查询词典 classification theorem

Hausdorff convergence; almost nonnegative Ricci curvature; Betti number; harmonic 1-form; nilpotency; splitting theorem; positive sectional curvature; gradient curve

基础科学，数学，几何、拓扑Hausdorff收敛；几乎非负Ricci曲率；贝蒂数；调和1-形式；幂零指标；分裂定理；正截面曲率；梯度曲线

Instead of Gronwall\'s inequality,the non-linear Bihari inequality is crutial in dealing with the non-Lipschitz equations.Moreover,we emphasize that the dominating functions in non-Lipschitz conditions always satisfy concavity and some non-integrability near zero.The concavity is for using Jensen\'s inequality.Because of the non-integrability near zero,we can apply the comparison theorem of ordinary differential equations together with Bihari\'s inequality to yield many results.

3作为Gronwall不等式的推广，Bihari不等式在处理具有非Lipschitz系数的方程时不可或缺；同时应当注意，非Lipschitz条件中所涉及的控制函数总是满足凹性和某种零点处的不可积性：凹性是为了利用Jensen不等式；零点处的不可积性使得Bihari不等式与常微分方程中的比较定理结合在一起从而完成很多结论的证明。

A theorem giving the expansion of a binomial raised to a given power.

将二项式扩展到规定幂的定理。

If the power series ∑anxn an ∑anxn and ∑bnxn satisfy the condition r =∑bn xn, we obtain the twin combinatorial identity theorem between the sequences {an} and bn}.We also obtain some specific twin combinatorial identities by using the expansion on the binomial expression formula, including two expansions of combinatorial number(rsn and ...

如果幂级数∑anxn与∑bnxn满足条件r＝∑bnxn 时，获得数列｛an｝与｛bn｝之间孪生组合恒等式的定理，应用在二项式定理等展开式上得出具体的多组孪生组合恒等式，其中包含组合数的两种展开法，Bernoulli数直接表达式的新证等结果。

Functions, relations and graphs; inverse functions; inequalities; theory of equations; introduction to matrices; determinants; binomial theorem; sequences and series.

函数， 图表，曲线。反函数，不等公式，等式，矩阵的介绍，定列式，序列和系列等。

He initiated his pupils into the mysteries of the binomial theorem.

他给他的学生们讲授二项式定理的奥秘。

By the age of 20, Sir Isaac Newton found a general binomial theorem which lead to the later development of calculus.

20岁的时候，牛顿发现了一个二项式地理，为以后发展微积分做好了准备。

It included Karaji's binomial theorem and rules of the arithmetic polynomial operations and developed Karaji's theory of polynomial.

其中保存了凯拉吉的关於二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。

In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that would later become infinitesimal calculus.

1665年，他发现了广义二项式定理，并开始开发一种数学理论，后来成为微积分。

This book included Karaji's binomial theorem and rules of the arithmetic polynomial operations and it developed Karaji's theory of polynomial.

算术珍本》中保存了凯拉吉的关于二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。

My father is over 60 years old, and he lifts weights every day.

我爸爸六十多岁了，他每天都练习举重。

Then in a serious tone she declared:"It doesn't pay, dear boy, to look like a ninny with one's wife the first night."

两眼湿润了，她把身子蜷得很小，这样似乎可以更好地闻闻自己。