众所周知

Chain complexes of projective space and Klein bottle are well known.

射影空间和克莱因瓶链复合物是众所周知的。

The second fact of our knowledge is that things are known according to the nature of the knower.

第二，其实我们所知的是，事情是众所周知的，根据性质能知。

Thus, knowledge is a transactional product of the knower and the known.

因此，知识是交易产品的认知者和众所周知的。

A known quantity; the limits of the known world; a musician known throughout the world; a known criminal.

已知的数量；已知世界的界限；世界文明的音乐家；众所周知的罪犯。

While blood-brothers to the Rajputs, while their brethren hail entirely from the Kshatriya caste, the Jats contain a multitude of Shudra or Vaishya peasants, known for being both hard-working farmers and diligent warriors albeit without the proud origins of Jat or Rajput Kshatriya.

然而他们和有血亲关系的拉起普特人，这些完全来自于刹帝利种姓的兄弟不同，贾特人中有大量的首陀罗和吠舍。他们是众所周知的勤劳农民和勤苦斗士，尽管他们不具备引以为豪的贾特血统或者拉其普特人的武士种姓刹帝利。

Born in Tikrt, Iraq, Saladin, as he is known in the West, was a Kurd; his Arabic name is Salah ad-Din Yusuf. At the age of 14 he joined other members of his family in the service of the Syrian ruler Nur ad-Din.

出生于tikrt ，伊拉克，萨拉丁，因为他是众所周知的，在西方，是一个库尔德人，他的阿拉伯语名字是萨拉赫专案- Din的优素福在年满14岁，他加入了其他家庭成员在服务叙利亚统治者努尔专案声浪。

It is well-known that reduced Hessian method is one of the most efficient methods for solving large scale constrained optimization problems. However, the convergence analysis for the method requires of the positive definiteness of the reduced Hessian of Lagrangian function.

众所周知，既约Hessian方法是求解较大规模约束优化问题的一类有效方法，但已有的这类方法的全局收敛性分析需假定拉格朗日函数的既约Hessian矩阵的一致正定性。

Therefore, from the theoretical point of view, a solution of the constrained problem and the corresponding values of the Lagrange multipliers can be found not only by the well known method of multipliers but also by performing a single unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers.

因此，从理论的观点来看，原约束问题的解和对应的拉格朗日乘子值不仅可以用众所周知的乘子法求得，而且可以通过对Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上执行一个单一的无约束极小化来获得。

We all know that China is still a developing country and its education still lags behind that of developed countries.

众所周知，作为一个发展中国家，中国的教育水平还是落后于发达国家。

As it's all known, English is a most writen and spoken langue in the world.

众所周知，英语是世界上使用最广的语言。

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