## All Questions

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### An operation on binary strings

Consider the “product” $\gamma = \alpha \times \beta$ of two binary strings $\alpha$, $\beta$ $\in \lbrace 0,1\rbrace^+$ which one gets by replacing every 1 in $\beta$ …
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### On Perelman’s paper

In section 5 in "The entropy formula for the Ricci flow and its geometric applications" Grisha Perelman has written: Fix a closed manifold $M$ with a probability measure $m$, and …
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### can we say that $(p^2+1)/2\ne p_0^2$ where $p$ is a Mersenne prime

Let $p=2^a-1>7$ be a Mersenne prime and so $a$ is an odd prime. Can we say that $(p^2+1)/2$ is not equal to the square of a prime number? Many thanks for your help BHZ
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### Hyperbolic pair of pants.

Suppose $Y$ is a pair of pants with a hyperbolic structure and $\gamma_i; i = 1, 2, 3$ are the geodesic boundaries of length $l_i; i=1, 2, 3$ respectively. Now consider a essential …
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### Help me on proof of an equation.

I wanna prove following equation $\sum_{i=1}^n \prod_{k=1,k\neq i}^n \prod_{j=1,j\neq k}^{n+1}(x_j - x_k) = -\prod_{i=1}^n \prod_{j=1,j\neq i}^n (x_j - x_i)$ I have verified sev …
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### $f^{-1}\mathcal I \cdot \mathcal O_X$ vs $f^\ast \mathcal I$

Let $X$ ad $Y$ be (noetherian) schemes and let $\mathcal I \subseteq \mathcal O_Y$ be a sheaf of ideals on $Y$. Let $f \colon X \to Y$ be a morphism of schemes. In general the shea …
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### Why don’t more mathematicians improve Wikipedia articles?

Wikipedia is a widely used resource for mathematics. For example, there are hundreds of mathematics articles that average over 1000 page views per day. Here is a list of the 500 mo …
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### Subquotients in ZF

In ZF we have the two relations $A \leq B$ and $A \leq^\ast B$ which relate the size of sets: the first says there is an injection from $A$ to $B$, the second that there is a surje …
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### Growth of Thompson’s group $F$

EDIT: Mark Sapir pointed a reference (in the comments) giving a lower bound of $2^{1/4}$ for the minimal rate. Is this the state of art? The third question remains unanswered. EN …
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### Effective Chebotarev without Artin’s conjecture

Iwaniec and Kowalski, in their famous book Analytic Number Theory states a strong form of the effective Chebotarev density theorem page 143, and prove it assuming both GRH for Arti …
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### Phase transition in dynamical systems

There are several occasions in the study of dynamical systems that are called phase transitions. For example the parameters $t$'s where the pressure $P(f,t\phi)$ fail to be $C^k$ …
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### A group G acting Properly Discontinuously and Cocompactly on a Proper geodesic space X [closed]

Let G be a group acting properly discontinuously and cocompactly on a proper geodesic space X. How can I show that: (a) G is finitely generated; (b) G is quasi-isometry to X?
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### What is the name of this measure of matrix “degenerateness”

Given a spanning set, consider the minimum number of vectors that you must remove in order to make it no longer span. What is this number called? If the vectors are columns in a …