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Mirillis Action! 1.9.1 key by Senzati.rar DownloadJohn Buchanan (footballer, born 1904)
John Buchanan (15 May 1904 – 22 November 1981) was a Scottish footballer who played as a centre forward in the Football League for Derby County and Aston Villa. He was on the books of Celtic, Aberdeen and St Johnstone without appearing in their first-team.
References
Category:1904 births
Category:1981 deaths
Category:People from Arbroath
Category:Scottish footballers
Category:Association football forwards
Category:Celtic F.C. players
Category:Aberdeen F.C. players
Category:St Johnstone F.C. players
Category:Derby County F.C. players
Category:Aston Villa F.C. players
Category:English Football League playersDay: September 19, 2016
Today in History September 19: In 1776, George
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Fitting a square step as a triangle
Let $f$ be a monotone increasing function with $f(0)=0$ and there exists $\alpha > 0$ such that $f(x)-f(y)\ge \alpha (x-y)$.
I want to prove that there exists a $\beta >0$ such that
$$\beta(a-b)+\beta^2(b-c)+\beta^2(c-a) \le (\alpha-\beta)(a+b+c).$$
Is the idea right to decompose the function into three parts and prove it?
A:
Write $f(x) = f(0) + (\alpha – \beta)x + h(x)$, and use the fact that $f(0)=0$. Also, $h$ is $L_2$ since $f$ is monotone increasing. Then, by the monotone-convergence theorem, there exists $M \in \Bbb R$ so that $|h(x) – M| 0$. Then
$$\beta (a-b) + \beta^2(b-c) + \beta^2(c-a) \le h(a) + h(b) + h(c) – \alpha (a+b+c) = (\alpha – \beta) (a+b+c).$$
The desired result follows from the triangle inequality.
6 F.Supp. 604 (1934)
MARSHALL
v.
UNITED STATES.
No. 20709.
District Court, E. D. New York.
August 5, 1934.
*605 Hiscock & Barnard, of New York City (John F. McAuley, of New York City, of counsel), for plaintiff.
W. P. Rogers
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