# All Questions

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### Analogues of the Lagrange inversion theorem.

Does anyone know if there exists other theorems similar to the Lagrange Inversion Theorem. I'm interested in collecting methods for determining the asymptotic behaviour of implicitly defined ...
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### Is it consistent that $\frak{d} < 2^{\aleph_0}$?

Let $\omega^\omega$ denote the set of all functions $f:\omega\to\omega$. We write $f <^* g$ if there is $N\in\omega$ such that $f(n) < g(n)$ for all $n>N$. A set $D\subseteq \omega^\omega$ is ...
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### Probably some naive question on conditional probability [on hold]

As known, three variables x_1, x_2 and y, if x_1 and x_2 are conditional independent given y, we have p(x_1, x_2|y) = p(x_1|y)p(x_2|y). I was wondering about p(y|x_1, x_2), is that possible to get ...
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### Powers in compact coset spaces

Let $G$ be a topological group, let $K$ be a closed cocompact subgroup (i.e. the coset space $G/K$ is compact in the quotient topology) and let $g \in G$. Is there a sequence of positive powers ...
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### Two (strictly related) proofs by induction of inequalities

This is a question I originally asked on MSE, receiving no answer, even with a bounty (which expired) on it. Therefore I am crosslinking in order to prevent duplication of effort: see here for the ...
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### Proving integration techniques [on hold]

I've recently competed my A levels and now that I'm in the university I finally found the time to understand calculus on a intuitive level. So I've been reading up on books such as "Calculus with ...
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### Inequivalent definitions of Cartan subalgebra

As far as I can tell, there exists no acknowledgment on the internet of the fact (or maybe it's not a fact) that inequivalent definitions of "Cartan subalgebra" of a real Lie algebra exist in the ...
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### Anti-compactness

Let $(X,\tau)$ be a topological space such that $\tau$ is a proper superset of $\{\emptyset, X\}$. We call an open cover $\mathcal{U}$ of $(X,\tau)$ proper if $X\notin \mathcal{U}$. Moreover we say ...
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### Sierpinski's construction of a non-measurable set

In the early 20th century there was a lot of fuss over the axiom of choice implying that there are Lebesgue non-measurable sets of reals. In his book about The Axiom of Choice, Gregory Moore points to ...
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### Two problems in functional analysis [on hold]

Let $f$ be linear functional on Banach space $B$ and $ker f$ is closed subspace of $B$, prove that $f$ is a bounded linear functional. Let $\{e_n\}$ be an orthonormal basis of Hilbert space H. T is ...
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### Blood type frequency given probability [on hold]

I have calculated the probability that any child will have a particular blood type from both the genotype level and the phenotype level assuming the human ABO Rh system is followed. Here are the ...
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### Connected curve

Assume we have a normal,connected quasi projective scheme $Y:=X\backslash D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not ...
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### on the existence of holomorphic coordinates under bounded curvature

Let $(X,g)$ be a complete Kahler manifold with the Riemann curvature and its derivatives bounded. Suppose also the injectivity radius of this manifold is bounded below by a constant $i_0>0$. My ...
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### Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified?

Consider an elliptic curve $E/\Bbb Q$ and let $\Phi:\Gamma_0(N)\backslash\overline{\mathfrak{H}}\rightarrow E(\Bbb C)$ be the analytical description of its modular parametrization. We know that this ...
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### Open problems in compressed sensing

What are the main open problems in compressed sensing? I am interested in theoretical as well as in numerical point of view.
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### How can i be distinguished from -i? [migrated]

Mathematicians designate one solution to x^2 = -1 as i and the other as -i. Would anybody notice if we switched their identities? Any polynomial p(x) with a complex root will also have its conjugate ...
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### Sets of squares representing all squares up to $n^2$

Let $S_n=\{1,2,\ldots,n\}$ be natural numbers up to $n$. Say that a subset $S \subseteq S_n$ square-represents $S_n^2$ if every square $1^2,2^2,\ldots,n^2$ can be represented by adding or subtracting ...
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### Primes $p=x^2+27y^2$ and Ramanujan's $x_1^{1/3} + x_2^{1/3} + x_3^{1/3}$

I was trying to generalize, ...
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### Prime labelling of graphs

A prime labeling of a graph is an injective function $f: V(G) \to \{1, 2, ..., |V(G)|\}$ such that for every pair of adjacent vertices $u$ and $v$, $\text{gcd}(f(u), f(v)) = 1$ (labels of any two ...
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### Model of function of 2 random variables [on hold]

In my model W = f(E, K). f is a complex function (several operations on E and K). for any W, infinity pairs of (E, K) exist that satisfy f. E and K are between [0, +oo] I have observations for W ...
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### On a continuous extension of a linear 2nd order PDE

Consider an elliptic (hyperbolic) equation $A(x,y) u_{xx} + 2B(x,y) u_{xy} + C(x,y) u_{yy} = 0$ in a bounded open plane set $D$, with real-valued functions $A$, $B$, and $C$. Is it true that at least ...
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### How the modular theory of von Neumann algebras, deal with generating C*-algebras?

Let $H$ be a separable infinite dimensional Hilbert space, $M \subset B(H)$ a von Neumann algebra and $A \subset M$ a separable $C^*$-algebra such that $A''=M$. Suppose the existence of a bicyclic ...
I will follow a preliminary exposition for the problem in question, which will essentially follow the format on http://www4.ncsu.edu/~singer/papers/model_diff_fields.pdf [pg. 87]: Let $K$ be a real ...
### Murray–von Neumann equivalence on C$^*$-algebra and von Neumann algebra
Let $H$ be a separable infinite dimensional Hilbert space, $M \subset B(H)$ a von Neumann algebra and $A \subset M$ a separable $C^*$-algebra such that $A''=M$. Let $p,q \in M_{\infty}(A)$ be ...