证明

Proving theorems in Coq is an interactive process: some decision procedures automate equational reasoning or Presburger arithmetic, for example, but most of the proofs consist in sequences of "tactics" entered by the user to guide Coq in resolving proof obligations.

在Coq中的证明定理是一个交互过程：比如部分判定过程可以自动完成等式推论或者Presburger算法，不过，更多的证明则是由用户输入用以指导Coq完成证明任务的tactics序列。

We analyse the Lewy theorem and the provement idea of the theorem, and find the equation (7)and (8)are not equivalent under the reversible transformation, this lead to the absurdity in the provement does not come into existence .

分析Lewy定理及定理的证明思想，发现在证明中所述的可逆变换下，方程（7）与（8）并不等价，导致Lewy定理证明中归谬不成立。

In the nature of foreign law, whether ex officio application of proven methods, and can not prove that a foreign law or have proved inadequate when to how to resolve and so on will have their own unique characteristics.

在外国法的性质、是否依职权适用、证明方法以及在无法证明外国法或证明不充分的时候该如何解决等各方面均有其独有的特点。

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。

In this paper we prove that it is sufficient to prove for Fermat's last theorem using the complex hyperbolic functions in the hypercomplex variable theory.

摘要∶本文利用 P 阶复双曲函数，证明了只要证明就全部证明了费马大定理。

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。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

And made a comparison between the Han nationality and the BouYei nationality students in learning geometric proof, we sum up the defferences between learning geometric proof abilities and the general proof process.

针对问卷和测查题的定量统计分析和个案定性分析，得出被试学生学习几何证明的一般过程和证明能力发展的差异情况，在此基础上进行了几何证明的微型教改实验，得到以下的结果： 1。

In this paper, we just consider the initial-boundary value problems of aclass of two-dimensional nonlinear integro-differential equation, simultaneouslyconsidering the damped term and memory termThe details will go as follows. Firstly, the c...

本文同时考虑耗散项和记忆项等因素，讨论了一类具有记忆项的二维非线性积分微分方程的如下初边值问题具体研究内容如下：首先，文章简单介绍了国内外当前对非线性积分微分方程的研究现状；其次，文章给出了一些重要概念和引理，并对部分符号做了说明；第三，利用Galerkin方法证明了问题(1)-(3)的变形问题弱解的存在唯一性；第四，证明了问题(1)-(3)强解的存在性和能量的指数衰减性；第五，进一步证明了问题(1)-(3)经典解的存在性。

Objective: To study the effect of polycythemia on blood oxygen saturation.

裴蕾目的：观察RBC剧增而引起的高粘血症对血氧饱和度的影响。

Based on SIMPLER algorithm in the curvilinear body-fitted coordinates, the calculations were performed for Pr=0.7, Re=10~1000 on non-orthogonal non-staggered grids which are generated by elliptic equation systems.

采用曲线坐标系下压力与速度耦合的SIMPLER算法，数值研究了周期性渐扩渐缩波纹通道内脉动流动与换热情况，流动Re数的范围为10~1000，Pr数为0.7。