# All Questions

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### Log-concave distributions: Weighted sum of pdfs

Assuming $f_n(\cdot)$ is a log concave function (e.g., pdf of Gaussian distribution) and $0\le q_n\le 1$ for all $n\le N$, I am trying to find conditions under which the following holds ...
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### Bateman-Horn, continued even further

As before, consider the "singular series", which shows up in the Bateman-Horn conjecture: for an irreducible polynomial $f,$ this is equal to $$s(f) = \prod_p \frac{1-\frac{n_f(p)}p}{1-\frac1p},$$ ...
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### upper bound for a convex fractional function [on hold]

Consider the following convex fractional function $$f\left( {\bf{x}} \right) = \frac{1}{{1- {\bf{x}}}}$$ where ${1- {\bf{x}}} > 0$. Is it possible to obtain a linear or quadratic upper bound ...
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### Odds of residue being small

Given $\mathsf{c\geq1}$, what is the probability that if you choose $\mathsf{A,B,\alpha\in\Bbb N}$ such that $\mathsf{A,B<\alpha<AB}$ holds we will have both ...
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Let $\Phi$ be the root system of a split group $G$ over a field $k$. The differentials $d\alpha$ of the roots define a polynomial called the discriminant $$\prod_{\alpha\in\Phi}d\alpha$$ on $\mathfrak ... 1answer 58 views ### Is every pair of writable reals one-tape-ITTM-computable? I've been reading this paper, in which authors prove that not all ITTM-computable functions$\Bbb R\rightarrow\Bbb R$are 1-tape-computable, but if we put some restriction on the output of the ... 2answers 227 views ### cup product and Steenrod operations in Serre spectral sequence Let$F\to E\to B$be a fibration with$B$simply-connected. Suppose all differentials in the cohomology Serre spectral sequence (corresponding to the above fibration) are zero maps. Then as a graded ... 1answer 429 views ### Is an irreducible ideal in$R$also irreducible in$R[x]$? Let$R$be a commutative Noetherian ring and$I\subset R$an ideal that is irreducible in the sense that if$I = J_1 \cap J_2$, then$I=J_1$or$I=J_2$. Is (the ideal generated by)$I$irreducible in ... 1answer 78 views ### Projective dimension of a quotient ring Assume$A$and$B$are commutative algebras with$1$,$B = A[z] = A[Z]/(h(Z))$,$Z$an indeterminate. The first comment in this question says that, if$A$is noetherian, then$pd_{B\otimes_A B}(B) ...
Is this a right place to ask help for an exercise? Let $n\geq 2$ be an integer and $D=\mathbb Z[1/n]$. Let $A$ be a complete commutative ring with unit for the $I$-adic topology, where $I$ is an ...
Brouwer famously proved, using principles motivated by intuitionistic choice sequences, that every function $\mathbb{R}\to \mathbb{R}$ is continuous. In Sheaves in geometry and logic (section VI.9), ...