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visits member for 2 years, 2 months
seen Jul 23 at 2:54

A mathematician, a programmer, etc. etc.


Jul
20
comment An English question for a logical term
Well, be fair, the three google results are: this thread, the other thread you linked to, and a paper which has the exact phrase "...depend only on the presence, in the tuple, of implications...". It looks like no one uses the term "tuple of implications", per se.
Jun
17
comment How to compute this integral involving sech?
I think you might want to consider the stationary phase approximation...or method of steepest descent, whichever (I always get them confused!).
Jun
17
comment How to compute this integral involving sech?
What have you tried? (And is $\epsilon$ "small and positive"?)
Jun
17
comment Question on $\mathfrak{sl}(2,\mathbb R)$
@PeterFranek, could you remind me why it's not a group? I thought it was a subgroup (since it has the identity element and the Baker-Campbell-Hausdorff formula suggests it is closed under multiplication, right?) but rarely is it the full group...am I mistaken?
Jun
8
comment Intuition behind the definition of a derivative by Lang
Maybe it's because I'm drunk, but isn't the $\lambda y$ term merely the linear term (i.e., derivative) and $\varphi(y)$ the "bonus parts which vanish in the appropriate limit"? Just as if for a usual function in calculus 101 we would Taylor expand $f(x+h)=f(x)+f'(x)h+g(h)$ where $g(h)\sim o(h^{2})$. The derivative would naturally be the linear (first) term...well, the coefficient to $h$...
May
11
comment What's the term for a “physical vector space”?
@RobertIsrael perhaps use the "accountant's trick" and let negative fruit be a deficit owed to someone, and fractional fruit be a fraction of a fruit? (It works in Sraffian economics!)
May
3
comment How would you evaluate $I:=\int_ {0}^{\infty} \frac {\cos(ax)} {(x^2 + b^2)^n} \ \mathrm{d}x$?
This is really a cute way to solve the problem, I'm glad you pointed this out :)
May
3
comment How would you evaluate $I:=\int_ {0}^{\infty} \frac {\cos(ax)} {(x^2 + b^2)^n} \ \mathrm{d}x$?
Consider the real part of the integral $\int(x^2+b^2)^{-n}\exp(iax)\,\mathrm{d}x$ might help...
Apr
22
comment What's the name of this category
Isn't it isomorphic to the category $C_{A\times B}$?
Apr
20
comment Link between a topological space and a manifold
The topology is the collection of open sets of the space (by definition, a member of the topology is called an "open set"). But when a manifold "locally looks Euclidean", you're talking about charts...the image of a chart is itself an open set in the manifold, which requires a topology to talk about...
Apr
20
comment Why the $\zeta$ letter is like this?
@Goos, the difference is really negligible. Once you get one method of writing a zeta, it's not terribly difficult to deform the orthography into the one you desire. But starting with some zeta, I found, has been the hard part (for me anyways).
Apr
20
comment Why the $\zeta$ letter is like this?
foundalis.com/lan/hw/grkhandw.htm
Apr
15
comment Solve $\sqrt{1+\sqrt{1-4x^2}}=x\left( 1+\sqrt{1+\sqrt{1+2\sqrt{1-4x^2}}}\right).$
Perhaps set $u=\sqrt{1-4x^{2}}$, so $x = \sqrt{1-u^{2}}/2$ and the problem becomes $2=\sqrt{1-u}(1+\sqrt{1+\sqrt{1+2u}})$...?
Apr
11
comment Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x $
So...what have you attempted so far?
Mar
31
comment Tensor fields and vector bundles
To be precise, on the level of sections, don't we have an isomorphism $\Gamma(E\otimes F)\cong\Gamma(E)\otimes\Gamma(F)$ and not a strict equality?
Mar
31
comment Divergent Alternating Series
But if $p=1/2$ then $b_{9} = -1/2 < 0$, contradicting one of the premises of the problem ($b_{n}>0$ for all $n$).
Mar
30
comment Tangent space of the tangent bundle
Well...is $dg_{(x,0)}$ surjective?
Mar
8
comment Topological Quantum Field theories
@SanathDevalapurkar, also, where I'm studying -- I studied at UC Davis as an undergraduate. My current situation is rather strange (not that I'm private about it, I just cannot describe it in 140 characters!). I still study quantum gravity, though :)
Mar
8
comment Topological Quantum Field theories
In, e.g., 1+1 dimensional TQFT, dynamics is done by specifying the number of loops you begin with at time $t=0$, and how many you have at $t=1$, as well as the topology of the world-sheet for $0<t<1$. BUT the partition function (controlling dynamics) then becomes a function of the topological invariants (which invariants depends on the TQFT). This is good for, e.g., BF-theory since computing topological invariants is simpler than, say, solving the Wheeler-DeWitt equation :)
Mar
8
comment Topological Quantum Field theories
@SanathDevalapurkar, time reparametrization invariance forces the Hamiltonian to be a constraint; a great review of this can be found in Henneaux and Teitelboim's Quantization of Gauge Systems, viz. chapter 4.