Continuous extension of maps between sequential cascades

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for iterated contours of sequential cascades. A related problem of continuous extension of maps between maximal elements of sequential cascades to full subcascades is solved in full generality.     

Constructions of 1 1/2-designs from symplectic geometry over finite fields

In this paper, we construct some 1(1/2)-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1(1/2)-designs yield six infinite families of directed strongly regular graphs.     

Graphs obtained from Moufang loops and regular maps

Using ideas from regular maps, we prove the existence of infinitely many non‐vertex‐transitive Cayley graphs obtained from Moufang loops. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory     

Approximation of an optimal control problem governed by a differential parabolic inclusion

In this article, we investigate the optimal control problem governed by parabolic inclusion. We describe the Galerkin approximation and we demonstrate the existence of the strong condensation points of the set of solutions of approximate optimization problems. Each of these points is a solution of the initial optimization problem.     

Backlund变换理论发展简述及其新方法

本文首先简要介绍Bcklund变换理论的发展过程,然后介绍一种寻找微分方程Bcklund变换的新方法——wahlquist-Estabrook过程。该方法是目前处理微分方程Bcklund问题的最有效方法.尽管该方法在理论上可应用于任意维数的偏微分方程组,但是实际上它所能处理的主要是二维问题。例如,在应用该方法处理完整Navicr-Stokcs方程(四维问题)时,所得到的是无意义结果.但是,在应用该方法处理定常二维Navicr-Stokcs方程时,确实可以得到正常的Bcklund映射,以及Bcklund变换.     

Special properties of Eshelby tensor for a regular polygonal inclusion

When studying the regular polygonal inclusion in 1997, Nozaki and Taya discovered numerically some remarkable properties of Eshelby tensor: Eshelby tensor at the center and the averaged Eshelby tensor over the inclusion domain are equal to that of a circular inclusion and independent of the orientation of the inclusion. Then Kawashita and Nozaki justified the properties mathematically. In the present paper, some other properties of a regular polygonal inclusion are discovered. We find that for an N-fold regular polygonal inclusion except for a square, the arithmetic mean of Eshelby tensors at N rotational symmetrical points in the inclusion is also equal to the Eshelby tensor for a circular inclusion and independent of the orientation of the inclusion. Furthermore, in two corollaries, we point out that Eshelby tensor at the center, the averaged Eshelby tensor over the inclusion domain, and the line integral average of Eshelby tensors along any concentric circle of the inclusion are all identical with the arithmetic mean.The project supported by the National Natural Science Foundation of China (10172003 and 10372003) The English text was polished by Keren Wang.     

基于有限元理论绘制等高线的新方法

由于传统绘制等高线的方法存在很多的缺点，如相邻等高线不协调，等高线交叉重叠等．为了克服这些现象，提出了一种根据地形特征点自动绘制等高线的高效、简便、实用的新方法，其基本思想是建立在样条函数的力学模型基础上，利用弹性薄板的竖向位移比拟地形特征点的标高，从而利用有限元，高精度地绘制出等高线．还通过两个算例，利用有限元通用程序ANSYS进行绘制等高线，来进一步说明该方法的实用性．     

Nonlinear Dynamic Stability of Normal and Arthritic Greyhounds

In this paper the dynamic stability of greyhound gait was analyzed within the framework of nonlinear dynamics theory. A video based motion analysis system was utilized to obtain the kinematic data of the hindlimb joints of greyhounds at trot. Phase plane portraits and first return maps for the coxofemoral, femorotibial, and the tarsal joints were calculated from averaged kinematic data for each dog. The analysis was based on the assumption that the steady state dog locomotion could be represented as a nonlinear periodic system. Using the Floquet theory, the dynamic stability of gait was quantified by computing the characteristic multipliers from experimental data. A stability index based on multipliers was used for comparison between normal and arthritic dogs. Phase plane portraits and first return maps of the dogs with transient synovitis were compared with the averaged portraits of the normal dogs. It was observed that the coxofemoral angle exhibited the maximum difference while the femorotibial and the tarsal joints showed little or no difference from those of the normals. Comparison of the Floquet multipliers indicated that the dogs with synovitis had a less stable gait than that of the normal dogs.     

Use of Magnetic Resonance Imaging as a Tool for the Study of Foamy Oil Behavior for an Extra‐Heavy Crude Oil. T2 /Viscosity Correlation with Respect to Pressure

The purpose of this work is to present the results of the phase behavior study for a live heavy oil during a pressure depletion process using magnetic resonance imaging (MRI) as a tool to characterize foamy oil phenomena. The experiments were carried out in the pressure range of 13.1 to 1.4MPa. Signal intensity images were obtained at each pressure and with respect to time, that is, approximately for a total time of 3h after each pressure change. It is possible to see a variation in intensity across the sample. These changes can be associated with changes in mobility as well as segregation of the oil. It was also possible to observe that what we trust is the formation of gas channels at the last two pressure values, as it comes out of solution. A correlation between the transverse relaxation time T2 and temperature was established with the aim of producing one between T2 and viscosity. In this way viscosity maps for the live oil were obtained as a function of pressure and time. It was observed that above the bubble point, the viscosity maps varied from low to high to low with respect to time for the same pressure. Below the bubble point the situation is reverse. The viscosity map changes from high to low to high with respect to time for the same pressure. The study shows the potential use of MRI to follow viscosity changes during pressure depletion test in a PVT MRI cell.     

Two-dimensional lattice gases for regular binary mixtures

This paper reports on the development of two-dimensional lattice gas models for regular binary mixtures. In particular, results are reproduced concerning equilibrium solutions and an expression for the diffusion coefficient. In our model, a volume force is incorporated, and the system of macroscopic evolution equations resembles the Boussinesq approximation in convection theory. As an example, a lattice gas Rayleigh-Bénard system is considered. We conclude with a few remarks on implementation and optimisation of the program using a SIMD parallel computer.