查询词典 proved

The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm.

利用矩阵理论证明了差分解的存在惟一性，并利用一个重要的不等式在先验估计的基础上，运用能量估计的方法证明了该格式按无穷范数以二阶精度收敛到真实解。

Although the localic Urysohn lemma was proved by Papert in 1958 early, and then Dowker and Papert improved this proof, but the localic Tietze extension theorem, which is stronger in form and is more convenient to be used, has not been proved for more than thirty years.

虽然Locale形式的Urysohn引理早在1958年即已由Papert证明，9年后Dowker和Papert又对此证明加以改进，但形式上更强、更便于应用的Locale形式的Tietze扩张定理却三十余年未获证明。

L In any case, the studies by Jiang Chun-xuan have not been accepted by the international mathematical community, it is commonly recognized that the Goldbach conjecture has not been proved, and it is commonly recognized that Fermat's Last Theorem was proved by Wiles and not Jiang Chun-xuan.

l 根据评估报告的标准，普林斯顿高等研究院没有被列入"数学领域国际1%顶尖科研机构"的前五十名，任何一位数学家都会说普林斯顿高等研究院是世界顶尖的数学研究机构。他认为从这个角度来讲，中国数学家还要努力。

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

Firstly, it's proved that the base of free monoid is unique, and that the equation of a base, a generating set and a irreducible generating set in the semigroup with length; Secondly, it's given the relation of a primitive word and a word of indecomposable--Let and is indecomposable, then is primitive ;And by using the length's method and chart,some properties of primitive word have been proved and the solutions of the equation , are discussed; Lastly, on the base of some proposition in Free monoids and Languages ,the proofs of some properties are improved by instruction. For example: Let be a primitive word over X, where .Then is a code. And let then if and only if {} is a code.

首先，讨论了含幺半群中基的基本性质及基与最小生成元集的联系，并给出了含幺半群中基、生成元集、不可约生成元集三者之间的关系；证明了在有唯一长度的半群S中，不可约生成元集、基、最小生成元集三者之间的等价关系；其次，讨论了字的组合与分解性，得出了字的本原性与不可分解性之间的关系---若为不可分解的，则一定是本原的，反之，不一定真；并运用图示法证明了字的可补性理论，讨论了方程，的可解性；在此基础上，用归纳法进一步证明了本原字与码的有关命题--若是X上的一个本原字，其中，则是一个码；若则当且仅当{}是一个码。

Minerals found in the region has 31 major categories, representing the province's mineral resources have been found in 23% and found that more than 160 types of mineral point, the proved reserves of 15 kinds of minerals, of which: ilmenite, graphite ore are domestic large mineral reserves of 6,000,000 tons and 4,000,000 tons or more; limestone, gypsum, Glauber's salt, granite and coal and other non-metallic fuel and energy resources in the northwest edge itself, which proved coal reserves of 1.068 billion tons, oil-page rock 248 million tons, 7.73 million tons of Glauber's salt, 1.17 billion tons of limestone, gypsum 140 million tons, due to a low degree of geological exploration, the comprehensive development of a low utilization rate, at present the development and utilization of mineral ores accounted for only 30% of the region, cooperating with the outside great potential for development.

全区已发现矿产9大类31种，约占全省已发现矿产的23%，发现各类矿产点160余处，探明储量的矿种15种，其中：钛铁矿、石墨矿属国内特大型矿产，储量分别为600万吨和400万吨以上；石灰石、石膏、芒硝、花岗岩和煤炭等非金属和能源燃料类资源在西北占居优势，其中煤炭探明储量10.68亿吨、油页岩2.48亿吨、芒硝773万吨、石灰岩11.7亿吨、石膏1.4亿吨，由于地质勘探程度低，综合开发利用率低，目前开发利用的矿种仅占全区矿种的30%，对外合作开发潜力巨大。

In general, through the hydrothermal fluid geochemical study of the Carlin-type gold deposits in the area, the author believes that some progresses have been achieved.(1) Various types of CO〓-rich inclusions have been discovered and the immiscibility process of the hydrothermal fluids was believed to have been involved in the Carlin-type gold mineralization in the area;(2) It is further proved that the organic matters involved the process of the mineralization;(3) the over-pressure basin fluids is proved to have been existed and played important role in the large scale Carlin-type gold mineralization.

在前人研究的基础上，本次对该区卡林型金矿成矿流体地球化学的研究，作者认为在以下方面取得一定进展：(1)发现了该区卡林型金矿富含CO〓相包裹体，并且种类众多，提出了卡林型金矿的成矿作用，经历了流体不混溶的过程；(2)进一步证实了有机质参与卡林型金矿的成矿过程；(3)证实了盆地超压流体的存在，并提出了卡林型金矿的大规模成矿作用是"盆地超压流体—矿源岩—盆地伸展"耦合的观点。

In allusion to Funar Conjecture :"If a random triangle lies in a closed unit square,then its inscribed circle s radius,r≤(5-1)/4",an equivalent minimum problem about a function of 2-variables is studied;the stagnation point and its value,value on the boundary of the function of 2-variables are studied,the equivalent problem is proved correct,so the Funar Conjecture is proved correct.

针对Funar猜想："设任意三角形位于闭单位正方形内，则该三角形的内切圆半径，r≤(5-1)/4"，研究了与其等价的某二元函数的最小值问题；利用对此二元函数驻点及其取值、边界取值讨论，证明了等价问题成立，进而此Funar猜想得证。

In this paper, the existence of isometric mapping between the manifold in the high-dimensional data space and the parameter space is proved. By distinguishing the intrinsic dimensionality of high-dimensional data space from the manifold dimensionality, and it is proved that the intrinsic dimensionality is the upper bound of the manifold dimensionality in the high-dimensional space in which there is a toroidal manifold.

首先给出了高维数据的连续流形和低维参数空间之间的等距映射存在性证明，然后区分了嵌入空间维数、高维数据空间的固有维数和流形维数，并证明存在环状流形高维数据空间的参数空间维数小于嵌入空间维数。

Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.

本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失