All Questions

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Is the group of rational points of an anisotropic absolutely quasi-simple algebraic group over a non-archimedean local field known to be perfect?

Suppose that $G$ is an algebraic group defined over a non-archimedean local field $k$ which is absolutely quasi-simple and anisotropic over $k$. Is it known whether the group $G(k)$ is necessarily ...
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Is the diameter of a centrally symmetric convex body realized by a pair of antipodal points?

Is the diameter of a centrally symmetric convex body realized by a pair of antipodal points? Given a convex body K,, such that t K=-K, is there a point; such that $diam(\partial K)=d(x,-x)$ I am ...
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Isoperimetric inequality, isodiametric inequality, hyperplane conjecture… what are the inequalities of this kind known or conjectured?

I duplicate here a question I asked on math.stackexchange. Question: Which inequalities similar to the famous isoperimetric inequality is known? conjectured? I recently learned about some ...
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Algebra and Cancer Research

Let me start by acknowledging the existence of this thread: Mathematics and cancer research ? It is well-known that mathematical modeling and computational biology are effective tools in cancer ...
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Bounding Rayleigh quotioent for stochastic matrix

Suppose you have an irreducible, stochastic matrix $A$ with left Perron-Frobenius eigenvector $v$ (corresponding to the eigenvalue $1$), and suppose the next largest eigenvalue for $A$ is $\lambda$. ...
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cardinals below the critical point of a generic embedding

This may be an easy question. Are the cardinals below the critical point of a precipitous ideal embedding always absolute between the generic ultrapower and the generic extension? To focus on the ...
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a special filtration satisfying $0$-$1$ law

Let $\xi$ be a uniformly random variable on $[0,1]$ defined on some probability space $(\Omega,\mathcal{F})$. Define the process $\xi_t:=\min(\xi,t)$ for $0\le t\le 1$. And let ...
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Why tangent vector of statistical manifold is a function?

In differential geometry, tangent vectors are considered operators. At point p, the local tangent space is defined as $$T_p(M)=\{X^i\partial_i|X\in R^n\}$$ This is quite easy to understand for me. ...
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About the integral of the plurisubharmonic functions on the whole manifold

Let $(M,\omega)$ be a Kahler manifold with positive first Chern class. $\omega\in c_1(M)$ is a Kahler current. $D$ is a smooth simple divisor in $-K_M$. $s$ is a determining section of $D$. The ...
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What is the status of the Friedlander-Milnor conjecture today?

For the purposes of this question, the Friedlander-Milnor (FM) conjecture asserts an equality of the group homology for algebraic groups, and their discretizations in the following sense: Conjecture ...
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Books and papers on differential equation method [on hold]

I wanted to understand the differential equations method for analyzing stochastic sequences. Is there a good book/ papers that provide a gentle survey this topic with a good number of examples? A good ...
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Equating coefficients [migrated]

Heading Excuse me,i don't know how to deal with this problem,i try it for all time of last night, this equation is on "Concrete Mathematics" page 200: d(n) is the number of derangements,e^z is the ...
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solving an exponential inequality with parameters [on hold]

Can someone help me how I can solve this inequality: $$b^{x/2-3/2} - b^{ax} - 2c > 0$$ where $b, a, c$ are the parameters. I want to solve it to have a range for $x.$ If I should do it with a ...
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?

Let me start by recalling some basic definitions (just for the sake of avoiding misunderstandings due to the vocabulary of the post). Basically following some ideas of W. Lawvere (but not his ...
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Geometric explanation of Hutton's formula?

$$\frac{\pi}{4} = 2 \tan^{-1} \frac{1}{3} + \tan^{-1} \frac{1}{7} \;.$$ Is there some geometric construction that explains this beautiful equation (known as Hutton's formula)? Perhaps a "proof without ...
317 views

On quantities with no very small odd prime factors; a response to Wlodzimierz Holsztynski

In response to a comment posted under Powers of $2$ and the products of initial odd primes , I shall raise some questions about quantities near $O_n= P_{n+1}/2$, the product of the first $n$ odd ...