# All Questions

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### A tricky 2d integral

I tried to calculate such integral: $$\int d^2q \frac{\bf{q+q_2}}{(\mathbf{q}^2+m^2)((\mathbf{q-q_1})^2)^{1-i\eta}(\mathbf{q+q_2})^2}$$ where $q$,$q_1$ and $q_2$ are two dimensional vectors. Can ...
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### Obtaining the metric from the mixed Ricci tensor $R^i{}_j$

In chapter 5 of the book "Einstein Manifolds", Arthur Besse discusses the possibility to find the metric $g$ when knowing the Ricci curvature tensor $Ric(g)$ ($=R_{ij}$). But what do we know about ...
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### Simple question about notation: formulas starting with a quantification [on hold]

Let $C\subset\mathbb{R}$ and suppose that $f:C\to2^C$ is a point to set map. Suppose that $f(x)$ is a set containing only negative real numbers for every $x\in C$. Are there any problems with the ...
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### On linear integer programs with infinitely many solutions

Suppose that a linear system of inequalities $Ax \le b$, where $A\in Z^{m\times n}$ and $b\in Z^m$, hav integral coefficients, has an infinite number of integral solutions $x$. Can one conclude that ...
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### Show that $G$ a group? [on hold]
Suppose that $G$ is a semigroup , and for every $a$ in $G$ there is unique $a^*$ in $G$ that $aa^*a=a$ Prove that $G$ is a group.