john mangual

1,837 reputation

211

bio	website	math.ucsb.edu/~mangual
	location	New York, NY
	age	28
visits	member for	2 years, 5 months
	seen	May 18 at 19:31
stats	profile views	186

Graduate Student at UCSB. Interested in Statistics, Geometry and Physics. Asking the questions I've always wanted to ask.

	1,837 reputation	bio	website	math.ucsb.edu/~mangual	visits	member for	2 years, 5 months
211 badges		location	New York, NY		seen	May 18 at 19:31

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32 Favorites

added views newest activity votes

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kviews

Trigonometric sums related to the Verlinde formula

may 14 at 20:55 Philippe Blanc 86

votes

answer

656

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Is there a proof of Benford's Law?

statistics intuition

may 14 at 11:04 Community♦ 1

votes

answer

254

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Universal Cover of projective plane glued to Möbius strip

algebraic-topology covering-spaces

may 10 at 13:20 azimut 5,478

votes

answer

370

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Geometry IMO 1988

euclidean-geometry analytic-geometry contest-math

may 8 at 15:03 Community♦ 1

votes

answer

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Proving upper limit on number of moves?

combinatorics recreational-mathematics puzzle dynamical-systems

feb 20 at 16:52 Ivan Loh 6,783

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answers

kviews

Beta function derivation

probability-theory statistics special-functions

jan 23 at 16:17 Scortchi 109

votes

answer

148

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Bicartesian squares of abelian groups

homework homological-algebra

dec 1 at 21:42 jmracek 344

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answers

848

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An Inequality problem relating $\prod\limits^n(1+a_i^2)$ and $\sum\limits^n a_i$

inequality

nov 17 at 5:05 y zhao 833

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answers

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How difficult is it to impose a differential structure on a fractal?

differential-geometry algebraic-topology fractals geometric-topology geometric-measure-theory

nov 14 at 4:22 user32240 4,846

votes

answer

288

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Prove that $\int_0^1[f''(x)]^2dx\ge4.$

calculus real-analysis analysis inequality calculus-of-variations

oct 27 at 9:02 commenter 1,007

votes

answer

745

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Ellipse 3-partition: same area and perimeter

geometry partitions

oct 14 at 11:38 Jack D'Aurizio 2,937

votes

answers

157

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In a graph, the vertices can be partitioned $V=V_1\cup V_2$ so that at most half of all edges run within each part?

graph-theory

oct 10 at 19:05 David Harris 572

votes

answers

187

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General term of a double dimensional sequence

sequences-and-series

oct 6 at 12:05 Gottfried Helms 7,197

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answer

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Action of $\mathfrak{sl}_2(\Bbb{C})$ on $\textrm{Sym}^2 V$

representation-theory lie-algebras

sep 19 at 1:08 Michael Joyce 7,058

votes

answers

465

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Inequality. $\sqrt{\frac{11a}{5a+6b}}+\sqrt{\frac{11b}{5b+6c}}+\sqrt{\frac{11c}{5c+6a}} \leq 3$

inequality

sep 11 at 13:06 Iuli 3,095

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answers

kviews

Are non-circular manholes possible?

geometry

aug 1 at 15:15 Hans-Peter E. Kristiansen 445

votes

answer

374

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Prove that: $ \int_{0}^{1} \ln \sqrt{\frac{1+\cos x}{1-\sin x}}\le \ln 2$

calculus real-analysis integral inequality definite-integral

jul 30 at 22:11 Zarrax 19.7k

votes

answers

107

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Finding $a$ from $\lim\limits_{x\rightarrow0}(1+a\sin x)^{\csc x} =4$

calculus limit

jul 29 at 17:32 Gigili 3,153

votes

answers

115

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Non-Galois cubic extensions

abstract-algebra galois-theory

jul 7 at 17:30 Arturo Magidin 158k

votes

answers

608

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How can I prove $\underbrace{\int \ldots \int}_{n} |x| dx = \frac{x^n |x|}{n+1}+C$?

calculus

apr 27 '12 at 12:45 J. M. 38.9k

votes

answer

120

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Is there a neat way to show $\int_{-1}^1 \frac{ U_n(z) U_n(z)}{\sqrt{1-z^2}} \mathrm{d} z = \pi (n+1)$

calculus polynomials special-functions orthogonal-polynomials

apr 17 '12 at 1:20 J. M. 38.9k

votes

answer

149

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How does one prove that $\frac{1}{2}\cdot\frac{3}{4}\cdots \frac{2n-1}{2n}\leq \frac{1}{\sqrt{3n+1}}?$

discrete-mathematics

mar 13 '12 at 18:56 Martin Argerami 16.9k

votes

answers

266

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Embedding Mazes - Spanning Trees of a Grid Graph

graph-theory

mar 12 '12 at 20:55 utdiscant 1,459

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answers

766

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Prove $\int_0^1 \left| \frac{f^{''}(x)}{f(x)} \right| dx \geq4$

calculus real-analysis

mar 11 '12 at 4:55 Nick Strehlke 3,057

votes

answers

436

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Determinant of a generalized Pascal matrix

linear-algebra combinatorics matrices determinant

dec 5 '11 at 10:42 Marc van Leeuwen 23.8k

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answer

221

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Hyperbolic area and $SL_2$

complex-analysis measure-theory hyperbolic-geometry

sep 15 '11 at 3:01 J. M. 38.9k

votes

answers

204

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Differentiability of $f(x)$ and continuity of $f'(x)$: same thing or different?

calculus

sep 8 '11 at 21:20 Srivatsan 15.6k

votes

answer

481

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IMO 2011 Problem 5 - Show that $f(m) \mid f(n)$ if $f(m) \leq f(n)$

number-theory contest-math

jul 21 '11 at 18:40 Luboš Motl 3,707

votes

answer

251

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Euler class and Vandermonde polynomial

algebraic-topology characteristic-classes

jun 25 '11 at 10:42 Grigory M 6,842

votes

answers

247

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Analogies between Prime Ideals and Knots

number-theory soft-question arithmetic-geometry

may 14 '11 at 2:15 Community♦ 1