运用直线参数方程简解高考解析几何题

本文笔者就以近几年各省份有关解几的高考题与模考题为例来说明直线参数方程的巧妙应用.

几题一章,结构化讲评——以“圆”学情调研试卷的讲评为例

“几题一章,结构化讲评”是选择试卷中同一章的几道核心题目,进行有效整合、归纳拓展,科学、合理、有序地组织学生进行数学探索的教学活动,这样的讲评既反映本章主要知识和思想方法,又从新的视角生成新的结构。教学的基本策略是试题问题化,问题结构化。教学的基本路径是用初始问题打好结构的地基,用动态问题浇筑结构的框架,用特殊问题夯实结构的节点,用小结问题显化结构的样态。

浅谈极坐标法在平面几何中的应用

本文对极坐标法解平几题进行分析：通过先取坐标、解题步骤、举例及注意的问题进行论证。

A New Rational Algebraic Approach to Find Exact Analytical Solutions to a （2＋1）-Dimensional System

In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.

Some Open Problems in Geometric Topologyof Low Dimensions

ＳｏｍｅＯｐｅｎＰｒｏｂｌｅｍｓｉｎＧｅｏｍｅｔｒｉｃＴｏｐｏｌｏｇｙｏｆＬｏｗＤｉｍｅｎｓｉｏｎｓ￥ＡｌｂｅｒｔｏＣＡＶＩＣＣＨＩＯＬＩ（ＤｅｐａｒｔｍｅｎｔＯｆＭａｔｈｅｍａｔｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＭｏｄｅｎａ，ＶｉａＣａｍｐｉ２１３／...

Stress on Ballast-Bed and Deterioration of Geometry in a Railway Track

In Greece extended cracking of twin-block concrete sleepers （ties） and fouling of the ballast-bed were observed with implied problems of gauge widening and deterioration of track＇s geometry. This led to a ten-year investigation program, during which a new method was developed for the estimation of actions on track panel as well as of the pressures / stresses that develop under the seating surface of the sleeper on the ballast-bed. Results from the tests performed on the ballast used in the Greek network are also presented, conducted in laboratories in France, Austria, and Greece. The influence of the actions -static and mainly dynamic- on the track response and the stress and strain of the ballast-bed are also discussed as derived from the tests and theoretical analysis.

ON THE HEILBRONN NUMBER OF n-NONCOLINEAR POINTS IN THE PLANE

In this article,we have given the definition of the Heilbronn number of n-noncollinear points in the plane. By this, we got the exact value of H5 which is the exact upper bound of H5 (K), where H5 (K) is any Heilbronn number in common sense.

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.

On Simultaneous Exact Controllability

We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as well as D. Russell. By using convenient modified multipliers we obtain an observability inequality provided suitable geometric condition on the domain is valid and the speed velocity of the models are related.

Fast image matching algorithm based on affine invariants

Feature-based image matching algorithms play an indispensable role in automatic target recognition （ATR）. In this work, a fast image matching algorithm （FIMA） is proposed which utilizes the geometry feature of extended centroid （EC） to build affine invariants. Based on at-fine invariants of the length ratio of two parallel line segments, FIMA overcomes the invalidation problem of the state-of-the-art algorithms based on affine geometry features, and increases the feature diversity of different targets, thus reducing misjudgment rate during recognizing targets. However, it is found that FIMA suffers from the parallelogram contour problem and the coincidence invalidation. An advanced FIMA is designed to cope with these problems. Experiments prove that the proposed algorithms have better robustness for Gaussian noise, gray-scale change, contrast change, illumination and small three-dimensional rotation. Compared with the latest fast image matching algorithms based on geometry features, FIMA reaches the speedup of approximate 1.75 times. Thus, FIMA would be more suitable for actual ATR applications.

Duality of Unary Convex Functions Programming

Most nonliner programming problems consist of functions which are sums of unary,convex functions of linear fuctions.In this paper.we derive the duality forms of the unary oonvex optimization, and these technuqucs are applied to the geometric programming and minimum discrimination information problems.

考试悲剧

上课铃响了,老师抱着一大摞试卷来了。原本吵闹的教室一下子安静了下来。有的同学摆弄着自己的笔,有的同学安静地坐着,一声也不吭。我的心里好像装了一只小兔,忐忑不安,就怕考试太难。试卷发下来了,同学们开始翻看题目。我浏览了前几题,不是很难,准备开始答卷。教室里一片寂静,只能听见笔的“唰唰”声和修正带的“咔嚓”声。

A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides

In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry.With the use of the direct global matrix approach,this method is numerically stable.In addition,by introducing appropriately normalized range solutions,this model is free from the numerical overflow problem.Furthermore,we put forward source conditions appropriate for the line-source problem in plane geometry.As a result,this method is capable of addressing the scenario with a line source on top of a sloping bottom.Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column.The numerical simulations indicate that the proposed model is accurate,efficient,and numerically stable.Consequently,this model can serve as a benchmark model in range-dependent propagation modeling.Although this method is verified by an ideal wedge problem in this paper,the formulation applies to realistic problems as well.

Efficient design of rotary traveling wave oscillator array via geometric programming

This paper presents an efficient method for globally optimizing and automating component sizing for rotary traveling wave oscillator arrays. The lumped equivalent model of transmission lines loaded by inverter pairs is evaluated and posynomial functions for oscillation frequency, power dissipation, phase noise, etc. are formulated using transmission line theory. The re- sulting design problem can be posed as a geometric programJning problem, which can be efficiently solved with a convex opti- mization solver. The proposed method can compute the global optima more efficiently than the traditional iterative scheme and various design problems can be solved with the same circuit model. The globally optimal trade-off curves between competing objectives are also computed to carry out robust designs and quickly explore the design space.

On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov＇s positive annulus in R^3.

ALMOST GLOBAL EXISTENCE OF DIRICHLETINITIAL-BOUNDARY VALUE PROBLEM FORNONLINEAR ELASTODYNAMIC SYSTEMOUTSIDE A STAR-SHAPED DOMAIN

This paper deals with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a star-shaped domain. The almost global existence of solution with small initial data to this problem is proved and a lower bound for the lifespan of solutions is given.

Global Geometry of 3-Body Motions with Vanishing Angular MomentumⅠ

Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）. In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.

The Cauchy problem of generalized Landau-Lifshitz equation into S^n

In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.

Algebraic solution of differential geometric guidance command and time delay control

According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution is much simpler and better for the further research of the characteristics of DGGC.Time delay control(TDC)is a useful method to tackle the uncertainty problem of a control system.Based on TDC,taking the target maneuvering acceleration as a disturbance,the estimation algorithm of the target maneuvering acceleration is presented,which can be introduced in DGGC to improve its performance.Then,the augmented DGGC(ADGGC)is obtained.The numerical simulation of intercepting a high maneuvering target is conducted to demonstrate the effectiveness of ADGGC.