证明是...

In the thesis , we give combinatorial proof of some q-identities using integer partition.In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proof using integer partition.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从分拆的角度给出了一些q-恒等式的组合证明，其中突出的成果是给出了平方和恒等式的一个直接的组合证明并给出了偶数平方和与奇数平方和的q-模拟及组合证明。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

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。

Additional, director of delegate of town National People's Congress, public security is OK reach relevant website to mention to promulgator of article of Huang Youjie, net criminal private prosecution is civil perhaps lawsuit, but because they are exercise the service personnel of public authority, belong to " public character ", it is so when adjudgement, lv of take an examination " actual ill will " the world general rule of the principle -- press down director of delegate of National People's Congress, public security to ought to prove net article promulgator and relevant website know perfectly well Huang Youjie namely appeal for help material is fictional fact and be determined to publish, if indemonstrable this, the accused need not assume corresponding responsibility; And to Huang Youjie, pressing down director of delegate of National People's Congress, public security to want to prove him is " intended and concoctive fact " is not wrong accuse, or impeach inconsistent with the facts, also should not be otherwise adjudicate Huang Youjie assumes corresponding responsibility.

另外，镇人大代表、公安局长可以向黄有杰、网文发布者及相关网站提起刑事自诉或者民事诉讼，但由于他们是行使公共权力的公职人员，属于"公众人物"，所以在审判时，应考虑"实际恶意"原则的世界通例——即镇人大代表、公安局长应当证明网文发布者及相关网站明知黄有杰的上访材料是编造事实而执意刊登，如果不能证明这一点，被告就可以不承担相应责任；而对于黄有杰，镇人大代表、公安局长要证明他是"故意捏造事实"而不是错告，或者检举失实，否则也不宜判决黄有杰承担相应的责任。

Their theory fits in well with primitive and peaceful periods of history; but in its application to complicated and stormy periods in the life of nations, when several different authorities rise up simultaneously and struggle together, the inconvenience arises that the legitimist historian will assert that the National Assembly, the Directorate, and Bonaparte were only violations of real authority; while the Republican and the Bonapartist will maintain, one that the Republic, and the other that the Empire were the real authority, and that all the rest was a violation of authority.

他们的理论只适用于原始的、和平的历史时期，而当各民族处在复杂而动乱的时期，各种权力同时并起，互相斗争，他们的理论就不适用了，因为正统派的史学家将会证明，国民议会，执政内阁和波拿巴都不过是真正权力的侵犯者，而共和派将会证明，国民议会是真正的政权，波拿巴派将会证明帝国是真正的政权，其他一切都是权力的侵犯者。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

Proof steps and proof states in the theorem prover Isabelle are very referable proof information , but now there is no tool that can manage them efficiently.

Isabelle定理证明器中的证明步骤和证明状态是非常具有参考价值的证明信息。然而目前没有工具可以有效管理这些信息。

By employing the Jordan-Wigner transformation and a modified mean field method, we are able to determine its ground-state quantum phase diagram approximately. The chapter IV is the main part of this Thesis. It contains the main innovations in our work. We propose and study in detail a S=1 Ising chain with the interplay of single-ion anisotropy and dimerization. The main results and innovations are the following: We show that the total number of the zero-component of spins at each site is a conserved quantity. This quantity, which may intuitively called as hole's quantum number, is hidden in the system. We show further that the hole's number in the ground-state is zero; By using the Jordan-Wigner transformation, we map this model onto a series of subsystems described by the spin 1/2 dimerized transverse Ising model. We solve the subsystems exactly, by presenting the exact wave functions and spectra;We show that this system exhibits a series of quantum phase transitions by varying the dimerization strength. We determine the quantum critical points exactly. We also show that the criticality is the same as that of the uniform S = 1/2 transverse Ising chain.

第四章是本文的重点及主要创新内容，我们具体研究了自旋为1的在横向单离子晶格场中的一维二聚化Ising链，我们得到的主要结果和创新之处是：(1)证明了这一模型具有一种隐藏的对称性，即自旋第三分量为零的格点数目是一个守恒量，并证明基态出现在空穴数目为零的子空间中；(2)利用Jordan-Wigner 变换将此模型变换到一系列自旋为1/2的横磁场中的二聚化Ising 模型，并给出了相应严格的波函数及能谱；(3)我们发现系统的基态随着二聚化强度的变化将呈现出一系列量子相变，我们得到了量子临界点的精确位置，并证明其临界性质与自旋为1/2的横磁场中的均匀Ising 链中的临界行为属于同一普适类。

From the view of procedure law, proof standard is the mark that whether the onus probandi on the subject is end

从程序角度看，证明标准是证明主体的证明任务是否完成及其证明责任是否及时卸除的客观标志。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。