多讲?少讲?不讲?

近日读到著名经济学家张五常回忆其大学老师的一篇文章 ,引起我的一些思考 .文章说 ,老师让学生花了四个星期的时间自己去研究问题解决的办法 ,但学生们都找不到办法 .第五个星期 ,老师进入课室 ,“在五十分钟内 ,他如长江大河 ,滔滔不绝 ,使我听得呆了 .……”作者说 ,“假若没有经过那四个星期去想 ,我不会在五十分钟之内被老师说服的吧” .虽然故事讲的是大学教学 ,但是 ,我想我们的中学教学中 ,不也存在一个“讲”与“不讲” ,“多讲”与“少讲”的问题吗 ?在“满堂灌”的授课方式受到批评后 ,不少老师又都在培养学生能力的口号下祭起了…     

O?shore ?oating wind turbine and its dynamic problems?

Green energy sources and ocean wind power are plentiful in deep sea. More and more o?shore wind power plants are constructed in the deep water over hundred meters below the surface. While o?shore ?oating wind turbine system is working, wind turbine, ?oating foundation, and mooring system a?ect each other with wind, waves, and currents acting on them. Various o?shore ?oating wind turbine systems and the encoun-tered environmental loads are brie?y reviewed and discussed. It is di?cult and crucial to comprehensively analyze the aerodynamic-hydrodynamic-service system-structure un-der the coupling e?ect of o?shore ?oating wind turbine system. The environmental ?ow ?eld, structure scale, and rational applications of theories and approaches should be well considered in advance.     

Beitr?ge zur St?rungstheorie

Ohne ZusammenfassungHerrn Professor Dr. H.Kneser zum 60. Geburtstag gewidmet     

What lifts?

As is well known, idempotents in any ring R lift modulo any nil idea I. That is, if a ? R and (a₂-a) ? I there is an i ? I with (a + i)²-- (a + i) = 0. An idempotent is a zero of the polynomial x ²?x ², and a nil element satisfies x ⁿfor some n. Seen this way, lifting occurs in considerable generality We assume R has a unit, and handle the non-unital case at the end of this paper.     

陷阱有多深?

正青青草原的春天来了,灰太狼一家外出踏青。小灰灰忙着抓蝴蝶,正玩得起劲,突然听到爸爸妈妈的求救声。呀!爸爸妈妈掉进陷阱里了。一家人想了很多办法,又是跳又是爬,但是陷阱太深了,灰太狼和红太狼怎么都出不来。小灰灰急得快要哭出来了。突然,他想起了羊村里的朋友们,就急忙去羊村求救。羊村的羊羊们来救援了。为了教育一下灰太狼,喜羊羊想出了一个主意,说:"灰太狼先生,我这儿有一根绳子,把绳子放到一口井里,单根放到井底,井外会多出15米。对折后再放入,会多出井口1米。你知道这口井有多深,绳子有多长吗?"     

A Bernstein type theorem in ? × ? n

In this paper, as suitable application of the so-called Omori-Yau generalized maximum principle, we obtain a Bernstein type theorem concerning to complete hypersurfaces immersed with constant mean curvature in the product space ℝ × ℍ ⁿ . Furthermore, we treat the case that such hypersurfaces are vertical graphs.     

How Close is the Sample Covariance Matrix to?the?Actual Covariance Matrix?

Given a probability distribution in ? ⁿ with general (nonwhite) covariance, a classical estimator of the covariance matrix is the sample covariance matrix obtained from a sample of N independent points. What is the optimal sample size N=N(n) that guarantees estimation with a fixed accuracy in the operator norm? Suppose that the distribution is supported in a centered Euclidean ball of radius $O(\sqrt{n})$ . We conjecture that the optimal sample size is N=O(n) for all distributions with finite fourth moment, and we prove this up to an iterated logarithmic factor. This problem is motivated by the optimal theorem of Rudelson (J. Funct. Anal. 164:60?C72, 1999), which states that N=O(nlog?n) for distributions with finite second moment, and a recent result of Adamczak et al. (J. Am. Math. Soc. 234:535?C561, 2010), which guarantees that N=O(n) for subexponential distributions.     

问题何在?

题:若复数z满足z~10=-1,则z~4-z~6-z~2 1的值是( )。0(A)-1;(B)1;(C)0;(D)以上都不对。此题见于一些书刊,其答案为(A) 解法一:(方程法或设值法) 设(1) (1)式两边同乘以z~4得 z~8-z~6-z~2 1=z~4t(2) 因为z~10=-1,(1)式分子,分母同乘以-z~6。并整理得 z~8-z~6 z~4-z~2=t(3) 由(2)得z~8-z~6-z~2=z~4t-1(4) (4)式代入(3)得 z~4t-1 z~4=t ∴(z~4-1)t=1-z~4 (5) 两边同除以z~4-1得:t=-1,故选(A)。解法二:(用数列求和解) ∵ z~10=-1, ∴原式的分子、分母同乘以-z~6,得: =-z~2 z~4-z~6 z~8 (看成首项,公比皆为-z~2的等比数列) 故选(A)。以上两种解法及原书刊给出的答案都是(A),可是若本题用满足z~10=-1的一值z=i(或-i)代入,得上面结果都错了,这就奇怪了,问题何在?     

Moir? Separations

The analysis of the moir? phenomenon by means of elementarygeometry which was begun by Firby (1984) and Firby & Stone(1984) is extended from first order to all integral and fractionalorders, and from consideration of the plane only to considerationof a general finite-dimensional space . The idea of the -curve, which forms the boundaryof the set in in which first-order interference might be observed, is extended to the idea of aboundary in for any given integral or fractional order of interference. Separating setsin , which form the boundary of regions in which two given integral or fractional ordersof interference might dominate relative to one another, areintroduced. The wavelength and contrast analysis previouslycarried out only for first-order interference in is extended to deal with all integral and fractionalorders of interference, and this is used to explain why highintegral orders, and all fractional orders, of interferenceare observed only in exceptional circumstances.     

Exponential moving average versus moving?exponential?average

In this note we discuss the mathematical tools to define trend indicators which are used to describe market trends. We explain the relation between averages and moving averages on the one hand and the so called exponential moving average (EMA) on the other hand. We present a lot of examples and give the definition of the most frequently used trend indicator, the MACD.     

怎样过桥?

据《报刊文摘》载,某著名公司招聘人员面试时,曾出这样一道智力题. 一合唱团4名演员赶往一演出地,途中须经过一座小桥,他们必须在17分