查询词典 fixed point theorem

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

Thence in a southeasterly direction to Corner Point No. CP14 (X = 484 330, Y = 683 415); thence in a. northeasterly direction to Corner Point No. CP15 (X = 484 390, Y = 683 490); thence in a southeasterly direction to Corner Point No. CP16 (X = 484 415, Y = 683 470); thence in a southwesterly direction to Corner Point No. CP17 (X = 484 355, Y = 683 395); thence in a southeasterly direction to Corner Point No. CP18 (X = 484 430, Y = 683 335); thence in a southeasterly direction to Corner Point No. CP1, the point of beginning.

从该点起向东南延伸至隅角点CP14（X = 484 330，Y = 683 415）；从该点起向东北延伸至隅角点CP15（X = 484 390，Y = 683 490）；从该点起向东南延伸至隅角点CP16（X = 484 415，Y = 683 470）；从该点起向西南延伸至隅角点CP17（X = 484 355，Y = 683 395）；从该点起向东南延伸至隅角点CP18（X = 484 430，Y = 683 335）；从该点起向东南延伸至隅角点CP1。

Based on the existence of the " mean point s"in Differential mean value Theorem,This paper futher studies the problem of the number of the " mean point s" in Differential mean value Theorem.

在微分中值定理"中值点"存在的基础上，进一步研究微分中值定理"中值点"的个数问题。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

Presenting a theorem of one dimensional time multiplying ,also a demonstration to the theorem which says that Any point in 3 dimensional spaces of the universe at an certain universal moment possesses equivalent physical quantities of one dimensional time that is equal to total amounts of one dimensional time of the universe at same universal moment; Any point in 3 dimensional spaces of the universe at an certain universal moment , its possessed physical quantities of one dimensional time has an constant ratio with respect to one dimensional space , which is universally equal to space time impedance.

给出了一维时间增殖定理及其证明。该定理指出：在任意宇宙时刻，宇宙三维空间中任意一点具有的一维时间物理量量值均相等并等于在该宇宙时刻宇宙具有的一维时间物理量总量；在任意宇宙时刻，宇宙三维空间中任意一点的一维时间物理量的一维空间变化率均相等且恒等于时空阻抗。

In chapter 5,we introduce the De Morgan algebra of metric and investigate the pseudo-metric Uniformity and the pseudo-metric topology and the separation axioms in De Morganalgebra of metric.We establish the Baire category theorem and the Banach contraction theo-rem,the Edelstein contraction theorem and other fixed quasi-atom theorems in De Morganalgebra of metric.In final,we give a sufficient condition for the metrization of a De Morganalgebra of topology.

在第五章里，我们地德摩根代数中引进了伪度量，探讨了伪度量一致和伪度量拓扑以及德摩根度量代数的分离公理，得到了Baire范畴定理、Banach收缩定理、Edelstein收缩定理以及其它不动拟原子定理，最后给出一个德摩根拓扑代数可度量化的充分条件。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

In this paper, a fixed value theorem for direct areas of height triangle s in circular inscribed polygons is obtained, and some results, including the famous height theorem in a triangle, are deduced.

给出圆内接 2n +1边形中高线三角形有向面积的定值定理及其推论，其中包括著名的三角形的高线定

However, since the fixed-point calculation maybe cause cumulative quantization error, the convergent performance of fixed-point equalizer is not better than that of floating-point equalizer.

但由于定点数运算会引起量化累积误差，均衡器的收敛速度比浮点数运算均衡器的收敛速度要慢，收敛后的稳定性也较差。

The median voter theorem is a mathematical result that shows that if voters are choosing a point along a line and each voter wants the point closest to his most preferred point, then majority rule will pick the most preferred point of the median voter.

中值选民定理是一个数学结论，这个结论表明如果要选民沿着一条线选择一个点，而且每个选民都想选离他最偏好的点最近的点，那么多数规则将选出中值选民最偏好的点

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。