# All Questions

100,158 questions
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### Trigonometry Functions Help! [on hold]

I'm having some trouble trying to figure out the amplitude, period, phase shift, and vertical displacement of the trigonometric function: f(x)=3sin[2(x+2pi/3)].
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### How many lattices require exactly 3 elements to generate them?

This question by Moshe Newman: How many different lattices are there on n points, that require exactly 3 elements to generate them? This sequence seems to start 0,0,1,0,4,3 (for n = 1 to 6) and seems ...
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### Can one use forcing as a step to prove the Keisler-Shelah isomorphism theorem?

Can one use forcing (perhaps at the expense of using larger ultrafilters) to prove the Keisler-Shelah isomorphism theorem? My idea is to use an ultrafilter $U$ on a set $I$ such that if $M=V^{I}/U$, ...
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### What matrix has only negative or zero real part for all the eigenvalues?

Say $X \in \mathbb{R}^{m\times m}$, Is it possible to have a constraint on $X$, such that all the eigenvalues has negative or zero real part? What I conjecture The following $X$ has only negative ...
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### Leray-Serre spectral sequence for projective bundles

Let $\mathcal{E} \rightarrow X$ be a complex vector bundle of rank $r+1$ and let $F=\mathbb{P}^r \rightarrow E = \mathbb{P}\mathcal{E}\rightarrow X$ be the associated projective bundle. We know that ...
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### Morita equivalence for graded von Neumann algebras

I am interested in understanding Morita equivalence of $Z_2$-graded von Neumann algebras. In the ungraded case, Rieffel showed that all Type I factors are Morita-equivalent, while for Type III factors ...
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### switching the order of composition of two functions [on hold]

Let $f_a(x)=x+\exp(-ax)/a$ be a function, defined on $R_+$ for $a$ positive. Fix $a$ and $b$ positive, can we show that the sign of $f_a\circ f_b - f_b\circ f_a$ does not change on $R_+$, with $\circ$ ...
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### Does there exist a non-trivial elementary embedding from an ultrapower $V^{I}/U$ to $V^{I}/U$?

Does there exist a set $I$ and an ultrafilter $U$ on $I$ and a non-trivial elementary embedding $j:V^{I}/U\rightarrow V^{I}/U$? So the Kunen inconsistency result states that there does not exist a ...
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### Hochschild Homology and Formal Geometry

My question concerns the degeneration of the spectral sequence computing Hochschild homology of differential operators on a smooth affine variety $X$. The spectral sequence arises from the ...
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### questions about a finite solvable group

These questions are by Moshe Newman Let G be a finite solvable group of derived length d, with the property that every proper subgroup and every proper quotient of G has derived length less than d. ...
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### Berthelot’s comparison theorem and functoriality

Let $A$ be a noetherian $p$-adically complete ring with an ideal $I$ equipped with a PD structure and such that $p$ is nilpotent on $A/I$. Let $S = \text{Spec}(A)$, $S_0 = \text{Spec}(A/I)$, $Y\to S$ ...
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### Is the integral closure of a valuation ring in a finite separable extension of its fraction field étale?

Let $K$ be a field endowed with a rank (height) one valuation with completion $\hat{K}$, which is not discrete. Let $R$ be the valuation ring of $K$. Let $L \subset \hat{K}$ be a separable finite ...
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### Homeomorphism type of the horofunction boundary for nilpotent Lie groups

Consider a metric space $(X,d)$ and fix a base point $w$. A horofunction is a function of the form $$\beta_y(x)=d(x,y)-d(w,y).$$ The map $y\mapsto \beta_y$ is an embedding of $X$ into the space of $1$-...
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### Good UPPER bounds for $\log(\sum_{i=1}^n p_ie^{z_i})-\sum_{i=1}^np_iz_i$ where $(p_i)_i$ is a probability vector

Let $x=(z_1,\ldots,z_n)$ be real vector and $(p_1,\ldots,p_n)$ be a probability vector. Question $\log(\sum_{i=1}^n p_ie^{z_i})-\sum_{i=1}^np_iz_i \le ???$ Observation This paper allows us to ...
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### Maximizing the expectation of a polynomial function of iid random variables

Let $f \colon \mathbb R^N \to \mathbb R$ be a smooth function. Let $\mu$ be a probability measure on $[0,1]$ and $X_1, \ldots , X_N$ be i.i.d. random variables on $\mathbb R$. Question 1. What is ...
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### On spectral multiplicity of left shift operators

Let $U$ be an operator defined on $l^{2}(\mathbb{Z})$ by $U(e_{n})=e_{n-1}$, where $e_{n}$ is an orthonormal basis of $l^{2}(\mathbb{Z})$. $U$ is a left shift operator. Since $U$ is unitary operator ...