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Maybe I do not understand the question, but since the vector of eigenvalues of $C(y)$ is $A^t y$, computing the spectral decomposition for $y = e_1, \dotsc, e_m$ (the basis vectors) gives you $A.$ The …

I suspect your fears are justified. You are basically trying to integrate the integrand from $0$ to $a$ (since, as you have noted, and Mathematica confirms, the integral from $0$ has a closed form) Yo …

The set of $u$-cycles of a graph $G$ spans $\mathbb{R}^{E(G)}$ if and only if $G$ consists has only the single vertex $u$. For otherwise, the space spanned by the cycles in the graph is a vector space …

After thinking about this question for two hours, my belief is strengthened that there cannot be a proof of the vanishing of the A-genus for spin manifolds with positive scalar curvature without usin …

The main question of the PI has been beautifully answered by Moret-Bailly, but not the secondary question arisen from his expectation: "I would expect that it should be possible to write down a power …

I had a minor thought. Did you ever look the paper Multiplicity of the special fiber of blowups by Corso,Polini, Vasconcelos. In particular, they give an upper bound on the number (I realize that …

Since Henry also discusses the property of being equationally Noetherian, I think the following observation is worth posting. And it is too long for a comment, so I post it as an answer. The observa …

This already got asked, and I answered it: Is there an integration free proof (or heuristic) that once differentiable implies twice differentiable for complex functions?

A necessary criterion is that, if $g \in G$ has order $m$, and $k$ is relatively prime to $m$, then $f(g) = f(g^k)$. Proof: Let $\rho$ be a rational representation. Let the eigenvalues of $\rho(g)$ …

Let $X$ be locally noetherian. Then $\{x\}$ is constructible if and only if $\{x\}$ is locally closed (for non-noetherian schemes the notion of constructibility is more complicated and all kind of ter …

Let $(x,y)$ and $(x+2a,y+a)$ be points in space. Then clearly the distance between these two points is $a$. Therefore, the unit ball around 0 must contain the octagon with vertices $(2,1)$, $(1,2)$, $ …

It can be instructive to consider the Cauchy-Riemann equations as an elliptic system of partial differential equations. For elliptic systems, there is a $C^\infty$-regularity result similar to the one …

William Fulton, Flags, Schubert polynomials, degeneracy loci, and determinantal formulas, Duke Math J. 65 (1992) 381--420

Edit: Avoided by $C^2$ by using integrals. Edit 2: I believe that the following manipulations of $U,V$ work out right... If $f$ satisfies the Cauchy-Riemann equations, then write $f(x,y) = (u(x,y), …

Hi. I know this is over a year late, but I the proof you're looking at matches that given on page 61-62 of "Cardinal Arithmetic". The argument can be finished along the following lines: (1) First, …