初中数学“锐角三角比”的常见应用及教学策略浅析

近几年上海中考数学试卷中动态几何问题出现比重越来越大,并且在动态几何问题中出现一种新题型,即在图形的变换过程中,探究图形中某些不变因素,它把操作、观察、探求、计算和证明融合在一起.笔者通过对上海2007—2016年共10年中考数学试卷统计发现,锐角三角比在应用题、等腰三角形、二次函数、圆中出现的次数分别为5次、5次、10次、6次,并通过分析中考题中锐角三角比在上述四方面的应用,与读者一同探索未来上海中考出题的动向和策略.

Fractal identification of wear debris group in sliding wear process

Fractal geometry was used to describe the distribution characteristics of wear debris group collected from pin-on-disc wear tester under dry friction conditions, and experimental study and theoretical analysis were made for the distribution features of wear debris group. It was found that the wear debris size distribution conforms to the fractal distribution law. Two numerical parameters, fractal dimension D and scale coefficient C, were defined with their geometric and tribological meanings and calculating methods given. It was discovered that these two parameters can be used to describe the variation law of wear status, which provide the basis for diagnosis and prognosis of tribological systems.

Dynamic Geometry Monitoring System and Its Application in Sutong Bridge Construction

The construction period of large cable-stayed bridges is long, and the structure deformation is complicated. Any error during construction will potentially affect the cantilever alignments and the internal forces. In order to ensure safety during construction and exactly determine the cantilever alignments, dynamic deformation monitoring is needed immediately when the con struction of the superstructure starts. This paper aims at the requirement of deformation monitoring during the Sutong Bridge construction, and introduces the realization and observing schemes of the GPS and georobot based on remote real-time dynamic geometrical deformation monitoring system, then researches the data processing methods and enumerates some of the application achievements. Long-term operation during the Sutong Bridge construction indicates that the system runs steadily and the results are reliable.

A SURVEY ON SEMI-TENSOR PRODUCT OF MATRICES

Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.

A New Fractal Model of Elastic,Elastoplastic and Plastic Normal Contact Stiffness for Slow Sliding Interface Considering Dynamic Friction and Strain Hardening

The deflection properties of elastic stage, elastoplastic stage and plastic stage of elastomer were analyzed. Taking account of the kinetic friction force in friction interface and strain hardening in slow sliding interface, the elastic, elastoplastic and plastic normal contact stiffness model for harsh surface was established, which revised the Majumdar-Bhushan fractal model and made it more perfect. In the combination of macro and micro perspective, the effects of coarse surface fractal variables, kinetic friction force in the friction interface, material characters of the friction couples on the contact status and contact property were discussed by the study of digital analysis. Results imply that the normal contact stiffness improves with the increasing real contact area and normal contact load, and reduces with the augment of kinetic friction coefficient. When the kinetic friction coefficient is smaller than 0.3, the normal contact stiffness comprises a linear decrease with the increment of kinetic friction coefficient. When the kinetic friction coefficient is bigger than 0.3, the normal contact stiffness has an exponential decrease with the increasing kinetic friction coefficient. © 2017, Shanghai Jiaotong University and Springer-Verlag GmbH Germany.

Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions

An approach is presented to investigate the nonlinear vibration of stiffened plates.A stiffened plate is divided into one plate and some stiffeners,with the plate considered to be geometrically nonlinear,and the stiffeners taken as Euler beams.Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system.Besides,the effect caused by boundary movement is transformed into equivalent excitations.The first approximation solution of the non-resonance is obtained by means of the method of multiple scales.The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method.The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS.Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance.In addition,the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out.Some nonlinear vibration characteristics of stiffened plates are obtained,which are useful for engineering design.

A method of separating blended images in space debris observation

Due to the relative movement between space debris and background stars,the blending of objects and stars is ineluctable through observation.It brings down position accuracy of objects and even makes the tracking break down in worse conditions.In view of the difference of geometry between stars and objects in space debris observation,a technique for separating blended objects based on mathematical morphology is presented.It's sufficiently flexible to be applied in image processing,and the blending images can be separated effectively with a high degree of centroid precision.