# All Questions

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### Lower bounds for norms of commutators

For various reasons I became interested in bounds on the norm of commutators of operators. For instance, if $B(H)$ is the algebra of bounded operators on a Hilbert space, one may ask for a lower bound ...
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### Cech cohomology.

Let us consider the scheme $X$ and the coherent sheaf $\cal F$ on it. We consider finitely many affine open covers $U_{\lambda}$ with $\lambda \in \Lambda$. When I calculate Cech cohomology with ...
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### How to use, $(|u|^{2}u - |v|^{2}v)(s)= (u-v)|u|^{2}(s)+ v(|u|^{2}-|v|^{2}) (s)$; to prove contraction in a Banach space $C([0,T]; M^{p,1})$?

(May be this is very basic question for MO) (For details or this question you may see the paper page no. 9, MR2506839, Local well-posedness of nonlinear dispersive equations on modulation spaces; ...
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### K-Theory and completion [duplicate]

I vaguely remember the existence of a statement that relates the $K$-theory (in the sense of Quillen) of a noetherian local ring $A$ with maximal ideal $\mathfrak{m}$ with the $K$-theory of the ...
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### Is $\lfloor \log(n!)\rfloor \alpha$ equidistributed on the unit circle?

In this question $\lfloor a\rfloor$ means the greatest integer not exceeding $a$. Using van der Corput's inequalities one is able to show that $\log(n!)\alpha$ is equidistributed on the unit circle ...
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### Property of $L$ Relating to Reflection

The idea of the question is whether it is ever possible that $L$ is so nice in the sense that $\{L_\alpha\}$ does not incorrectly "guess" a bigger inaccessible than $L$ really has, as long as ...
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### Generalized Eigenvalue problem solution

$\circ$ Consider the following eigenvalue problem : $$XY^{T}YX^{T}w=\lambda XX^{T}w \hspace{0.5cm} (1)$$ Matrices $XY^{T}$ and $XX^{T}$ $\in \mathbb{R}_{n \times n}$ are positive semi-definite and ...
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### Weak derivatives and dual of Hölder functions

Let $0<\alpha<1$ and $f \in C^{\alpha}$ be a Hölder function (either with compact support on $\mathbb R^n$ or on a closed Riemaniann manifold). From what I understand, the derivative of $f$ in ...
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### Fourier inversion

I have certain doubts about a classical Fourier inversion theorem. According to it (this is a theorem from "Panorama of Harmonic Analysis" by Krantz), if $f$ and $\hat{f}$ are both in $L_1(R)$ and ...
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### Can inverse Lipschitz function approximate continuous function?

Let $(X,d)$ be a compact metric space and $C(X, R^n)$ the space of continuous funcions from $X$ to $R^n$. Given $f\in C(X, R^n)$ and $r>0$. My question is: Can we find a inverse Lipschitz function ...
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### Stop Loss insurance [on hold]

I need help in this question, I shall be very thankful if anyone can help me in it.
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### Degeneracy divisor of the “trace” morphism

Let $f\colon X\to Y$ be a finite morphism of smooth curves over an alg. closed field of characteristic zero. I recently asked how methods reminiscent of basic algebraic number theory can be used to ...
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### Is there a natural notion of completion of a Coxeter system?

Let $(W,S)$ be a Coxeter system. Then any element of $W$ can be written as a finite products of elements of $S$. I want some notion of a "completion" of $W$, call it $\hat{W}$, whose elements are ...
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### Does anybody know if the Fourier algebra of SL(3,Z) has an approximate identity?

(Note to those who like to tidy LaTeX, or ${\rm \LaTeX}$: I kindly request that you don't put any LaTeX in the title of this question, nor change the bolds below to blackboard ...
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### Classifying two-faces of four-polytopes

Motivation: This question is related to my study of hyperbolic Coxeter polytopes. In general, if one put some restrictions on the type of their dihedral angles (say, all dihedral angles are equal to ...
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### adjoint orbit of (twisted) loop group

Let $G$ be the twisted loop group of $SL_2(\mathbb C)$ and let $g$ be its Lie algebra, where diagonal entries are even functions and off diagonal entries are odd functions (of loop parameter lambda). ...
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### Complete classification of complexity classes / infinite approaching sequences

http://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities For complexity as seen in the above link, complexity classes can be log, polynomial, exp, or composition of any of these ...
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### Arithmetic progression and most significant digits in different bases

Given a number $x \geq 3$, let $b(x) \in \{0,1\}$ be the second most significant digit (bit) of its binary representation, and $t(x)\in \{1,2\}$ the most significant digit of its ternary ...
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### largest size for a randomness extractor

I am not so expert in theoretical computer science, so sorry if the question is trivial, i just could not find it in literature. Suppose we have a source $X$ with min-entropy $\ell$, the randomness ...
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### What happens to simple modules under Ringel duality?

If $A$ is a quasi-hereditary algebra then its Ringel dual $A'=End_A(T)$ is the endomorphism algebra of a (minimal) full tilting module $T$ for $A$. The algebra $A'$ is again quasi-hereditary, although ...
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### Is symbolic logic overemphasized in the foundations of mathematics? [on hold]

I am an amateur. My questions generally go unanswered because many prevalent views concerning the nature of mathematics reduce the subject to meaningless syntax. I disagree with this view and do not ...