Approximating the relationship among the degree of the reaction forces and the nodes on footprint during a stance phase

This study examined the foot biomechanics that are utilized when foot is in contact with the ground during a stance phase. The purpose of the study was to investigate the normalized ground reaction forces that impacted certain sections and points on the footprint, and to identify patterns in the degrees to which these forces occurred. Foot was modeled in such a manner that a vertex represented a bone and an edge represented a joint, and a graph that depicted the foot was created. Twelve nodes were marked on the footprint and these were linked together to create a gait path. By fusing the graph and the gait path and by manipulating the mathematical models, a profile for an ideal bipedal walking locomotion was developed. A male subject performed bipedal walking through a force plate system in order to obtain the profile that reflected actual bipedal walking. The actual and the proposed profiles were compared and there were significant similarities between the two profiles, with both exhibiting an double-bump pattern. It is therefore viable that the approximation techniques proposed in this work may provide an alternative means over the application of a force plate system to generate a profile for bipedal walking. However, the accuracy and reliability of the results yielded from this technique need further investigation.     

Modelling and simulation of wave transformation in porous structures using VOF based two-phase flow model

This paper represents the results of wave transformation in porous structures and hydraulic performance of a vertical porous seawall. The study was carried out using a VOF based two-phase numerical hydrodynamic model. The model was developed by coupling an ordinary porous flow model based on extended Navier–Stokes equations for porous media, and a two-phase flow model. A unique solution domain was established with proper treatment of the interface boundary between water, air and the structure. The VOF method with an improved fluid advection algorithm was used to trace the interface between water and air. The resistance to flow caused by the presence of structural material was modeled in terms of drag and inertia forces. The parameters that govern resistance to flow in a porous media were calibrated for a typical structural setup and then the computational efficacy of the model was evaluated for several wave and structural conditions other than the calibrated setup. A set of comparisons of wave properties in and around the structure showed that the model reproduced reasonably good agreement between computed results and measured data. The model was then applied to investigate wave transformation in a vertical porous structure. The role of porosity and width of a structure in reducing wave reflection and increasing energy dissipation was investigated. It is confirmed that there exists an optimum value of structure width and porosity that can maximize hydraulic performances of a porous seawall.     

Finding Sets of Points without Empty Convex 6-Gons

Abstract. Erd?s asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast incremental algorithm for finding such 6-gons was designed and implemented and a heuristic search approach was used to find promising sets. The experiments also led to two observations that might be useful in proving that large sets always contain an empty convex 6-gon.     

管道内激波的不稳定性

本文将无限大激波阵面的激波不稳定性理论[1]推广到矩形截面管道内的激波不稳定性问题.首先,给出这个问题的数学提法,包括扰动方程与三类边界条件.其次,给出扰动方程的普遍解.上游和下游的普遍解分别含有5个待定常数.再次,在一类边界条件和一个假定下,证明了激波前扰动为0,激波后两个声扰动之一为0.边界条件是,X→±∞处扰动物理量为0.假定只讨论激波不稳定性问题,从而可先设ω=iγ,γ是不稳定性增长率,为正实数.另一类边界条件是管壁上法向速度扰动为0,它使波数只能取一组离散值.最后,用扰动激波上的5个守恒方程这一边界条件来决定激波后4个待定常数和扰动激波振幅这个未知量时,导出了色散关系.结果表明,正实数γ确是存在.不稳定激波有两种模式,一种模式为γ=-W·k(W<0)它代表激波的绝对不稳定性,是新得到的模式.另一种模式与过去工作中给出的[2,3]大体相同.本文则进一步给出了这种模式的激波不稳定性增长率,并指出j2((?V/?P)_H=1+2M为最不稳定点(即无量纲化的不稳定性增长率Г=∞).如果不假定ω是纯虚数,而是复数,其虚部为正实数Im(ω)≥0.本文也严格证明了其不稳定性判据仍有两种模式,ω仍为纯虚数.     

非传播孤立波及其相互作用的数值模拟

通过数值求解由Miles导出的目前公认的的非传播孤立波的控制方程——一个带复共轭项的非线性立方SchrLdinger方程,对非传播孤立波进行研究。讨论了Miles方程中的线性阻尼系数α的值,计算表明,线性阻尼α对形成稳定的非传播孤立波影响很大,Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件,而不是充分条件。模拟了两个非传播孤立波的相互作用,数值模拟表明,两个波的作用模式依赖于系统的参数,对不同的初始扰动及其演化的计算表明,只有适当的初始扰动才能形成单个稳定的非传播孤立波,否则扰动可能消失或发展成多个孤立波。     

BCHK-代数的亚原子

在BCHK-代数中引入了亚原子的概念,给出了亚原子的一些性质.证明了有限偏序BCHK-代数一定存在亚原子,且X\{0}等于其所有亚分支的并集.证明了一个BCHK-代数的亚原子和元素0做成的集合是X的一个子代数,不变亚原子和元素0做成的集合是X的一个理想.     

The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions

The immaculate basis of the non-commutative symmetric functions was recently introduced by the first and third authors to lift certain structures in the symmetric functions to the dual Hopf algebras of the non-commutative and quasi-symmetric functions. It was shown that immaculate basis satisfies a positive, multiplicity free right Pieri rule. It was conjectured that the left Pieri rule may contain signs but that it would be multiplicity free. Similarly, it was also conjectured that the dual quasi-symmetric basis would also satisfy a signed multiplicity free Pieri rule. We prove these two conjectures here.     

Finding Sets of Points without Empty Convex 6-Gons

   Abstract. Erd?s asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast incremental algorithm for finding such 6-gons was designed and implemented and a heuristic search approach was used to find promising sets. The experiments also led to two observations that might be useful in proving that large sets always contain an empty convex 6-gon.     

Issues of feasibility,coherence, and robustness in a premise-to-claim model of argumentation: Results from four experiments

The paper considers several issues. (1) The feasibility of a premise to claim model of dialogue: the results show that a rule-based system can generate claims in the same sequence as they appear in a real discussion. (2) The relationship between the increased knowledge created in the leap from premise to claim on the perceived coherence and comprehensibility of dialogue: the system’s reaction to making available all premises before run time was to provide a rapid summary of the debate, whereas the result of randomly rearranging the order of introduction of premises showed that the majority of claims were still made, and that a very similar sequence of claims was followed; for the first half the observed sequence was taken by the simulation program, because initially the number of (randomly introduced) premises was so small that they did not match the available warrants. (3) Robustness of a rule-based argumentation system in the face of expert fallibility: the test condition here was a reduced set of rules (as a proxy for lack of expert knowledge) which however, showed an overall convergence to the same claims in the same sequence as when all the rules were used.     

Production scheduling with applications in the printing industry

This paper presents a technique for the solution of scheduling problems encountered in a printing company that can be applied to a range of practical industrial problems. The aim of the research was to develop a due date scheduling algorithm within the framework of the scheduling system already in use by the company. The objective was to enable jobs to be scheduled as close to their due dates as possible, while ensuring that the resultant schedule was feasible with respect to work centre capacities and earliest start date constraints.     

Woodhouse, babbage, peacock, and modern Algebra

In a recent article, J. M. Dubbey [Historia Mathematica 4 (1977), 295–302] showed that George Peacock's A Treatise on Algebra (1830) was similar to an unpublished work written by Charles Babbage in 1821. Evidently perplexed about the absence of a dispute over priority, Dubbey concluded that Peacock had unconsciously assimilated Babbage's ideas, and that Babbage was too busy with other activities to be concerned. The thesis of this article is that the innovative aspects of the work of both Babbage and Peacock are extensions of ideas put forth in 1803 by Robert Woodhouse, and that probably neither Babbage nor Peacock was overly concerned with acknowledgments because their approach to algebra was not unique at Cambridge.     

From Planning Board to Welding Hall: A Case-Study in O.R./Client Involvement

Danish shipyard building supertankers was faced with a production-planning problem in one of its welding-halls, where the bow and stern sections were fabricated. The mandatory constraint of completing each section by a specified day in the production cycle was complicated by a number of other practical constraints. A trial exercise demonstrated that human skills were unbeatable in solving aspects of planning concerned with fitting shapes into spaces-and that the major planning problems were keeping track of planning-progress and computing the labour load. An interactive planning computer-system was devised which gave full rein to the complementary skills of planner and computer. This system had the merit, from management's point of view, that the fullest use could be made of existing planning expertise. The system was designed and implemented in stages over about four months: training sessions at each stage provided valuable input for the design of the next stage.     

Integrating Science and Mathematics: Perceptions of Preservice and Practicing Elementary Teachers

One hundred and sixty-one undergraduate elementary education majors and sixty elementary teachers completed an eight-item questionnaire designed to assess their perceptions toward integrating science and mathematics in the elementary grades. The two groups of subjects differed significantly on their responses to five of the eight items. Chi square analyses suggest that practicing elementary teachers felt they had more background in mathematics and science, were more aware of curriculum materials in this area, did not think that integration was currently a common practice, and were more likely to indicate that there was not sufficient time in the school day to integrate the subjects. Preservice teachers were more likely to indicate that integrating the disciplines was preferred to teaching them separately. In addition to the analyses of data, a list of recommendations are provided for teachers, curriculum developers, and policy makers interested in advancing the concept of integrating science and mathematics in instruction.     

Simple calculation of moments of inertia for polygons

Recently the problem of finding the mass, centre of gravity and moments of inertia for laminae bounded by polygons arose in a programming course for first year civil engineering degree students. It was suggested that it would be useful for them to construct a program that would take as input the vertices of the polygon, and print out area, centroid and moment of inertia. In order to make the program have a logically simple structure, the method presented in this note was devised. After consultation with many standard textbooks and engineering handbooks it was discovered that the method was either original or completely neglected. Since in many respects the method compares favourably with the subdivision techniques of the standard sources it would appear to be worth publicising the technique.     

动载荷下不可压缩超弹性球形薄膜的若干定性性质

对于由横观各向同性不可压缩的Rivlin-Saunders材料组成的球形薄膜,研究了薄膜的内、外表面在周期阶梯载荷作用下的轴对称变形的非线性动力学特性．通过令球形结构的厚度趋近于1,得到了近似描述薄膜径向对称运动的二阶非线性常微分方程．详细讨论了解的定性性质．特别地,给出了球形薄膜随时间的运动产生非线性周期振动的可控性条件,证明了在某些情形下周期振动的振幅会出现“∞”型同宿轨道以及周期振动的振幅会出现不连续增长现象,并给出了相应的数值模拟．     

A Cutting Stock and Scheduling Problem in the Copper Industry

This case study was carried out for Thomas Bolton Ltd, a copper component manufacturer. The focus was on the first major production operation that is carried out in the foundry. This operation consists of three processes — melting scrap metal, casting it as ‘logs’ and cutting logs into ‘billets’. The timely production of the billets is essential as these feed a bottleneck process. The objective of the study was to investigate alternative methods of generating a production plan for the foundry that minimized costs whilst meeting the demand for billets at the bottleneck. The production plan was required to include a daily production schedule and a list of the cutting patterns to use when cutting the logs into billets. Thus, both the scheduling and cutting stock problems were addressed. A two-stage solution procedure was proposed. Alternative heuristic methods were investigated at the first stage and an optimal solution using Integer Programming (IP) was proposed for the second stage. It is shown that current performance could be improved using all of the heuristics considered at the first stage, but that using an IP-based heuristic method gives the best results.     

The use of an atomizer for chemical pleurodesis

Summary An atomizer had been designed that could create an aerosol of a liquid with high viscosity. The amount of additional driving gas that had to be used was very low. In a cooperation with the University Hospital in Zurich the atomizer was miniaturized and used for treating six patients.     

Analytical solution of coupled soil erosion and consolidation equations by asymptotic expansion approach

In this work, one-dimensional approximation of internal erosion taking place in a soil made from sand and clay mixture was considered. The clay phase that is susceptible to experience erosion under water flow discharge was assumed to be small. A new erosion law fixing the initiation threshold of erosion and integrating the effect of soil consolidation on internal erosion was proposed. Conversely, the effect of erosion on elastic soil deformation was also integrated through damage mechanics concepts. Asymptotic expansion of the coupled equations in terms of a perturbation parameter linked to the total amount of internal erosion that is likely to occur has been performed. This has enabled to view the internal erosion phenomenon occurring inside the soil as a perturbation affecting the classical soil consolidation equation, and further to evaluate the critical discharge gradient for which internal erosion starts. Equations at order zero that are provided by the asymptotic expansion were exactly integrated while an adequate finite difference scheme was introduced to solve the equations at order one. A parametric study was conducted after that in order to assess effects of the main factors on internal erosion and soil deformation.     

两相流体非线性渗流模型及其应用

基于三参数非线性渗流运动定律、质量守恒定律及椭圆渗流的概念,建立了低渗透介质中两相流体椭圆非线性渗流数学模型,运用有限差分法与外推法求得了其解,导出了两相流体椭圆非线性渗流条件下油井见水前后开发指标的计算公式,进行了实例分析。结果表明:非线性渗流对含水饱和度分布影响较大;非线性渗流使得水驱油推进速度比线性渗流的快,使油井见水时间提前,使得石油开发指标变差;非线性渗流使得同一时刻的压差比线性渗流的大,使石油开发难度加大。这为低渗油藏垂直裂缝井开发工程提供了科学依据。