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bio website shapetales.wordpress.com
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age 29
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Math PhD. student and functional programming enthusiast.


Jan
22
comment Why does a circle cut a torus into an annulus?
I think you assume that $\phi$ is not contractible in $T^2$ for otherwise, $T^2 \setminus \phi(S^1)$ has two components whereas $T^2 \setminus \iota(S^1)$ has just one and so can't be homeomorphic. But $\psi$ would induce such a homeomorphism.
Jan
22
answered Determine whether the given function is an integrating factor for the DE
Jan
22
comment Adjoint operator on subspace
That's not much better for two reasons. First, $f$ can belong to $H_2 \setminus V_2$, so the expression is again not defined and second, $T$ need not be either injective or surjective, so $T^{-1}$ is not defined in general and even when it is, not for all $f \in V_2$. I think not much can be said about your question unless you add more requirements either on some of the spaces or on the map $T$.
Jan
22
comment What is the last index of a third-order tensor called?
@Giuseppe: I agree with your sentiment of giving names but I stand by what I said. If the question were reformulated so as to use the word matrix instead of tensor (since it moreover doesn't really involve tensors at all -- it's only a question on the terminology of generalized matrices), I will remove the downvote. But I'll leave it here precisely because I am not a fan of the engineering attitude of thinking about the tensor as a matrix (of course, you can treat tensors that way, but then, you can treat almost anything that way, so that's not exactly a great argument..).
Jan
22
comment Adjoint operator on subspace
What do you mean interpret? Also, how could it possibly be $Tf$ when $f \in V_2^*$ while $T$ acts on the elements from $V_1$? This expression would not make any sense. Is there something you are not telling us?
Jan
22
answered Another simple/conceptual limit question
Jan
22
comment What is the last index of a third-order tensor called?
-1 Tensor is not a matrix, so the question doesn't really make sense.
Jan
22
answered Connection between Euler characteristic and degree of the Gauss map
Jan
22
answered Is there some difference between the two definition of integration along curves about complex function
Jan
19
comment The solution of the following two equations in two unknowns
Is this a homework? Also, what have you tried and what kind of help (e.g. full solution) do you expect? Be more specific..
Jan
19
comment topological group operation vs homotopy group operation
Ah, I see, I misunderstood your construction. Sorry.
Jan
18
comment Invariants of representation theory of Lie groups
Special linear group has determinant equal to one by definition, so I have no idea what you are asking. For the second part, if by generator you mean an element of the representation of the corresponding Lie algebra (the derived representation) then this vanishes since $\exp {\rm tr} A = \det \exp A$.
Jan
18
comment topological group operation vs homotopy group operation
I don't see how to use E-H here since you don't have two operations on one set but here each operation is on a different set. Anyway, interesting question and I'm curious about the answer in either direction. Can we say anything concrete e.g. about $SU(2)$?
Jan
18
revised Computing derivative $x^{x^x}$
Fixed an incorrect formula
Jan
18
suggested approved edit on Computing derivative $x^{x^x}$
Jan
18
comment Monic polynomial divided by $x-r$
I didn't notice that assumption, sorry. Nevertheless, I think it's worth pointing out that the assumption that $R$ be a field is not necessary here and that recalling general division algorithm is quite an overkill when dividing by linear monic.
Jan
18
comment Monic polynomial divided by $x-r$
Your $(1)$ is not true in an arbitrary ring. For example consider $x^2 / 2x$ in $(\mathbb Z / 4 \mathbb Z)[x]$. It holds however when dividing by the monic polynomials, which is the case here.
Jan
18
answered Monic polynomial divided by $x-r$
Jan
18
revised Multiple Choice question about a continuous function
Added further discussion
Jan
18
answered Multiple Choice question about a continuous function