摩擦承重实验的设计及分析

介绍了三种演示摩擦承重的实验方法，并进行了有关分析。     

Speckle time evolution characterization by the co-occurrence matrix analysis

We describe some aspects of the measurement of dynamic speckle activity. We propose the use of the co-occurrence matrix of the time history of the intensity of a speckle pattern. Then we suggest a measure of the activity based on the use of one of its second order moments. Some numerical simulations were performed for testing purposes. The method was applied to the study of the drying of paint and was compared with gravimetric measurements. Experimental results obtained are shown and a good correlation is obtained.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

Parity patterns associated with lifts of Hecke groups

Let q be an odd prime, m a positive integer, and let Γ _m (q) be the group generated by two elements x and y subject to the relations x ^2m =y ^qm =1 and x ²=y ^q ; that is, Γ _m (q) is the free product of two cyclic groups of orders 2m respectively qm, amalgamated along their subgroups of order m. Our main result determines the parity behaviour of the generalized subgroup numbers of Γ _m (q) which were defined in Müller (Adv. Math. 153:118–154, 2000), and which count all the homomorphisms of index n subgroups of Γ _m (q) into a given finite group H, in the case when gcd (m,| H |)=1. This computation depends upon the solution of three counting problems in the Hecke group ℋ(q)=C ₂*C _q : (i) determination of the parity of the subgroup numbers of ℋ(q); (ii) determination of the parity of the number of index n subgroups of ℋ(q) which are isomorphic to a free product of copies of C ₂ and of C _∞; (iii) determination of the parity of the number of index n subgroups in ℋ(q) which are isomorphic to a free product of copies of C _q . The first problem has already been solved in Müller (Groups: Topological, Combinatorial and Arithmetic Aspects, LMS Lecture Notes Series, vol. 311, pp. 327–374, Cambridge University Press, Cambridge, 2004). The bulk of our paper deals with the solution of Problems (ii) and (iii). Research of C. Krattenthaler partially supported by the Austrian Science Foundation FWF, grant S9607-N13, in the framework of the National Research Network “Analytic Combinatorics and Probabilistic Number Theory”.     

Arithmetical thinking in children attending special schools for the intellectually disabled

This article focuses on spontaneous and progressive knowledge building in “the arithmetic of the child.” The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical interviews. Theoretical models elucidate behavior patterns and the corresponding mental structures underlying them. The individual interviews of the pupils were video recorded. The results show that the activated behavior patterns, which are responses to well-adapted contexts presented by the researcher, are compatible with findings in Swedish compulsory schools. Six of the pupils’ mental structures in the study are numerical. A substantial implication for special education is the harmonization of the content in teaching with the children's own ways of operating, which implies a triadic teaching process.     

The extent to which triangular sub-patterns explain minimum rank

For any zero-nonzero pattern of a matrix, the minimum possible rank is at least the size of a sub-pattern that is permutation equivalent to a triangular pattern with nonzero diagonal. For certain numbers of rows and columns, the minimum rank of a pattern is k only when there is a k-by-k such triangle. Here, we complete the determination of such sizes by showing that an m-by-n pattern of minimum rank k must contain a k-triangle for m=5, k=4; m=6, k=5; and m=6, k=4. A table is given showing whether or not this happens for all m, n, k. In the process, a Schur complement approach to minimum rank is described and used, and simple ways to recognize the presence of triangles of sizes less than 7 are given.     

Some flower-like gaits in the snakeboard’s locomotion

The snakeboard is a modified version of the skateboard in which the front and back pairs of wheels can pivot freely about a vertical axis (see Fig. 1). The rider can generate motion by coupling a turning of his/her feet which lie on wheel platforms with an appropriate twisting of his/her body without kicking off the ground. The snakeboard was first presented in details by [Lewis et al., in Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, USA, May 1994, pp. 2391–2400]. In literature, it also has been studied as a prototype of the symmetrical nonholonomic locomotion systems. Geometrical modeling, finding the gaits, presenting the controllability ideas and designing desired trajectories are the subjects that can be found in the literature of the snakeboard. In this paper, we present some symmetric sensitive flower-like gaits for the snakeboard by suitable tuning of the input parameters. The highly symmetric patterns generated by these gaits, besides their inherent beauty, sensitivity to parameter variations and coherency; exemplify the rich information content of the underlying nonlinear system.     

Single machine stochastic JIT scheduling problem subject to machine breakdowns

In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.     

Model for evolution of periodic layered structure in the SiO2/Mg system

A mathematical model for the growth of MgO/Mg₂Si periodic layered structure (PLS) is presented based on Fick's diffusion law and conservation of matter. The model explains the temporal evolution of the width of periodic layers at different temperatures, for layers distant enough from the Mg source. It is demonstrated that the difference in thickness of a pair of any two adjacent layers decreases with increasing temperature.