Linear bottleneck assignment problem: Difference between revisions

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{{distinguish|Cartan's theorem}}
In [[potential theory]], a branch of [[mathematics]], '''Cartan's lemma''', named after [[Henri Cartan]], is a bound on the measure and complexity of the set on which a logarithmic [[Newtonian potential]] is small.  The following statement can be found in Levin's book.<ref>B.Ya. Levin, ''Lectures on Entire Functions''</ref>


Let ''&mu;'' be a finite positive [[Borel measure]] on the complex plane '''C''' with ''&mu;''('''C''')&nbsp;=&nbsp;''n''.  Let ''u''(''z'') be the logarithmic potential of&nbsp;''&mu;'':


:<math>u(z) = \frac{1}{2\pi}\int_\mathbf{C} \log|z-\zeta|\,d\mu(\zeta)</math>
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Given ''H''&nbsp;&isin;&nbsp;(0,&nbsp;1), there exist discs of radius ''r''<sub>''i''</sub> such that
 
:<math>\sum_i r_i < 5H\,</math>
 
and
 
:<math>u(z) \ge \frac{n}{2\pi}\log \frac{H}{e}</math>
 
for all ''z'' outside the union of these discs.
 
==Notes==
 
<references/>
 
{{mathanalysis-stub}}
[[Category:Complex analysis]]

Latest revision as of 17:07, 3 October 2014


I've seen worse, fallen from worse, but there is a nice ride-around if you don't want to start the ride off with wounded bike or body parts. For more serious cyclists, next to bicycles themselves, proper shoes are the most important piece of equipment. You will find two main forms of mountain and road bike stems. If you don’t need the overly aggressive styling of the Scapel 5 then you will find the Rush 6 a welcome alternative. However, due to its high price tag and light weight, it is seldom used for jumping and downhill races.

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