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Inequality

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pankaj

Post subject: Inequality

Posted: Sat, 7 Jul 2012 02:42:38 UTC

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Joined: Tue, 13 Jun 2006 11:57:53 UTC
Posts: 232
Location: new delhi

For

, prove that

$\sin\pi x\leq4x(1-x)$

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outermeasure

Post subject: Re: Inequality

Posted: Sat, 7 Jul 2012 02:55:27 UTC

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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6004
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)

pankaj wrote:

For

, prove that

$\sin\pi x\leq4x(1-x)$

Hint: second derivative.

_________________
$\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}$

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pankaj

Post subject: Re: Inequality

Posted: Sat, 7 Jul 2012 04:20:50 UTC

S.O.S. Oldtimer

Joined: Tue, 13 Jun 2006 11:57:53 UTC
Posts: 232
Location: new delhi

Should I invoke Rolle's

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