Haskell Curry

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bio	website	math.jussieu.fr/~leila/…
	location	Lhasa, Tibet
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We choose to do mathematics, not because it is easy, but because it is hard.

$$ \text{Einstein's Field Equations:} \quad \mathbf{G} = \frac{8 \pi G}{c^{4}} \mathbf{T}. $$

	11,063 reputation	bio	website	math.jussieu.fr/~leila/…	visits	member for	8 months
855 badges		location	Lhasa, Tibet		seen	Mar 19 at 2:45

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Mar 19	comment	Norms involving positive operators A simple counterexample comes from $ -2I \leq I $. Of course, if both $ A $ and $ B $ are required to be positive, then a counterexample is a little harder to find.
Mar 19	comment	Norms involving positive operators @julien: I think saying that $ A \leq B $ requires both $ A $ and $ B $ to be at least self-adjoint operators.
Mar 19	comment	Help with proving: If $X$ is a Hilbert $A$-$B$-module, then $ \\| _A \langle x,x \rangle \\| = \\| \langle x,x \rangle _B \\| $ for all $x\in X $. @Euthenia: Do you understand the explanation given here? I hope that I’ve managed to clear your doubts. Wegge-Olsen’s book K-Theory and C$ ^{\ast} $-Algebras also contains a proof of this result.
Mar 18	revised	Help finding a norm and using the Riesz Representation Theorem. added 325 characters in body; edited title
Mar 18	revised	If $ \eta $ and $ \varphi $ are closed differential forms, then prove that $ \varphi \wedge \eta $ is a closed differential form. added 93 characters in body; edited tags; edited title
Mar 18	revised	Help with proving: If $X$ is a Hilbert $A$-$B$-module, then $ \\| _A \langle x,x \rangle \\| = \\| \langle x,x \rangle _B \\| $ for all $x\in X $. edited tags
Mar 18	comment	*In a C-algebra, put $a^a \sim aa^$. Transitivity fails?** I get your point now, Mike. Yes, it’s important to show that $ a_{1} \in A $ because it’ll be used to establish an equivalence between $ x^{1/2} $ and $ y^{1/2} $ within $ A $ itself, and you certainly don’t want to step outside of $ A $ into $ B(\mathcal{H}) \setminus A $ in order to do that. It’s a clever argument! :) Once again, impressive job!
Mar 18	revised	Extension of a continuous map on $ {\mathbf{GL}_{n}}(\mathbb{R}) $ to $ {\mathbf{M}_{n}}(\mathbb{R}) $. added 7 characters in body
Mar 18	revised	*Find ${T^{}}(p(x))$ for an arbitrary $p(x) = a+bx+cx^2$** edited title
Mar 18	reviewed	Approve suggested edit on *Find ${T^{}}(p(x))$ for an arbitrary $p(x) = a+bx+cx^2$**
Mar 18	answered	Extension of a continuous map on $ {\mathbf{GL}_{n}}(\mathbb{R}) $ to $ {\mathbf{M}_{n}}(\mathbb{R}) $.
Mar 18	reviewed	Approve suggested edit on calculate $\lim_{x \rightarrow 0}\left ( x^{-6}\cdot (1-\cos(x)^{\sin(x)})^2 \right )$
Mar 18	answered	Help with proving: If $X$ is a Hilbert $A$-$B$-module, then $ \\| _A \langle x,x \rangle \\| = \\| \langle x,x \rangle _B \\| $ for all $x\in X $.
Mar 18	comment	*In a C-algebra, put $a^a \sim aa^$. Transitivity fails?** Yes. My comment was simply a prompt to you to provide some explanation for that fact, which isn’t immediately obvious. Further, as $$ a = w x^{1/2} = w x^{1/4} x^{1/4}, $$ you can simply write $ a_{1} = w x^{1/4} $ without the need of mentioning any polynomial approximation. Otherwise, the proof looks watertight. Good job! :)
Mar 18	reviewed	Approve suggested edit on Let $A$ be a Lebesgue measurable subset of $\mathbb{R}$ with $m(A)>0$. Show that there is a bounded measurable $B$ subset $A$ with $m(B)>0$
Mar 18	revised	Showing that a certain inequality holds for all $ x \in \mathbb{R} $ and $ n \in \mathbb{N} $. added 27 characters in body
Mar 18	revised	Extension of a continuous map on $ {\mathbf{GL}_{n}}(\mathbb{R}) $ to $ {\mathbf{M}_{n}}(\mathbb{R}) $. added 122 characters in body; edited tags; edited title
Mar 18	reviewed	Close How do you determine if a function is nonelementary antiderivative
Mar 18	reviewed	Close Moving point along the vector
Mar 18	reviewed	Leave Open What is the Maths equation for positive integers?