analysis of the entire structure via symmetric properties of its simple generators. Here, a graph is considered as the general model of an arbitrary structure. The Laplacian matrix, as one of the most important matrices associated with a graph, is studied in this paper. The characteristic problem of this matrix is investigated using symmetry analysis via group theory enriched by graph theory. The method is developed and decomposition of the Laplacian matrix of such graphs is studied in a step-by-step manner, based on the proposed method. This method focuses on simple paths which generate large networks, and finds the eigenvalues of the network via analysis of the simple generators. Group theory is the main tool, which is improved using the concept of graph products. As a mechanical application of the method, a benchmark problem of group theory in structural mechanics is studied in this paper. Vibration of cable nets is analyzed and the frequencies of the networks are calculated using the combined graph-group method.     

Synthesis and comparative characterization of Al,B, Ga,and Fe containing Nu-1-type zeolitic framework

We synthesized four different Nu-1-type zeolites containing, respectively, Al, B, Ga, and Fe as the trivalent element. With the exception of B-Nu-1, the synthesis is difficult because of the competitive formation of other crystalline phases as sodalite, ZSM-39-type, or glassy phases. The trivalent elements isomorphous substitution was demonstrated by X-ray powder diffraction, FTi.r., e.s.r., u.v.-Vis., and ²⁷Al, ¹¹B, and ⁷¹Ga-MAS-n.m.r. By the same techniques and t.g.a. measurements, we evaluated the thermal stability of the different Nu-1-type zeolites.     

纳米Si02在电镀锌三价铬钝化中的作用

我国镀锌层三价铬钝化膜的性能仍不完善,为了进一步增加钝化膜的耐腐蚀能力,将纳米SiO2加入到三价铬钝化液中,对电镀锌层进行常温彩色钝化-封闭同步处理。通过中性盐雾试验与电化学极化曲线对钝化膜的抗腐蚀性能进行评价。结果表明：钝化液中纳米SiO2含量为3．5g／L时,钝化液稳定,与三价铬共沉积,产生协同作用,钝化膜光亮,镀...     

Augmented canonical forms and factorization of graphs

The main aim of this paper is to generalize the previously developed canonical forms by different types of alterations and/or augmentations. These forms provide suitable tools for the decomposition of the matrices of special patterns and lead to efficient aproaches for calculating their eigenvalues. Methods were developed for factorization of symmetric graphs into smaller subgraphs using decompostion and healings (Commun. Numer. Meth. Engng 2003; 19 :125–136, 2004; 20 :133–146, 2004; 20 :889–910; Comput. Struct. 2004; 18 :2229–2240). Further factorization was possible only when further symmetries were available. The main drawback was associated with non‐decomposiblity of some of the factors in early stages of decomposition, and in particular healing which often destroyed the symmetry. In this paper, the mathematical concepts related to certain symmetric and unsymmetric graphs are developed, making refined factorization of the graphs feasible. Examples are included to show the simplicity of the operations being involved. Copyright © 2005 John Wiley & Sons, Ltd.     

High-order dark solitons in nonlocal nonlinear media

Abstract

The high-order dark solitons in nonlocal nonlinear media are found up to fifth-order. The stability of high-order dark solitons is investigated numerically. The stability relation graphs of negative imaginary eigenvalues versus propagation constant are obtained. The propagation graphs of the input signal with noise added prove the result of the stability analysis to be correct.     

CeO1.5-stabilized tetragonal ZrO2

Ceria-stabilized tetragonal zirconia polycrystals show high toughness and high resistance to the low-temperature ageing degradation. However, ceria is less effective in stabilizing tetragonal zirconia compared to yttria and other trivalent oxides. The tetravalent oxide of CeO₂ can be easily reduced to the trivalent CeO_1.5, but phase separations occur leading to the destabilization of the tetragonal phase or the stabilization of the cubic phase. A procedure of high-temperature sintering and low-temperature reduction has been developed for preparing CeO_1.5-stabilized tetragonal zirconia. It was found that 9 mol% CeO_1.5 could stabilize the tetragonal zirconia to room temperature and that the stability region in the CeO_1.5-ZrO₂ system was extended to the lower dopant content region. The CeO_1.5-stabilized tetragonal zirconia had a lower tetragonality and lower transformability compared to the CeO₂-stabilized tetragonal zirconia with the same dopant mole percentage. The changes in the phase composition, tetragonality and stability caused by the reduction of CeO₂ to CeO_1.5 have been discussed in relation to the changes of oxygen stoichiometry, which is considered of the firstorder importance in the stabilization of polymorphous zirconia.     

Graph coloration and group theory for factorization of symmetric dynamic systems

Summary In this article the concept of graph coloration for factorization of the characteristic polynomial of a weighted directed graph is introduced and using the fundamental lemma of Petersdorf and Sachs, it is shown that this concept can be extended to other spectra of graph among which is the spectrum of the Laplacian matrix of graphs. The goal is to use this concept for factorizing the graphs having different types of symmetry properties. In order to present an efficient algorithm, some concepts from group theory are needed. The combination of group theory and graph coloration provides a powerful method for factorizing various structural matrices, an example of which is the stiffness matrices of mass-spring dynamic systems.     

三价低熔点氧化物对TiO_2压敏电阻器性能的影响

研究了三价低熔点氧化物Ｓｂ２Ｏ３、Ｂ２Ｏ３等对ＴｉＯ２压敏电阻器性能的影响,采用扫描电镜、Ｃ－Ｖ分析、Ｉ－Ｖ测量和介电测量等实验手段,并结合理论分析了它们的作用机理。结果发现,适当掺入这类氧化物能促进晶体生长,还有助于形成ＴｉＯ２的粒界层,提高样品的非线性系数和稳定性,改善样品烧结性能     

Bifurcation and stability of a three‐hinged rod under a conservative load

The bifurcation solutions and their stability of a three‐hinged rod under conservative compressive force are investigated. The equations for the system are non‐linear, and possess some symmetry properties. The symmerty group concepts are employed to exploit these symmetry properties. The symbolic computer software, Mathematica, is used for the analytical and numerical solutions. The loci of codimension‐one singularity are plotted on a two‐dimensional control parameter space. These curves partition the parameter space into regions of qualitatively similar bifurcation diagrams. The bifurcation solutions and their stability at typical points in the parameter diagram, and the perturbation of codimension‐one singularities are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Stresses set up by rotation in limacon-shaped blades

Summary This paper deals with finding the stresses in steadily rotating limacon-shaped thin blades of homogeneous isotropic elastic material. The complex potentials, involving real parameters, have been obtained in closed form. Giving suitable values to the parameters involved, the solutions are derived for the following four positions of the axis of rotation: (a) the line of symmetry of the limacon, (b) any line perpendicular to the line of symmetry and lying in the plane of the blade, (c) any line passing through a point on the line of symmetry and perpendicular to the plane of the blade, (d) normal axis passing through the centroid. The hoop stress and its stationary points have been calculated in all the cases. The results have also been derived for circular blades. The numerical results are presented in the form of tables and graphs.     

Chromium electroplating from trivalent chromium baths as an environmentally friendly alternative to hazardous hexavalent chromium baths: comparative study on advantages and disadvantages

In this communication, we present a generalization of our investigations concerning current state in the development of trivalent chromium baths as an environmentally friendly alternative to hazardous electroplating baths containing extremely toxic hexavalent chromium compounds. The main technological properties of sulfate trivalent chromium baths containing carbamide and formic acid as organic additives are described and compared to those typical of common Cr(VI) plating bath. It is shown that thick nanocrystalline chromium–carbon deposits may be obtained from the Cr(III) electrolytes under study, with some physicochemical and service properties of such coatings exceeding those of “usual” chromium deposits. The proposed trivalent chromium baths are distinguished by their high current efficiency and electrodeposition rate. The covering power of the Cr(III) baths is poorer than in case of hexavalent chromium baths; it may be improved by applying basic chromium sulfate (chrome tanning agent) instead of chromium sulfate as a source of Cr(III) ions in solution. There is no need to utilize toxic lead anodes in Cr(III) deposition processes. It is noted that a grave shortcoming of trivalent baths is their low conductivity in comparison with the hexavalent ones.     

三价铬镀铬阳极的研究

三价铬镀铬在实际应用中最大的问题是工艺的稳定性差,而阳极是影响硫酸盐三价铬镀液稳定性的关键.阐述了硫酸盐三价铬镀铬阳极的制备方法及工艺条件,分别采用电化学方法、扫描电镜、赫尔槽试验测定了阳极的电化学性能、外观形貌及电镀性能;用强化寿命试验测定了阳极的强化寿命时间.在此基础上测定了自制专用阳极在硫酸盐三价铬镀液中所得镀层的外观形貌、结合力、孔隙率及耐蚀性等性能.结果表明:所制备的阳极使用寿命长,电镀及镀层性能好.     

Synthesis,characterization and optical properties of bismuth germanate doped with trivalent europium

Bismuth germanate single crystals doped with trivalent europium were grown by the Czochralski method. Procedures and results of synthesis experiments are reported. Microprobe analysis reveals the segregation of doped rare-earth elements. Spectroscopic studies of Eu³⁺ ions suggests C_3v point symmetry for the cationic site. Oscillator strengths and τ_λ parameters for Eu³⁺ were calculated.