the battle took place over some land that was being contested on a frontier and they would go down to that area and pick a spot and there they would go and fight with one another.

战争爆发是为了争夺国境线上的争议地区,他们会到那个地区,挑好地方,然后在那里大打出手

耶鲁公开课 - 古希腊历史简介课程节选

He has this whole group of people out somewhere on the American frontier and they're a kind of a cult.

他描写了来自于美国边界某处的一群人,他们是一群狂热分子

耶鲁公开课 - 美国内战与重建课程节选

There is surrounding farmland going as far,typically, as there is either a natural or an artificial frontier.

周围环绕着农田,这些农田一般会延伸至一个自然边界,或者一个人工边界为止

耶鲁公开课 - 古希腊历史简介课程节选

But beyond that, if you were confined to just stocks and bonds, it would be a matter of taste where along this frontier you would be.

进一步，若仅限于投资股票和债券的组合，选择哪个组合,取决于个人的兴趣。

耶鲁公开课 - 金融市场课程节选

His Leatherstocking Tales are full of a certain anxiety about what might be happening to that frontier, what's coming from east to west.

他的《皮袜子故事集》里弥漫着某种焦虑不安,它讲述了西进运动开拓者们从东部来到西部,有可能会遇到的一些事情

耶鲁公开课 - 美国内战与重建课程节选

That means that you want to pick, ultimately, a point on this-- this line is tangent to the efficient portfolio frontier with all the other assets in it.

那意味着你会最终会在这上面选一个点-,这条直线是与有效边界相切的,后者包含了所有的资产组合。

耶鲁公开课 - 金融市场课程节选

If we want to add that asset to the portfolio, what it does is it produces an efficient portfolio frontier that is now a straight line; I show that on the diagram.

如果我们将其加入到投资组合中去，则会生成一条资产组合的有效边界,即一条直线;,我在图里把它画出来了。

耶鲁公开课 - 金融市场课程节选

Tangent means that it has the same slope, it just touches the efficient portfolio frontier for risky assets at one point, and the slope of the efficient portfolio frontier, including the riskless asset, is a straight line that goes through the tangency point, here.

相切意味着斜率相同，它与包含风险资产的有效边界,交与一点，而包含无风险资产的，有效边界，则是一条过切点的直线，切点在这里。

耶鲁公开课 - 金融市场课程节选

But when that's not true, then there is a typical sort of modern frontier, a land bridge which there a line is-a theoretical line is drawn through it, and on one side is one city, and the other side is another city.

但还不止这些天然边界,另外还有种边界形式,和现代国境线很类似,是由一座陆桥,分割出一条界线…假象的界线,界线的一边是一个城邦,另一边是另一个城邦

耶鲁公开课 - 古希腊历史简介课程节选

By the 1820s, already, within a decade of the War of 1812 and the opening of the frontier, cotton's future seemed limitless.

截至十九世纪二十年代,这其中包括了1812年开战的十年战争,以及边疆的开拓,棉花产业的未来似乎无限

耶鲁公开课 - 美国内战与重建课程节选

Irving Fisher also drew on the curve a production possibility frontier for society, which he made downward-curved.

欧文·费雪还画了一条曲线,代表了社会的生产可能性边界PPF,这是一条向下的曲线

耶鲁公开课 - 金融市场课程节选

But if we have credit markets, then people can individually choose to be off the production possibility frontier and at a higher level of consumption than otherwise would.

但如果存在信贷市场,那么个人可以选择超越,PPF曲线的范围,达到比没有信贷市场时更高的消费水平

耶鲁公开课 - 金融市场课程节选