# All Questions

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### Poincare inequality for connected Lie groups

Let $G$ be a compactly generated second countable locally compact group, and let $\mu$ be a probability measure which is: symmetric, adapted (in the sense that there is no proper subgroup $H$ such ...
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### One-sided local $L^p$ spaces

Consider the vector space $L^p_{\text{left-loc}}$ of measurable functions $f:[0,1]\to\mathbb R$ so that for all $x\in(0,1]$ there exists $\delta>0$ so that $f|_{[x-\delta,x]}\in L^p$. Does this ...
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### Linear Algebra classic books [closed]

I'm learning linear algebra at the moment, so I'm looking for some great old classic books. Something like Fermat's or Gauss books of some great mathematians. I don't really like the nowadays books ...
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### system with solutions $\{x-a:0\leqslant a\leqslant z-1\}$ [on hold]

What must be $F$ there where $0=F(1,x,0)=F(x-0,x,z)=F(x-1,x,z)=F(x-2,x,z)=F(x-3,x,z)=$ $\dots$ $=f(x-z-1,x,z)=0$? Define $F$ in the domain where a continuous function exists that behaves so for ...
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### interpreting the difference between curves [closed]

Is there any sophisticated mathematical method to interpret the difference between shape of two curves? (for example two log-logistic curves with different scale and shape) to be specific, I have two ...
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### Ricci Tensor and Directional Derivatives confirmation [closed]

I did a computation which, I feel, requires confirmation. Consider the metric on $\mathbb{R}^2$ given by $$g_{ij} = \dfrac{\delta _{ij}}{1 + x^2 + y^2} .$$ This yields the coefficients for the Ricci ...
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### “Friedrichs extension Laplacian” vs “Weak Laplacian” and fractional powers

Take $\Omega$ to be a bounded domain and consider Neumann BCs. In some works, I see that a Laplacian $(-\Delta_D)^{\frac 12}$ is defined as an operator with domain $H^1(\Omega)$, and in other works, ...
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### Can view the connected component of the Picard scheme $\text{Pic}^0(X)$ as a “kernel” of the first Chern class?

So on a curve, $\text{Pic}^0(X)$ is just the Jacobian variety, and just correspond to degree $0$ divisors. One way to extend the notion of divisors corresponding to a vector bundle is taking the first ...
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### I need to know all geometry source to study geometry [closed]

I'm not specialist in geometry and I try to start learn all ph.d student need to know for their works. could you please introduce me which book should I start and please mention all book which is ...
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I have three questions related to the theory of modular forms and it was frequently asked to me by my collegues and even my invited teacher in our seminars of the number theory at the faculty of ...
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### This is a quadratic equating question [closed]

If p,q,r,s are the roots of (x^2+x+4)^2 + 3x(x^2+x+4)+2x^2 = 0, then |p|+|q|+|r|+|s| is equal to :
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### Automorphisms of del Pezzo surfaces

Let $S$ be a del Pezzo surface of degree six over $\mathbb{C}$. Then $S$ is the blow-up of $\mathbb{P}^2$ in three general points $p_1,p_2,p_3$. Is it true that its automorphism group is ...
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### Is there a way to approximate a logarithmic function with a Gaussian at a point? [closed]

One way of Gaussian approximation to a function g(x) at a point x_0 is the Laplace approximation, but that requires an exp log g(x) transform, which would result in a log log f(x) expression if g(x) = ...
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### Lipschitz-like behaviour of quartic polynomials [migrated]

I have observed the following phenomenon: Let the biquadratic $q(x)=x^4-Ax^2+B$ have four real roots and perturb it by a linear factor $p(x)=q(x)+mx$, so that $m$ not too large with respect to ...
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### Modular property of indefinite degenerate theta series

Is there anything known about the (mock)modular properties, if any, of the following theta series, $\sum_{n\in {\mathbb Z}^r_+} e^{2\pi i \langle b, n\rangle} q^{\frac12 \langle n,n\rangle}$, where ...
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### Are all locally compact anisotropic groupoids etale up to equivalence?

By groupoid I mean "open topological groupoid",i.e. topological groupoids whose source and target maps are open surjections, and the notion of equivalence I'm considering is the isomorphism in the ...
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### Mathjax vs Katex [closed]

Whats the difference between KaTex and Mathjax. I think KaTex has a better Font while math rendered by MathJax looks so bulky and ugly. Are the MathJax people working on improving their program in ...
I need to code stochastic models: $x_{n+1} = f(x_{n},\theta)$ where $x_n$ is the state of my system at time $n$ and $\theta$ is a set of parameters for this model, constant through time, and ...