借助

In response to the difficulties in verifying his proof, in January of 2003, Hales launched the "Flyspeck project"("xxxxal Proof of Kepler") in an attempt to use computers to automatically verify every step of the proof.

数学是来不得半点虚假的，Hales在1997年借助计算机，完全证明了Kepler猜想，得到公认，文章即将发表在Annals of Math上，Hales本人也在ICCM上作了45分钟报告。

Ant algorithm is a new type of swarm intelligent algorithm. It takes inspiration from the observations of ant colonies foraging behavior that ants can find the shortest paths between food sources and their nests. It is simple, common, robust, excellent in self-adjusting, easy to expand and suitable for parallel process, etc.

蚂蚁算法是受大自然中蚂蚁觅食启发而产生的一种智能仿生算法，具有简单通用、鲁棒性强、自调节能力出色、易于扩展、适合分布处理等特点，因此借助蚂蚁算法解决VRP问题具有非常现实的意义。

Using computer aided geometrical drawing function,this method is introduced to draw force polygon conveniently and accurately under AutoCAD environment,which meets with the higher request in the engineering nowadays.

以手工作图为主的图解法是一种求解力系问题的常用方法，介绍此方法在Auto-CAD环境之下，借助其强大的几何设计绘图功能，方便、精确地做出力的多边形，从而更好地满足工程实际要求。

In this paper,by using the characteristic equation,some forced oscillation of certain delay hyperbolic differential equation s are obtained.

借助其特征方程，获得了一类时滞双曲型微分方程解的强迫振动的若干充分条

We can master a foreign language by the aid of a grammar and dictionary.

我们可以借助语法书和词典来掌握一门外语。

Ali software free of charge, on the surface is the traditional software business, but its fundamental reason for the study or SaaS platform strategy to develop network popularity, with the promotion of foreign trade version, to further expand the country's largest software operating platform of carrying capacity.

阿里软件的免费，表面上是针对传统软件企业，但究其根本原因还是为了SaaS平台战略开拓网络人气，借助外贸版的推广，进一步扩大这个全国最大软件运营平台的承载能力。

"It was the foreshock sequence that gave the solid prediction," Michael said.

从文章中看，借助动物预测地震是否可靠在学术界也没有统一的看法，中国、日本还在做，美国已经停止了官方的研究，停止的原因不是钱，而是"教条主义和小心眼"。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all th...

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all the angular interactions and spin sums involved in the problem have been worked out explicitly by using irreducible theory.

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

And the proof of the four color theorem relying on computer has also been involved.

互。地1和w.1柏卜n在美国数学会的通报上声明借助电子计算机解决了这个问题。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。