Link polynomials derived from magnetic graphs

We introduce a graph diagram which can be regarded as a generalized link diagram. By using it, we construct two polynomial invariants for knots and links which are distinct from both the HOMFLY and the Kauffman polynomials. We show some features of the polynomials including relationships with the HOMFLY and the Kauffman polynomials.     

Systeme Binaire AgNO3-LiNO3. Diagramme de phases et proprietes thermodynamiques des mélanges a l’etat liquide

To study the coherence of thermodynamic data of the AgNO₃-LiNO₃ -RbNO₃ ternary system, phase diagram of the binary system AgNO₃ -LiNO₃ has been obtained between 303 and 550 K by direct and differential thermal analysis technique. This system is characterized by an eutectic point (25% mol. LiNO₃ , 445±1 K) and a plateau due to the solid-solid transition in AgNO₃ at 434±1 K. In the solid state the solubility of each component in the other seems to be nil or negligible (no more than a few percents). Using other thermodynamic data, the excess properties of the binary liquid (AgNO₃ - LiNO₃ ) were calculated at 623 K. This revised version was published online in August 2006 with corrections to the Cover Date.     

Impedance of faradeic process with partial charge transfer

The electrochemical impedance of charge-transfer reaction involving the stages of adsorption and desorption of intermediate partially charged substance is analyzed theoretically in the frequency-potential plane in order to study the possibility for measuring the partial charge transfer. The simplest case of adsorption two-electron transfer, namely, the Langmuir adsorption with liner dependence of reaction rate on the coverage, is considered. It is assumed that the partial charge transfer is independent of the electrode potential.     

Computing the Topological Entropy for Piecewise Monotonic Maps on the Interval

A new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented. It uses a transition matrix associated with the transformation. For this matrix we give a spectral theorem. This can be used for an estimation of the accuracy of the algorithm.     

Verifying a new identity for Green’s functions of the n=1 supersymmetric non-Abelian Yang-Mills theory with matter fields

We use the higher covariant derivative regularization to investigate a new identity for Green’s functions. It relates certain coefficients of the matter superfield vertex function for which one of the external matter legs is not chiral. Calculations in the first nontrivial order (for the two-loop vertex function) demonstrate that the new identity also holds in the non-Abelian Yang-Mills theory with matter fields. We demonstrate that the new identity follows because the three-loop integrals determining the Gell-Mann-Low function are integrals of total derivatives. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 270–281, August, 2008.     

Two novel methods for vibration diagnosis to characterize non-linear response

Poincaré maps have been proved to be a valuable tool in the analysis of non-linear dynamical systems, which usually reduce a continuous phase flow into a two-dimensional discrete map. However, they may be inconvenient for reflecting some characteristics of the system response. In this paper, two novel methods, using the period sampling peak-to-peak value (PSP) diagram and the modified Poincaré map, are presented for characterizing different types of non-linear response. These two methods take advantage of some parameters of the response, such as the peak-to-peak value within an exterior excitation period and the mean value of the displacement. In the PSP diagram method, a two-dimensional graph is plotted by taking the peak-to-peak value as ordinate and the sequential periodically sampling number as abscissa. On the other hand, the modified Poincaré map takes the mean value of the velocity within an exterior excitation period as ordinate and the relevant mean value of the displacement as abscissa. The non-linear responses of a Duffing system, a pendulum with circular motion support and an oscillating circuit are studied by these methods. We also studied the intermittent chaos of the Lorenz system by the PSP diagram method. The PSP diagram is a set of mapping points, which form: a straight line for a one-period response; multi-straight lines for a multi-period response; orderly periodic curves for a quasi-period response; long lines interrupted by transitoriness confusion points for intermittent chaos; and totally out-of-order points for chaos. The figures for the modified Poincaré maps for the period, multi-period, quasi-period responses and chaos are almost identical to those for the Poincaré maps, but the modified maps take more sampling points and can reflect the mean values of the responses. Some numerical results are given based on these methods to show their efficiency in distinguishing different non-linear responses.     

Numerical simulations of the steady Navier–Stokes equations using adaptive meshing schemes

In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible Navier–Stokes equations by finite element discretization. The mesh refinement and optimization are performed based on an algorithm that combines the so‐called conforming centroidal Voronoi Delaunay triangulations (CfCVDTs) and residual‐type local a posteriori error estimators. Numerical experiments in the two‐dimensional space for various examples are presented with quadratic finite elements used for the velocity field and linear finite elements for the pressure. The results show that our meshing scheme can equally distribute the errors over all elements in some optimal way and keep the triangles very well shaped as well at all levels of refinement. In addition, the convergence rates achieved are close to the best obtainable. Extension of this approach to three‐dimensional cases is also discussed and the main challenge is the efficient implementation of three‐dimensional CfCVDT generation that is still under development. Copyright © 2007 John Wiley & Sons, Ltd.     

Physical chemistry of binary organic eutectic and monotectic alloys; 1,2,4,5-tetrachlorobenzene−β-naphthol and 1,2,4,5-tetramethylbenzene-succinonitrile systems

Phase diagrams of 1,2,4,5-tetrachlorobenzene–β-naphthol and 1,2,4,5-tetramethylbenzene–succinonitrile systems which are organic analogues of a nonmetal–nonmetal and a nonmetal–metal system, respectively, show the formation of a simple eutectic (melting point 103.7°C) with 0.71 mole fraction of β-naphthol in the former case and a monotectic (melting point 76.0°C) with 0.07 mole fraction of succinonitrile and a eutectic (melting point 52.5°C) with 0.97 mole fraction of succinonitrile in the latter case. The growth behaviour of the pure components, the eutectics and the monotectic studied by measuring the rate of movement of the solid–liquid interface in a capillary, suggests that the data obey the Hillig–Turnbull equation, v=u(ΔT)ⁿ, where v is the growth velocity, ΔT is the undercooling and u and n are constants depending on the nature of the materials involved. From the values of enthalpy of fusion determined by the DSC method using Mettler DSC-4000 system, entropy of fusion, interfacial energy, enthalpy of mixing and excess thermodynamic functions were calculated. The optical microphotographs of pure components and polyphase materials show their characteristic features.     

对用稳定图识别真假模态的一点改进

利用单位样值响应矩阵和自由响应的特征值分解形式中的特征值前的系数矩阵的范数作稳定判据，结合稳定图识别真假模态，计算表明，本方法具有较好的分解能力。