证明

Thirdly,quasi-normal inequalities of a-variation maximal operator and a-conditional variation maximal operator of scalar predictable tree martingales areidentified by the use of martingale transforms and by the construction of convex or concave function method;on this basis and with the help of previsiblity or regu-larity,Burkholder-Davis-Gundy\'s inequality of a-variation maximal operator and a-conditional variation maximal operator of scalar predictable tree martingales are iden-tified by the application of Hardy-Lorentz interpolation theory.At the same time,bythe use of G.

再次，应用鞅变换和构造凸或凹函数方法证明了标量值可料树鞅的α-方极大算子和α-条件方极大算子的拟范数不等式；然后，在这些拟范数不等式的基础上，应用Hardy-Lorentz空间插值方法证明了当树鞅是可控或正规树鞅时关于标量值可料树鞅α-方极大算子和α-条件方极大算子的Burkholder-Davis-Gundy's不等式成立。

In Chapter 4, in the above system, the definitions of sensitive dependence on initial value, strong sensitive dependence on initial value and chaos set of a sequence of maps are put forward; Meanwhile, sensitive dependence on initial value of a sequence of maps is promited, and the concept of N - sensitive factor is also proposed; That at the local connected space λ_2/(N-1) is a N—sensitive factor, and a chaotic map containing strong sensitive dependence on initial value of a sequence of maps is proved.

第四章，在上述系统中给出了一列映射的初值敏感依赖、初值强敏感依赖和混沌集的定义；同时又对一列映射的初值敏感依赖进行了推广，提出了该系统下一个N-敏感系数的概念：证明了在局部连通空间中λ_2/N-1是系统的一个N-敏感系数；又证明了一列映射的混沌集蕴涵一列映射对初始条件具有强敏感依赖性。

By re-prove the theorem on the relationship between information entropy and roughness of knowledge,this paper finds that it is conditional information entropy which exists one-to-one relationship with roughness of knowledge.Then several related theorems are given and proved.

该文通过重新证明知识粗糙性和信息熵的对应关系定理，找到与知识粗糙性存在一一对应关系的是条件信息熵，并给出相关定理及其证明。

The Act provides that before an application for Australian citizenship is approved (descent, conferral, resumption or renunciation) and before an application for evidence of citizenship is approved, the Minister must be satisfied of the person's identity.

新法案要求，在批准有关澳洲国籍的申请（由血缘申请入籍、通过"授予国籍"方式申请入籍、申请恢复国籍以及放弃国籍）以及获得澳洲国籍证明的申请之前，部长必须已获得令其满意的申请人身份证明。

At the same time, some properties of rough Set in quotient ring are given and proved. The fifth chapter is Rough Primary Ideals and Rough Fuzzy Primary Ideals in Semigroups, the concept of rough primary ideals and fuzzy rough primary ideals in semigroups are introduced. Under the condition of the complete congruence relation, a rough set of a primary ideal in semigroups is proved to be its primary ideal.

同时，在商环中讨论了粗糙集的一些性质，并给出这些结论的严格证明；第五章是半群中的粗准素理想和粗模糊准素理想，首次提出了半群中的粗准素理想与粗模糊准素理想的概念，证明了在完备同余关系下，半群中准素理想的粗糙集是准素理想。

Secondly, in our methods, the essential geometry of the image single axis geometry may be specified by six parameters and this may be estimated from one conic and one fundamental matrix (a total of 12 parameters) or may be minimally estimated from two conics (a total of 10 parameters).

本文证明了单轴旋转运动的不变量可以通过一个基本矩阵和一条二次曲线来确定，在这种情况下，由于基本矩阵的自由度为7，二次曲线的自由度为5，所需确定的参量个数仅为12，大大减少了不变量的计算量；本文同时证明单轴旋转运动的不变量可以通过最少两条二次曲线来确定，在这种情况下所需确定的参量个数仅为10，该方法是目前同类算法中参数最少的；本文提出了用多条二次曲线求解单轴旋转运动的不变量的最大似然估计算法，其所需确定的参量个数为6+2n，其中n为二次曲线的个数，该公式更深刻地反映了二次曲线与不变量的参数关系。

Examination and comparison show that two distinct forms of marriage are requisite to explain the Malayan and Turanian systems; whence the application, as tests of consanguine marriage in one case, and a punaluan marriage in the other.

通过观察与比较就可以看出：想要解释马来亚式和土兰尼亚式亲属制，必须有两种不同的婚姻形式；从而使前者证明了血婚的存在，后者证明了伙婚的存在。

In this case, legitimation is the process by which a'legislator'dealing with scientific discourse is authorized to prescribe the stated conditions （in general, conditions of internal consistency and experimental verification）determining whether a statement is to be included in that discourse for consideration by the scientific community.

换这之，内部一致性和经验实证是一个科学述句必备的两种性质，这也是"（in general， conditions of internal consistency and experimental verification）"的原义，但罗译译之「这些条件必须内在协调一致，并经实验证明」，（p.171），即将意思扭曲为：「述句必须符合才能成为科学述句的条件，必须有内在一致性和经实验证明。

To prove that OLS estimators are asymptotically efficient, one needs to (1) present an estimator that is consistent but its variance is larger.

为了证明OLS估计量是渐近有效的，我们需要(1)给出一致的估计量但证明它有更大的方差。

Copy of recent confirmation from government department / company to confirm the relevant contact is still in force.

批出有关合约之政府部门／公司近期发出的证明文件副本，证明该合约仍然生效。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！