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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
Mathoverflow.net news digest
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8 years
Are concatenations of two consecutive Mersenne numbers which are congruent to 6 ...
In this question on MSE, Enzo Creti asks for a prime number formed by concatenating the Mersenne numbers $2^n-1$ and $2^{n-1}-1$, for example, $40952047$. For all residues modulo $7$, he found primes except for the residue $6$. This is somewhat surprising...
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8 years
Mathematical games interesting to both you and a 5+-year-old child
Background: My daughter is 6 years old now, once I wanted to think on some math (about some Young diagrams), but she wanted to play with me... How to make both of us to do what they want ? I guess for everybody who has children, that question comes up...
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0 days
Global regularity for 3D Navier-Stokes with arbitrary large H¹ initial data - Cl...
Claim: I present a proof of global regularity for the 3D incompressible Navier-Stokes equations with arbitrary large H¹ initial data.
Main result: For divergence-free $u_0 \in H^1(\mathbb{R}^3)$, the unique Leray-Hopf weak solution satisfies$$\|u(t)\|_{L^2}^2 \leq C (1+t)^{-\delta}$$for some $\delta > 0$, with $C$ depending only on $\|u_0\|_{H^1}$. This energy decay rules out finite... -
0 days
What is a good approximating space for the following space of pairs of functions...
Let $\Omega^+$ be a finite polygonal domain in $\mathbb{P}^1(\mathbb{C})$, by which we mean that its boundary is a polygon with only finite points.
Let$$ \Omega^- = \mathbb{P}^1(\mathbb{C}) \setminus \overline{\Omega^+}.$$
Let $(f, g)$ be a pair of functions, where $f$, resp. $g$, is a continuous complex-valued function on $\overline{\Omega^+}$, resp. $\overline{\Omega^-}$, which is holomorphic on $\Omega^+$, resp. $\Omega^-$. Denote by $S$ the space of such pairs of functions...
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