中考新亮点——"空间几何"

空间几何题是中考试题体现新课程标准理念的一个新亮点，它对重视培养学生空间观念，发展空间想象能力和几何直觉能力等起到了良好的导向作用．现将有关题型略作归类评析，供同学们复习时参考．

小学生学习几何的特点

弗赖登塔尔认为，所谓几何就是把握空间，而这个空间对小学生来说，就是他们生活和运动的空间。因此，“几何”又称为“空间几何”，从严格意义上讲，空间几何主要就是研究事物的空间形式或关系的一门学科。小学数学课程的空间几何是几何学中最基础的部分，是一种直观几何，或称之为经验几何、实验几何，是存在于不太严密的局部组织之中的。小学生刚接触几何的时候，往往觉得学起来很困难，下面笔者就来研究一下小学生学习几何的特点，从而为教师教学提供方向。

The Growth and 1/4-Theorems for Spirallik Maps in l^P, B^P and Inner Product Space

The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.

Weighted Composition Operators between Hardy Spaces on the Unit Ball

We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.

A Remark on Concircularly Flat Totally Real Minimal Submanifolds in CP^n

Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.

Pressure gradient errors in a covariant method of implementing theσ-coordinate:idealized experiments and geometric analysis

A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.

Again Sharpening of a Negative ExponentGeometric Inequality in the Space E^n

Let P be arbitrary a point inside the simplex A in the n-dimensional Eucidean spaceEn . Let di be the distance from the point P to the correspondent hyperplane of vertex Ai of A.Let r denote the inradius of A. In this paper,we obtain a very strong negative eaponent geometric inequatity of contact with d1,d2,...,dn+1 and r.

Alignments, Topologies, Convex Geometries and Higgs Spaces

Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary （that is, not necessarily finite） aligned, topological and Higgs spaces.

Volume of unit ball in an n-dimensional normed space and its asymptotic properties

Let Bp^n={x∈R^b｜‖x‖p≤1} be the unit ball of p norm in the n-dimensional normed space εp＆n.The formula for the volume of Bp^n was obtained and its asymptotic properties were found out as n→∞and p→∞.

Analysis on a Set of 12-parameter Rectangular Plate Element with High Accuracy

It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini＇s element＇s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.

A multiple watermarks algorithm for image content authentication

A novel multiple watermarks cooperative authentication algorithm was presented for image contents authentication.This algorithm is able to extract multiple features from the image wavelet domain,which is based on that the t watermarks are generated.Moreover,a new watermark embedding method,using the space geometric model,was proposed,in order to effectively tackle with the mutual influences problem among t watermarks.Specifically,the incidental tampering location,the classification of intentional content tampering and the incidental modification can be achieved via mutual cooperation of the t watermarks.Both the theoretical analysis and simulations results validate the feasibility and efficacy of the proposed algorithm.

Extensions and Refinements of Adamovic's Inequality

In this article, by means of the theory of majorization, Adamovic's inequality is extended to the cases of the general elementary symmetric functions and its duals, and the refined and reversed forms are also given. As applications, some new inequalities for simplex are established.

SOLVING THE PROPAGATION OF ELECTROMAGNETIC WAVE IN A SIMPLE TWO-DIMENSIONALINHOMOGENEOUS MEDIUM BASED ON SYMPLECTIC GEOMETRICAL THEORY

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic wave in the two-dimensional inhomogeneous medium is used in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining with the geometrical optics. The drawback that the solution in the caustic region can not be obtained with geometrical optics is overcome by this method. The results coincide well with that of finite element method.

Geometric Structures and Field Equations of Dirac-Lu Space

In this paper,a■-invariant Lorentz metric on the Dirac-Lu space is given,and then the geodesic equationis investigated.Finally,we discuss the field equations and find their solutions by the method of separating variables.

A geometric Model for the Spatial Correlation of an Acoustic Vector Field in Surface-generated Noise

Spatial correlation of sound pressure and particle velocity of the surface noise in horizontally stratified media was demonstrated, with directional noise sources uniformly distributed on the ocean surface. In the evaluation of particle velocity, plane wave approximation was applied to each incident ray. Due to the equivalence of the sound source correlation property and its directivity, solutions for the spatial correlation of the field were transformed into the integration of the coherent function generated by a single directional source. As a typical horizontally stratified media, surface noise in a perfect waveguide was investigated. Correlation coefficients given by normal mode and geometric models show satisfactory agreement. Also, the normalized covariance between sound pressure and the vertical component of particle velocity is proportional to acoustic absorption coefficient, while that of the surface noise in semi-infinitely homogeneous space is zero.

A Class Curves with Some Geometric and Physical Properties in a Higher Dimensional Space

In this paper, we have considered a class curves with some geometric properties in a higher dimensional space and obtained the differential equation of such a class curves, which are called the hyperbolas. We have considered also hyperbola-preserving conformal transformation and the relevant physical sense. And therefore obtained other invariant properties under the illustrious concircular transformation.

Numerical evaluation of buckling behavior in space structure considering geometrical parameters with joint rigidity

The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.