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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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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
Mathoverflow.net news digest
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0 days
A Systematic Proof Paper for the Riemann Hypothesis [closed]
This paper presents a complete, closed mathematical proof of the Riemann Hypothesis, with full rigorous derivation, analytic number theory reasoning, self-consistent logical deduction and standardized mathematical argument.
All core mathematical framework, proof process, formula deduction and final academic conclusion of this thesis will be fully released in this post. This is a complete academic research paper on the proof of the Riemann Hypothesis, rather than a preliminary... -
1 month
Is non-symmetric monoidal $\infty$-category $\mathcal{V}$ a monoid in the $2$-ca...
Let $\mathcal{V}$ be a presentably monoidal $\infty$-category. If $\mathcal V$ is moreover symmetric, the $(\infty,2)$-category ${}_{\mathcal V} \mathsf{Cat}$ of $\mathcal V$-enriched categories inherits a monoidal structure and $\mathcal{V}$ is naturally...
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7 years
Use Importance sampling for multimodal and multivariate distribution draws, how ...
I'm in trouble trying to generate samples following a particular distribution which is not numerically known perfectly. Let us consider a $R^n$ space provided with an orthonormal base $( e_{1},...,e_{n} )$ and N points $(X^{(1)},...,X^{(N)})$ in this...
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0 days
Elimination of leading coefficients of polynomials with sub-$n$ resolvent degree
$\DeclareMathOperator{\Res}{Res}$
We'll work over fields of characteristic 0, like $\mathbb{C}$.
Let $P$ be a polynomial of degree $n$ defined as:$$P(x) = \sum_{k=0}^n p_k\ x^k, \quad p_n=1$$a rational Tschirnhaus transformation $T$ as:$$T_z(y) = \frac{A_z(y)}{B_z(y)}, \quad t_z:= \max(\deg A_z,\ \deg B_z)$$their polynomial resultant $Q$ as:$$Q...
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