Sunday, November 19, 2006

抽奖

3个人抽奖。9个箱子。
9个箱子里面:1个箱子里面有30万奖金,另外8个箱子都是空的。
3个人按照一定顺序逐个来抽箱子。
如果有人抽到那个奖金就游戏结束。如果抽不到就循环一直抽下去。


问题是:这3个人让A先抽,B第2抽,C最后抽,然后A再抽,BC这样下去.

刚才有个电视节目。A第2轮就抽中了。mm说不公平,我觉得公平。大家说公平吗?

btw,mm是理科生,我文科男的。

Wednesday, November 15, 2006

Don’t get a business degree, get angry

Don’t get a business degree, get angry

By Anita Roddick

Published: November 14 2006 18:48 | Last updated: November 14 2006 18:48

I never went to business school. I went to the business school of life. And I did so from an early age. I was brought up in an Italian immigrant family with a work ethic that teetered on the verge of slave labour.

We got up each morning at five to make breakfast for the local fishermen in our café in Littlehampton and did not close until the last customer wandered home. The other cafés opened at nine and shut at five. This was a clue to me about what makes some people entrepreneurs and not others. Our café was owned by ferociously determined immigrants; the others were not.

ADVERTISEMENT

This is an important difference and the reason that I do not advise new entrepreneurs to submit themselves first to the rigours of an MBA is that business schools do not understand it. The conventional advice to budding entrepreneurs is that they should groom themselves to be the whizz-kid with a suit and a fascination for spreadsheets that bank managers like.

Actually, potential entrepreneurs are outsiders. They are people who imagine things as they might be, not as they are, and have the drive to change the world. Those are qualities that business schools do not teach. An MBA can give you useful skills that can be applied to a life in business. But they will not teach you the most crucial thing: how to be an entrepreneur. They might also sap what entrepreneurial flair you have as they force you into the template called an MBA pass.

I often get asked to talk about entrepreneurship – even by hallowed institutions such as Harvard and Stanford – but I am not at all convinced it is a subject you can teach. How do you teach obsession – because often it is obsession that drives an entrepreneur’s vision? How do you learn to be an outsider if you are not one already?

In the business school model, entrepreneurs are most at home with a balance sheet, a cash-flow forecast and a business plan. They dream of profit forecasts and the day they can take the company public. These are just part of the toolbox of re-imagining the world: they are not the defining characteristics of entrepreneurship. The problem with business schools is that they are controlled by, and obsessed with, the status quo. They encourage you deeper into the world as it is. They transform you into a better example of corporate man. We need good administration and financial flair, after all, but we need people of imagination too.

So here are 10 lessons that entrepreneurs need more than what they teach in business school.

Tell stories. The central tool for imagining the world differently and sharing that vision is not accountancy. It has more to do with the ability to tell a story. Telling stories emphasises what makes you and your company different. Business schools emphasise how to make you toe the line.

Concentrate on creativity. It is critical for any entrepreneur to maximise creativity and to build an atmosphere that encourages people to have ideas. That means open structures, so that accepted thinking can be challenged.

Be an opportunistic collector. When entrepreneurs walk down the street they have their antennae out, evaluating how what they see can relate back to what they are doing. It might be packaging, a word, a poem or something in a different business.

Measure the company according to fun and creativity. Business schools are obsessive about measurement. The result is vast departments of number-crunchers, but often little progress. What is most important in a company – or anything else – is unquantifiable.

Be different, but look safe. If you are different, you will stand out. But do not take risks with people who can make the difference between success and failure, especially if you are a woman trying to borrow money from the bank – which is how I came to be turned down for my original loan.

Be passionate about ideas. Entrepreneurs want to create a livelihood from an idea that has obsessed them; not necessarily a business, but a livelihood. When accumulating money drives out the ideas and the anger behind them, you are no longer an entrepreneur.

Feed your sense of outrage. Discontentment drives you to want to do something about it. There is no point in finding a new vision if you are not angry enough to want it to happen.

Make the most of the female element. Companies as we know them were created by men for men, often influenced by the military model, on complicated and hierarchical lines and are both dominated by authoritarian principles and resistant to change. By setting up their own businesses, women can challenge these models and will be welcomed by customers for doing so.

Believe in yourself and your intuition. There is a fine line between entrepreneurship and insanity. Crazy people see and feel things that others do not. But you have to believe that everything is possible. If you believe it, those around you will believe it too.

Have self-knowledge. You do not need to know how to do everything, but you must be honest enough with yourself to know what you cannot provide yourself.

Until they can teach these lessons, business schools will remain the whited sepulchres of the status quo.

Dame Anita Roddick, founder of Body Shop, will speak at the British Library on Wednesday night for Enterprise Week on the subject of Commerce with a Conscience

Tuesday, November 14, 2006

Tensions run high over City payouts

Tensions run high over City payouts

By Lina Saigol, European M&A Correspondent

Published: November 14 2006 22:01 | Last updated: November 14 2006 22:01

Tensions are running high amid the rainmakers and shooting stars of the City as bosses at some of the world’s biggest investment banks decide who should pocket multi-million dollar bonuses.

The process is always fraught. But this year it will produce an unusually sharp division between those who produce real revenues and those coasting on the mergers and acquisitions boom.

ADVERTISEMENT

Although bonuses across the board are expected to rise between 10 and 35 per cent, only the stellar performers in high-margin growth areas will receive the big payouts. “The best people will be paid so well that rival banks won’t be able to hire them away,” predicted Matthew Osborne, partner at Armstrong International, the European executive search firm that carried out the survey.

Individual high-performers across structured credit, equity derivatives, fund derivatives, commodities and corporate finance will see increases of up to 30 per cent for year-on-year bonuses.

However, because of stronger differentiation at below managing director levels, second and third-quartile performers should expect bonuses that are flat-to-down on 2005 levels. Last year bonuses increased between 15 and 20 per cent across the board.

The surge in M&A has helped boost bonuses for corporate financiers. The biggest rainmakers in the sector will see payouts increase by up to 35 per cent, with top European heads raking in between $8m and $10m (£4.2m-£5.3m). Top country heads will earn more than $5m, while sector heads can expect to take home between $3m and $4m.

Managing directors will also be able to make up to $3m, while the broader pool of M&A bankers will be paid up to $1.3m.

Oil, gas and power commodity traders are also expecting fat bonuses. These traders, who buy from producers and sell to industrial consumers around the world, will receive payouts of between 15 and 20 per cent.

Top performing traders of structured credit products can expect to take home between $2m and $3m, while global heads of credit derivatives will receive north of $4.5m. Even the more junior structurers could earn an unprecedented $700,000.

Calculating compensation for equity research, which is still treated as a cost centre within most investment banks because it does not produce direct revenue, continues to create challenges for managers. Some research analysts can expect to receive bonuses of 20 per cent, with top managing directors receiving $1m payouts. However, many will be disappointed since, while revenues have increased, so have fixed costs.

In equity sales, bonuses are expected to be up between 20 and 35 per cent, with the focus on retaining key people.

Underwriting volumes have increased this year, despite a slowdown in the second and third quarters, and those responsible for debt capital markets efforts across Europe can expect payouts north of $4m. Good junior performers will expect to be up 15-20 per cent on last year, while even managing directors not managing significant teams could take home up to $1.5m.

Compensation in interest rate sales remains lucrative. Those with demonstrable records and relationships will receive total compensation of between $2m and $3m, while a small number of individuals will receive more.

At the vice-president and director level, however, those without a strong personal franchise who have relied solely on the strength of the platform will see their compensation range from $500,000 to $1.5m.

Key players in equity derivatives can expect to rake in a healthy part of the bonus pool, with stars receiving as much as 8 per cent of their personal production.

Demand for fund-linked products in Asia and the US has boosted bonuses for fund derivatives specialists, with expectations reaching 25 per cent for the top performers.

However, due to the shortage in talent at the associate and vice-president level, these bankers may see an increase of between 30 and 60 per cent.

The private bankers will also enjoy a large share of the bonus pool this year, as strong equity markets have underpinned wealth creation and the consequential asset inflows into Europe. Expectations of increases range from 20-25 per cent on last year.

This is the first year of Goldman Sachs’ new pay structure, under which bankers are no longer paid a commission but instead receive a salary and a discretionary bonus. Morgan Stanley and Merrill Lunch continue to pay bankers a percentage of revenues from all their accumulated assets under management.

Although the mood among the bankers is buoyant now, in the coming weeks those who have shared a spirit of camaraderie for the rest of the year may find it wearing thin if they are among the losers come bonus day.

Monday, November 13, 2006

100个著名初等数学问题

100个著名初等数学问题

以下100个问题大部分不需要复杂计算和高等数学知识,更不需要了解太多的
数学公式。如果建模正确,通常可以很快解答,非常适合面试的brain test,事实
上CS和Finance行业的很多面试问题都和他们大同小异。

有空的兄弟没事做做,可以锻炼思路。祝大家offer 多多。

第01题 阿基米德分牛问题Archimedes' Problema Bovinum
太阳神有一牛群,由白、黑、花、棕四种颜色的公、母牛组成.
在公牛中,白牛数多于棕牛数,多出之数相当于黑牛数的1/2+1/3;黑牛数多于棕
牛数,多出之
数相当于花牛数的1/4+1/5;花牛数多于棕牛数,多出之数相当于白牛数的1/6+1/7.
在母牛中,白牛数是全体黑牛数的1/3+1/4;黑牛数是全体花牛数1/4+1/5;花牛数
是全体棕牛
数的1/5+1/6;棕牛数是全体白牛数的1/6+1/7.
问这牛群是怎样组成的?
第02题 德·梅齐里亚克的法码问题The Weight Problem of Bachet de Meziriac
一位商人有一个40磅的砝码,由于跌落在地而碎成4块.后来,称得每块碎片的重量
都是整磅数
,而且可以用这4块来称从1至40磅之间的任意整数磅的重物.
问这4块砝码碎片各重多少?
第03题 牛顿的草地与母牛问题Newton's Problem of the Fields and Cows
a头母牛将b块地上的牧草在c天内吃完了;
a'头母牛将b'块地上的牧草在c'天内吃完了;
a"头母牛将b"块地上的牧草在c"天内吃完了;
求出从a到c"9个数量之间的关系?
第04题 贝韦克的七个7的问题Berwick's Problem of the Seven Sevens
在下面除法例题中,被除数被除数除尽:
* * 7 * * * * * * * ÷ * * * * 7 * = * * 7 * *
* * * * * *
* * * * * 7 *
* * * * * * *
* 7 * * * *
* 7 * * * *
* * * * * * *
* * * * 7 * *
* * * * * *
* * * * * *
用星号(*)标出的那些数位上的数字偶然被擦掉了,那些不见了的是些什么数字
呢?
第05题 柯克曼的女学生问题Kirkman's Schoolgirl Problem
某寄宿学校有十五名女生,她们经常每天三人一行地散步,问要怎样安排才能使每
个女生同其
他每个女生同一行中散步,并恰好每周一次?
第06题 伯努利-欧拉关于装错信封的问题The Bernoulli-Euler Problem of the
Misaddressed
letters
求n个元素的排列,要求在排列中没有一个元素处于它应当占有的位置.
第07题 欧拉关于多边形的剖分问题Euler's Problem of Polygon Division
可以有多少种方法用对角线把一个n边多边形(平面凸多边形)剖分成三角形?
第08题 鲁卡斯的配偶夫妇问题Lucas' Problem of the Married Couples
n对夫妇围圆桌而坐,其座次是两个妇人之间坐一个男人,而没有一个男人和自己
的妻子并坐,
问有多少种坐法?
第09题 卡亚姆的二项展开式Omar Khayyam's Binomial Expansion
当n是任意正整数时,求以a和b的幂表示的二项式a+b的n次幂.
第10题 柯西的平均值定理Cauchy's Mean Theorem
求证n个正数的几何平均值不大于这些数的算术平均值.
第11题 伯努利幂之和的问题Bernoulli's Power Sum Problem
确定指数p为正整数时最初n个自然数的p次幂的和S=1p+2p+3p+…+np.
第12题 欧拉数The Euler Number
求函数φ(x)=(1+1/x)x及Φ(x)=(1+1/x)x+1当x无限增大时的极限值.
第13题 牛顿指数级数Newton's Exponential Series
将指数函数ex变换成各项为x的幂的级数.
第14题 麦凯特尔对数级数Nicolaus Mercator's Logarithmic Series
不用对数表,计算一个给定数的对数.
第15题 牛顿正弦及余弦级数Newton's Sine and Cosine Series
不用查表计算已知角的正弦及余弦三角函数.
第16题 正割与正切级数的安德烈推导法Andre's Derivation of the Secant and
Tangent
Series
在n个数1,2,3,…,n的一个排列c1,c2,…,cn中,如果没有一个元素ci的值介
于两个邻近
的值ci-1和ci+1之间,则称c1,c2,…,cn为1,2,3,…,n的一个屈折排列.
试利用屈折排列推导正割与正切的级数.
第17题 格雷戈里的反正切级数Gregory's Arc Tangent Series
已知三条边,不用查表求三角形的各角.
第18题 德布封的针问题Buffon's Needle Problem
在台面上画出一组间距为d的平行线,把长度为l(小于d)的一根针任意投掷在台
面上,问针触
及两平行线之一的概率如何?
第19题 费马-欧拉素数定理The Fermat-Euler Prime Number Theorem
每个可表示为4n+1形式的素数,只能用一种两数平方和的形式来表示.
第20题 费马方程The Fermat Equation
求方程x2-dy2=1的整数解,其中d为非二次正整数.
第21题 费马-高斯不可能性定理The Fermat-Gauss Impossibility Theorem
证明两个立方数的和不可能为一立方数.
第22题 二次互反律The Quadratic Reciprocity Law
(欧拉-勒让德-高斯定理)奇素数p与q的勒让德互反符号取决于公式
(p/q)·(q/p)=(-1)[(p-1)/2]·[(q-1)/2].
第23题 高斯的代数基本定理Gauss' Fundamental Theorem of Algebra
每一个n次的方程zn+c1zn-1+c2zn-2+…+cn=0具有n个根.
第24题 斯图谟的根的个数问题Sturm's Problem of the Number of Roots
求实系数代数方程在已知区间上的实根的个数.
第25题 阿贝尔不可能性定理Abel's Impossibility Theorem
高于四次的方程一般不可能有代数解法.
第26题 赫米特-林德曼超越性定理The Hermite-Lindemann Transcedence Theorem
系数A不等于零,指数α为互不相等的代数数的表达式A1eα1+A2eα2+A3eα3+…不
可能等于零.
第27题 欧拉直线Euler's Straight Line
在所有三角形中,外接圆的圆心,各中线的交点和各高的交点在一直线-欧拉线上
,而且三点
的分隔为:各高线的交点(垂心)至各中线的交点(重心)的距离两倍于外接圆的圆心
至各中线的
交点的距离.
第28题 费尔巴哈圆The Feuerbach Circle
三角形中三边的三个中点、三个高的垂足和高的交点到各顶点的线段的三个中点在
一个圆上.
第29题 卡斯蒂朗问题Castillon's Problem
将各边通过三个已知点的一个三角形内接于一个已知圆.
第30题 马尔法蒂问题Malfatti's Problem
在一个已知三角形内画三个圆,每个圆与其他两个圆以及三角形的两边相切.
第31题 蒙日问题Monge's Problem
画一个圆,使其与三已知圆正交.
第32题 阿波洛尼斯相切问题The Tangency Problem of Apollonius.
画一个与三个已知圆相切的圆.
第33题 马索若尼圆规问题Macheroni's Compass Problem.
证明任何可用圆规和直尺所作的图均可只用圆规作出.
第34题 斯坦纳直尺问题Steiner's Straight-edge Problem
证明任何一个可以用圆规和直尺作出的图,如果在平面内给出一个定圆,只用直尺
便可作出.
第35题 德里安倍立方问题The Deliaii Cube-doubling Problem
画出体积为一已知立方体两倍的立方体的一边.
第36题 三等分一个角Trisection of an Angle
把一个角分成三个相等的角.
第37题 正十七边形The Regular Heptadecagon
画一正十七边形.
第38题 阿基米德π值确定法Archimedes' Determination of the Number Pi
设圆的外切和内接正2vn边形的周长分别为av和bv,便依次得到多边形周长的阿基
米德数列:a0
,b0,a1,b1,a2,b2,…其中av+1是av、bv的调和中项,bv+1是bv、av+1的等比中项
. 假如已知
初始两项,利用这个规则便能计算出数列的所有项. 这个方法叫作阿基米德算法.
第39题 富斯弦切四边形问题Fuss' Problem of the Chord-Tangent Quadrilateral
找出半径与双心四边形的外接圆和内切圆连心线之间的关系.(注:一个双心或弦
切四边形的定
义是既内接于一个圆而同时又外切于另一个圆的四边形)
第40题 测量附题Annex to a Survey
利用已知点的方位来确定地球表面未知但可到达的点的位置.
第41题 阿尔哈森弹子问题Alhazen's Billiard Problem
在一个已知圆内,作出一个其两腰通过圆内两个已知点的等腰三角形.
第42题 由共轭半径作椭圆An Ellipse from Conjugate Radii
已知两个共轭半径的大小和位置,作椭圆.
第43题 在平行四边形内作椭圆An Ellipse in a Parallelogram,
在规定的平行四边形内作一内切椭圆,它与该平行四边形切于一边界点.
第44题 由四条切线作抛物线A Parabola from Four Tangents
已知抛物线的四条切线,作抛物线.
第45题 由四点作抛物线A Parabola from Four Points.
过四个已知点作抛物线.
第46题 由四点作双曲线A Hyperbola from Four Points.
已知直角(等轴)双曲线上四点,作出这条双曲线.
第47题 范·施古登轨迹题Van Schooten's Locus Problem
平面上的固定三角形的两个顶点沿平面上一个角的两个边滑动,第三个顶点的轨迹
是什么?
第48题 卡丹旋轮问题Cardan's Spur Wheel Problem.
一个圆盘沿着半径为其两倍的另一个圆盘的内缘滚动时,这个圆盘上标定的一点所
描出的轨迹
是什么?
第49题 牛顿椭圆问题Newton's Ellipse Problem.
确定内切于一个已知(凸)四边形的所有椭圆的中心的轨迹.
第50题 彭赛列-布里昂匈双曲线问题The Poncelet-Brianchon Hyperbola Problem
确定内接于直角(等边)双曲线的所有三角形的顶垂线交点的轨迹.
第51题 作为包络的抛物线A Parabola as Envelope
从角的顶点,在角的一条边上连续n次截取任意线段e,在另一条边上连续n次截取
线段f,并将
线段的端点注以数字,从顶点开始,分别为0,1,2,…,n和n,n-1,…,2,1,0.
求证具有相同数字的点的连线的包络为一条抛物线.
第52题 星形线The Astroid
直线上两个标定的点沿着两条固定的互相垂直的轴滑动,求这条直线的包络.
第53题 斯坦纳的三点内摆线Steiner's Three-pointed Hypocycloid
确定一个三角形的华莱士(Wallace)线的包络.
第54题 一个四边形的最接近圆的外接椭圆The Most Nearly Circular Ellipse
Circumscribing
a Quadrilateral
一个已知四边形的所有外接椭圆中,哪一个与圆的偏差最小?
第55题 圆锥曲线的曲率The Curvature of Conic Sections
确定一个圆锥曲线的曲率.
第56题 阿基米德对抛物线面积的推算Archimedes' Squaring of a Parabola
确定包含在抛物线内的面积.
第57题 推算双曲线的面积Squaring a Hyperbola
确定双曲线被截得的部分所含的面积.
第58题 求抛物线的长Rectification of a Parabola
确定抛物线弧的长度.
第59题 笛沙格同调定理(同调三角形定理)Desargues' Homology Theorem (Theorem
of
Homologous Triangles)
如果两个三角形的对应顶点连线通过一点,则这两个三角形的对应边交点位于一条
直线上.
反之,如果两个三角形的对应边交点位于一条直线上,则这两个三角形的对应顶点
连线通过一
点.
第60题 斯坦纳的二重元素作图法Steiner's Double Element Construction
由三对对应元素所给定的重迭射影形,作出它的二重元素.
第61题 帕斯卡六边形定理Pascal's Hexagon Theorem
求证内接于圆锥曲线的六边形中,三双对边的交点在一直线上.
第62题 布里昂匈六线形定理Brianchon's Hexagram Theorem
求证外切于圆锥曲线的六线形中,三条对顶线通过一点.
第63题 笛沙格对合定理Desargues' Involution Theorem
一条直线与一个完全四点形*的三双对边的交点与外接于该四点形的圆锥曲线构成
一个对合的四
个点偶. 一个点与一个完全四线形*的三双对顶点的连线和从该点向内切于该四线形的
圆锥曲线所引
的切线构成一个对合的四个射线偶.
*一个完全四点形(四线形)实际上含有四点(线)1,2,3,4和它们的六条连线
交点23,14,
31,24,12,34;其中23与14、31与24、12与34称为对边(对顶点).
第64题 由五个元素得到的圆锥曲线A Conic Section from Five Elements
求作一个圆锥曲线,它的五个元素--点和切线--是已知的.
第65题 一条圆锥曲线和一条直线A Conic Section and a Straight Line
一条已知直线与一条具有五个已知元素--点和切线--的圆锥曲线相交,求作它们的
交点.
第66题 一条圆锥曲线和一定点A Conic Section and a Point
已知一点及一条具有五个已知元素--点和切线--的圆锥曲线,作出从该点列到该曲
线的切
线.
第67题 斯坦纳的用平面分割空间Steiner's Division of Space by Planes
n个平面最多可将整个空间分割成多少份?
第68题 欧拉四面体问题Euler's Tetrahedron Problem
以六条棱表示四面体的体积.
第69题 偏斜直线之间的最短距离The Shortest Distance Between Skew Lines
计算两条已知偏斜直线之间的角和距离.
第70题 四面体的外接球The Sphere Circumscribing a Tetrahedron
确定一个已知所有六条棱的四面体的外接球的半径.
第71题 五种正则体The Five Regular Solids
将一个球面分成全等的球面正多边形.
第72题 正方形作为四边形的一个映象The Square as an Image of a Quadrilateral
证明每个四边形都可以看作是一个正方形的透视映象.
第73题 波尔凯-许瓦尔兹定理The Pohlke-Schwartz Theorem
一个平面上不全在同一条直线上的四个任意点,可认为是与一个已知四面体相似的
四面体的各
隅角的斜映射.
第74题 高斯轴测法基本定理Gauss' Fundamental Theorem of Axonometry
正轴测法的高斯基本定理:如果在一个三面角的正投影中,把映象平面作为复平面
,三面角顶
点的投影作为零点,边的各端点的投影作为平面的复数,那么这些数的平方和等于零.
第75题 希帕查斯球极平面射影Hipparchus' Stereographic Projection
试举出一种把地球上的圆转换为地图上圆的保形地图射影法.
第76题 麦卡托投影The Mercator Projection
画一个保形地理地图,其坐标方格是由直角方格组成的.
第77题 航海斜驶线问题The Problem of the Loxodrome
确定地球表面两点间斜驶线的经度.
第78题 海上船位置的确定Determining the Position of a Ship at Sea
利用天文经线推算法确定船在海上的位置.
第79题 高斯双高度问题Gauss' Two-Altitude Problem
根据已知两星球的高度以确定时间及位置.
第80题 高斯三高度问题Gauss' Three-Altitude Problem
从在已知三星球获得同高度瞬间的时间间隔,确定观察瞬间,观察点的纬度及星球
的高度.
第81题 刻卜勒方程The Kepler Equation
根据行星的平均近点角,计算偏心及真近点角.
第82题 星落Star Setting
对给定地点和日期,计算一已知星落的时间和方位角.
第83题 日晷问题The Problem of the Sundial
制作一个日晷.
第84题 日影曲线The Shadow Curve
当直杆置于纬度φ的地点及该日太阳的赤纬有δ值时,确定在一天过程中由杆的一
点投影所描
绘的曲线.
第85题 日食和月食Solar and Lunar Eclipses
如果对于充分接近日食时间的两个瞬间太阳和月亮的赤经、赤纬以及其半径均为已
知,确定日
食的开始和结束,以及太阳表面被隐蔽部分的最大值.
第86题 恒星及会合运转周期Sidereal and Synodic Revolution Periods
确定已知恒星运转周期的两共面旋转射线的会合运转周期.
第87题 行星的顺向和逆向运动Progressive and Retrograde Motion of Planets
行星什么时候从顺向转为逆向运动(或反过来,从逆向转为顺向运动)?
第88题 兰伯特慧星问题Lambert's Comet Prolem
借助焦半径及连接弧端点的弦,来表示慧星描绘抛物线轨道的一段弧所需的时间.
第89题 与欧拉数有关的斯坦纳问题Steiner's Problem Concerning the Euler
Number
如果x为正变数,x取何值时,x的x次方根为最大?
第90题 法格乃诺关于高的基点的问题Fagnano's Altitude Base Point Problem
在已知锐角三角形中,作周长最小的内接三角形.
第91题 费马对托里拆利提出的问题Fermat's Problem for Torricelli
试求一点,使它到已知三角形的三个顶点距离之和为最小.
第92题 逆风变换航向Tacking Under a Headwind
帆船如何能顶着北风以最快的速度向正北航行?
第93题 蜂巢(雷阿乌姆尔问题)The Honeybee Cell (Problem by Reaumur)
试采用由三个全等的菱形作成的顶盖来封闭一个正六棱柱,使所得的这一个立体有
预定的容积
,而其表面积为最小.
第94题 雷奇奥莫塔努斯的极大值问题Regiomontanus' Maximum Problem
在地球表面的什么部位,一根垂直的悬杆呈现最长?(即在什么部位,可见角为最
大?)
第95题 金星的最大亮度The Maximum Brightness of Venus
在什么位置金星有最大亮度?
第96题 地球轨道内的慧星A Comet Inside the Earth's Orbit
慧星在地球的轨道内最多能停留多少天?
第97题 最短晨昏蒙影问题The Problem of the Shortest Twilight
在已知纬度的地方,一年之中的哪一天晨昏蒙影最短?
第98题 斯坦纳的椭圆问题Steiner's Ellipse Problem
在所有能外接(内切)于一个已知三角形的椭圆中,哪一个椭圆有最小(最大)的
面积?
第99题 斯坦纳的圆问题Steiner's Circle Problem
在所有等周的(即有相等周长的)平面图形中,圆有最大的面积.
反之:在有相等面积的所有平面图形中,圆有最小的周长.
第100题 斯坦纳的球问题Steiner's Sphere Problem
在表面积相等的所有立体中,球具有最大体积.
在体积相等的所有立体中,球具有最小的表面.

COMPANIES UK: Barclays buys in staff options

£185m in the first half of this year - or £211m minus the £26m exercise price

COMPANIES UK: Barclays buys in staff options

By: By Jim Pickard, Financial Times
Published: Aug 28, 2006

Barclays' asset management division has spent £211m in the first half of this year buying back share options awarded to staff three years ago, the bank admitted last night.

The generosity of Barclays Global Investors (BGI) to its staff is underlined by new figures showing it has spent hundreds of millions buying back share options from its employees since it launched its incentive scheme in 2000.

Under the scheme, staff are awarded options which after three years are bought back by the group.

The amount of money spent on this has been on the increase. In 2004 BGI spent £60m on share buy-backs, which rose last year to £160m.

A report by analysts at Evolution Securities, the stockbroker, said the scheme would constitute a "growing, but largely unseen" headwind for the group.

"One number you won't have seen in Barclays' recent results is the £211m cash cost of buying back BGI shares from BGI employees in the half year. You don't see it, because this is a cost that doesn't touch the profit and loss account."

Employees received £185m in the first half of this year - or £211m minus the £26m exercise price on the options.

Barclays would not comment on the specific figures yesterday. But it defended the scheme, saying that the purchase of shares wasnot a "cash outflow against which there is no value in return".

Analysts from Keefe, Bruyette & Woods said the figures were "not fresh news" and had been indicated in several ways through BGI's report and accounts.

The group, which has $1,600bn under management, is chaired by Bob Diamond, who is also head of Barclays Capital, the group's investment banking arm.

DJI plans hedge fund 'clone' launch

DJI tries to copy the hedge fund using simple rules, but the effect is not very clear.

DJI plans hedge fund 'clone' launch

By Steve Johnson

Published: November 13 2006 02:00 | Last updated: November 13 2006 02:00

Dow Jones Indexes is in talks to launch the world's first investable index trackers designed to mimic the behaviour of a range of hedge fund strategies.

The artificial trackers would potentially allow investors to access the returns of hedge funds without having to pay the high fees demanded by the industry, typically a 2 per cent annual fee and a 20 per cent performance fee.

If successful, the initiative would pose a threat to hedge funds that merely generate the beta of their chosen trading strategy without generating sufficient alpha to justify their high fee structure.

"We are thinking about this and are talking to institutions. I'm confident that it will happen," said John Prestbo, executive director of Dow Jones Indexes.

"We have gone through a period where everyone can proclaim to be a hedge fund manager. That kind of nonsense will be weeded out by these indices."

His comments come just days after Blake Grossman, chief executive of Barclays Global Investors, the world's biggest money manager, warned there were "too many" hedge funds and that pressure on them would grow to justify their fees.

DJI already operates a suite of hedge fund indices that invest in a basket of managed accounts operated by hedge funds. Now it believes it can go a step further and create the same performance attributes by investing directly in the assets that these hedge funds ultimately invest in.

"Theoretically, we can build a model that mimics the behaviour of the hedge funds," said Mr Prestbo, who believes the approach is best suited to strategies where performance is largely determined by market factors and there is adequate liquidity, such as equity long/short, equity neutral, convertible arbitrage and fixed income arbitrage.

Wider roaming strategies, which are seen as relying more on fund manager skill such as global macro, would be harder to replicate.

The mechanical index trackers would also be a huge boon to transparency in the notoriously opaque hedge fund sector as DJI would publish the rules determining the construction of each clone, replacing the "black boxes" of the industry with a "glass box".

Fees would be lower than those charged by existing hedge funds although a need for high levels of turnoverin each portfolio maymean charges remain higher than for long-only index trackers.

Benjamin Bowler, analyst at Merrill Lynch, predicted cloned hedge fund strategies would become commonplace.

"There are potentially ways you can use rules-based strategies to reduce the cost of generating hedge fund-type returns. These strategies will become increasingly attractive," said Mr Bowler, who doubted there were enough talented hedge fund managers to cope with an expected doubling of the sector to $2,500bn. "This is similar to the upspring of passive money in traditional fund management that we saw 20 years ago," he added.

However, Harry Kat, professor of risk management at London's Cass Business School, was cautious about the accuracy of such replication techniques.

"You can explain up to 60-70 per cent of the return for funds of funds specialising in equity long/short; you can call that replication," he said. "For equity market neutral, the fit will be a lot less. The same for fixed income arbitrage - there are a lot of different games they can play and it's hard to replicate that."

Mr Prestbo speculated that the clones could be launched if and when equity markets weakened.

"When markets are going up that doesn't breed change. When markets turn, different arrangements must be made.

"This might briefly accelerate turnover, that is to say hedge funds closing down because they can't deliver anything but beta. There are lots of weeds in the garden."

Bank revolving door spins faster

Barclays management changes after their chief takes the post: Deanna Oppenheimer

Bank revolving door spins faster

By Jane Croft

Published: November 13 2006 02:00 | Last updated: November 13 2006 02:00

By next spring, more than a third of the Barclays senior executive management team will be relatively new to the bank.

The revolving door at Barclays' Canary Wharf headquarters, which began with the appointment of Deanna Oppenheimer in August 2005, has drawn attention as it spins round ever faster.

ADVERTISEMENT

The UK's third-largest bank is in the middle of a rapid transformation under John Varley as the Barclays chief executive attempts to make the bank a force capable of competing with its rivals expanding round the world.

Mr Varley, who took over as chief executive in 2004, wants to graft the competitive global ethos and performance measures of Barclays Capital on to the underperforming parts of the business, such as the retail bank.

He has spoken openly of the need to raise the "metabolic rate" of Barclays. While Mr Varley is generally liked by investors, his boardroom changes and importing of executives at senior levels have raised eyebrows.

Critically, his management changes have removed or sidelined people once seen as rising stars, such as David Roberts, former head of international banking, and Roger Davis, former UK head of banking. Both were once considered contenders for the chief executive's position and left this year.

Gary Hoffman, who was head of Barclaycard and another contender for the top job, has been moved to be deputy chairman in charge of social responsibility.

Naguib Kheraj, the well-respected finance director, will also leave next April to be replaced by Chris Lucas, partner at PwC, after the youthful Mr Kheraj concluded that he wanted a new challenge outside the bank.

The upheavals have also led to a flood of departures at lower management levels - particularly at the UK retail bank.

They have instead found senior roles at a variety of consumer finance operators and investment banks.

Mike Rogers, managing director of UK retail banking at Barclays, left this year to become chief executive of Liverpool Victoria, the friendly society. Wai Au, chief operating officer at the UK retail bank, has also left.

Gary Jennison, former managing director of the branch network at Barclays, left to become chief executive of Secure Trust bank, owned by Arbuthnot, the investment bank.

Steve Clutton, former finance chief of Barclays' UK retail banking division, left to join IG Group, the spread betting firm as finance director.

Peter Crook, ex-managing director of Barclaycard's consumer finance division, left last year to become head of Provident Financial's home credit operation.

Tiku Patel, who was managing director at Barclays Premier banking, has joined Experian, the information company, as chief operating officer.

As existing staff left, so Barclays began aggressively hiring new staff from rivals such as Citigroup and Washington Mutual. By next April, eight of its 20-strong top executive management team - or 40 per cent - will be made up of executives who joined the bank only in the past 12 to 18 months.

The highest profile executive hiring is Frits Seegers, who was hired from Citigroup to be chief executive of global retail and commercial banking.

Some observers see the appointment of Mr Seegers as a move to counterbalance the power of Bob Diamond, who runs the best performing parts of the Barclays empire - Barclays Capital, the investment bank, and BGI, its asset management business.

Deanna Oppenheimer joined from Washington Mutual as head of UK retail banking and Antony Jenkins was hired from Citigroup to Barclaycard.

Chris Grigg, group treasurer, joined from Goldman Sachs, where he was a partner, and Ahmed Khizer Khan, who joined as chief executive of new markets including India, arrived from Citibank.

Marcus Agius, from Lazard, replaces Matt Barrett as the new chairman in January and Steve Booysen, chief executive of Absa, joined with Barclays' acquisition of Absa last year.

In turn, the new hires have also recruited for their teams - sometimes turning to their old employers for key staff. Since his arrival in July, Frits Seegers is understood to have hired up to 20 staff from Citigroup including Ahmed Khizer Khan.

Deanna Oppenheimer has hired former Washington Mutual staff such as Mike Amato, who is now chief distribution and product officer in UK retail banking.

At least 40 other senior executives have joined Barclays from other banks such as UBS, Citigroup, Morgan Stanley and Julius Baer since August 2005.

Many have been recruited into the wealth management division, where Barclays is investing £375m over three years developing the business and has hired 370 staff so far this year.

Simon Maugham, banks analyst at Blue Oak Capital, says: "I think it is unusual for a bank to go through change of this scope and indeed the continuing nature of it all begs the question, when is it going to end?"

Ian Gordon, Dresdner Kleinwort analyst, adds: "I guess we cannot object to an influx of new talent . . . I would struggle to say all the management changes have been because Barclays has suddenly found a pool of untapped talent from outside."

The rate of change is unusual because Barclays has continued reporting strong profit and is expected to report another solid pre-close trading statement on November 28.

One banking consultant said: "It is clear the executives want the rest of the bank to perform at the same level as Barclays Capital and Barclays Global Investors, otherwise earnings will be diluted."

Barclays says its latest employee survey showed an improvement in staff satisfaction. Staff turnover in the UK rose in 2005 to 20.4 per cent against 19.4 per cent in 2004.

It says: "We have 118,000 people worldwide and we do not think there has been an abnormal amount of change. We are an ambitious organisation and we believe our investment has paid off.

"The morale in the bank is very good and the new hires bring fresh ideas and perspectives, which therefore creates more opportunities."

Other banks such as HBOS and Lloyds TSB have also seen some changes over the past 18 months.

But these organisations have not seen the scale of the changes as at Barclays over such a relatively short period. Many of the new hires at Barclays are also new to the UK market.

However, analysts will not have long to wait before they can see whether the scale of changes at Barclays has the desired effect of lifting performance in sluggish parts of the group.