# All Questions

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### English translation of Gauss' “Principia generalia theoriae figurae fluidorum in statu aequilibri”

I have been unable to locate an English translation of Gauss' work, "Principia generalia theoriae figurae fluidorum in statu aequilibri". A German translation exists (PDF), but my German is not quite ...
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### Three variable equation using only natural numbers [on hold]

I am a high school student that has been working on amateur mathematics for about a year now. Lately, I have been encountering a particular type of equation that I have not yet solved. If I could ...
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### Topological Irreducible graphs for the projective plane

I learned that there are 103 topological irreducible graphs for the projective plane but I am unable to find examples of said graphs. I am unsure of how to find them on my own and I would like to see ...
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### Solve a linear equation with many variables using only 1 and -1

For a program I am writing, I would find it useful to find the least possible positive solution to a linear equation, using only -1 and 1 for roots. For example... ...
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### What is the state of art in Groebner bases

How big polynomial systems can we deal with? How do you know when you don't even have to try? Motivation: Recently I tried to solve a problem posed in another MO question and ultimately I got stuck ...
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### Searching after twin primes from primes [on hold]

Given a twin prime $p_n$, $p_{n+2}$ their average $s=p_n+1$ divided by 6 or 30 (for the case that the last digits of the twin primes ends up with 9 and 1) is often another prime. Thus, to get a twin ...
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### Talking about properties of “random” elements

I asked this in MSE but did not get a satisfying answer. I apologize in advance if this is not appropriate for MO. Suppose that we have some set X and we want to say that a "random" (or generic) ...
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### percolation probability in a hexagonal region

Suppose one takes a large hexagonal region in the tiling of the plane by unit hexagons, with $n+1$ hexagons on each side, as seen in the figure below (taken from the COMAP website) for the case $n=5$. ...
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### Quantum Logic - Irreducible Propositional System

I'm handling with Quantum Logic and I got, as a sub-propositional system, an irreducible complete orthomodular atomistic lattice satisfying the covering law and realized concretely as a sublattice of ...
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This question is somehow a follow-up to About Goldbach's conjecture. For a better understanding, I recall the main definitions of this previous question: Let's consider a composite natural ...
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### Number of curves over a finite field

Let $K$ be a finite field. Is there a formula for the number of isomorphism classes of genus $g$ smooth curves over $K$? In other words does there exists a formula for the number of rational points ...
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### Mathematical subjects to study to become attractive in industry [on hold]

For 2-3 years I've been studying mathematics both in education and spare time. I've gained skills in many fields from Linear Algebra to Calculus and recently Abstract Algebra. Even though I think ...
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### Projective matrix space [on hold]

Let $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ and $n \geq 2$ an integer. I am familiar with the projective space $\mathbb{P}(\mathbb{K}^n)$ however, I don't know how $\mathbb{P}(\mathbb{K}^{n\times n})$ ...
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### Probabilities in a riddle involving axiom of choice

The question is about a modification of the following riddle (you can think about it before reading the answer if you like riddles, but that's not the point of my question): The Riddle: We assume ...
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### Which rate of growth of the Sobolev norms guarantees analyticity?

Let $u\in C^\infty(\mathbb T^k)$, where $\mathbb T^k$ is the $k$-dimensional torus. (Equivalently, $u\in\mathbb R^k$ and $u$ is $2\pi$-periodic with respect of each argument.) We define the semi-norm ...
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### Proof that finite prefixes do not alter the set of factors of infinite sequences if considering long enough factors

Let $\xi \in X^{\omega}$ be an infinite sequence and consider all factors of length $n$. Also let $w \in X^*$ be a finite sequence. Then there exists some $m > 0$ such that if $\eta$ has the same ...
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### Faltings height of a CM abelian variety

Let A be a CM abelian variety, say simple of dimension g, with $End(A) = O_K$, where $K$ is a CM field of degree $2g$. Is there an upper bound for the Faltings height $h(A)$ in terms of the ...
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Let m and n be natural numbers, and consider the set of all possible products of m (not necessarily distinct) elements from the set $\{1,2,\ldots,n\}$, that is consider the set $\{1^{a_1} \cdot ... 1answer 64 views ### Counting the number of$(d_v,d_c)$regular bipartite graphs I am trying to count the number of$(d_v,d_c)$regular bipartite graphs. To be specific, let$n,m,d_v,d_c$be positive integers such that $$n\times d_v=m\times d_c.$$ Then, what is the number of ... 1answer 100 views ### Connected cycles of Shimura curves in$A_{g}$not contained in larger Shimura subvarieties Is there always a finite family of Shimura curves$(C_{i})$in$A_{g}$the moduli space of principally polarized abelian varieties of dimension$g(\geq 2)$, such that the union$\cup C_{i}$is ... 0answers 33 views ### What is a necessary and sufficient condition that the kernel of a semi-module homomorphism is a partitioning sub-semi-module? I would like to identify a representation of the subcategory of a comma category of semi-rings, whose objects are abelian group objects. When attempting to identify the representation, the following ... 1answer 129 views ### Looking for a handy inequality, Cauchy-Schwarz-style I am interested in upper bounds for the following ratio: $$\frac{n\sum_{i=1}^{n}{x_{i}}}{\sum_{i=1}^{n}{x_{i}^{2}}}.$$ In terms of Reznick's paper Some inequalities for products of power sums that ... 2answers 217 views ### Irreducible polynomials in$\mathbb{Q}_p((X))[Y]$I'm looking for some criteria for the irreducibility of polynomials with coefficients in$\mathbb{Q}_p((X))$. In particular, is the polynomial$Y^2+1$irreducible over$\mathbb{Q}_3((X))$? And how ... 0answers 62 views ### Planar algebraic translation of a subfactor property Let$N \subset M$be an irreducible finite depth and finite index subfactor.$M$is a completely reducible (algebraic)$N$-$N$bimodule, it decomposes into irreducibles as follows : ... 4answers 453 views ### How do most people write permutations? I'd like to know how people prefer to write permutations, or elements of the symmetric group$S_n$for$n\ge0$. The most natural way to define a permutation in$S_n$is as a bijection on the set ... 0answers 55 views ### Is set packing easier when the sets are squares? I am interested in the following problem: ... 1answer 92 views ### Analytic continuation of Arithmetic function [on hold] Given an Arithmetic function, (or even better who's values are integers), how can I tell if it has an Analytic continuation to the whole plane, or maybe half plane? I guess it might be too general a ... 0answers 105 views ### Is mod p Hecke algebra gorenstein? [on hold] Barry Mazur proved a certain Hecke algebra T is gorenstein in his famous paper Eisenstein Ideal. Now Wiles proved that T is a complete intersection, too, so T/pT is also complete intersection by ... 1answer 169 views ### Representation-theoretic operations on modular forms Let$A$and$B$be Hecke eigenforms of some weight$k$and level$N$. We know that there are irreducible representations$\rho_a$,$\rho_b$of the absolute Galois group of$\mathbb{Q}$whose trace of ... 1answer 113 views ### Intermediate submodels and the continuum hypothesis Let$V$be a model of$ZFC+GCH$and let$V[G]$be a generic extension of$V$in which$CH$fails. Question 1. Is there a model$W$such that: 1)$V \subseteq W \subseteq V[G],$2)$W\models CH,$... 0answers 84 views ### A probability/counting question [on hold] Suppose you have$(\Omega,\mathcal{B},\mu)$a finitely additive atomless probability algebra. Then say you have an infinite collection of sets$(B_i:i\in\mathbb{N})$in$\mathcal{B}$such that for ... 2answers 226 views ### Why is there no product type in simply typed lambda-calculus? Consider simply typed$\lambda$-calculus that has only the unit type as primitive. We would like to encode the product and the sum types. An encoding of the product type in the untyped ... 1answer 136 views ###$\text{mod} \, p^2$trace identity Let$p$be a prime, and let$\text{GL}_n \big( \Bbb{Z} / p^2 \Bbb{Z} \big)$be the group of$n \times n$invertible matrices over the ring$\Bbb{Z} / p^2 \Bbb{Z}$. Does there exist a positive integer ... 0answers 133 views ### I seem to have them stumped at MSE, what ideal is this? [on hold] http://math.stackexchange.com/questions/598978/what-ideal-is-this Basically, given an ideal$I$of$S = R[x_1, \dots, x_n]$, with$R$a commutative ring, and any set of$n$polynomials$f_i \in S$, ... 1answer 241 views ### Can there be only one (uncountable transitive model of ZFC)? It is an immediate consequence of Cohen's forcing that if there is one countable transitive model of$\sf ZFC$, then there are many of them. Even if all of these models are of the same height, there ... 0answers 64 views ### Determine if a cycle from graph embedded in surface is contractible Given a graph$G$embedded in Surface$S$(orientable or non-orientable), and a cycle(a closed walk with no repeated vertex)$C$from$G$, how to determine if$C$is contractible based on the rotation ... 0answers 26 views ### Probability density function in embedded space I have a 1D noisy time series X which has a probability density function (pdf) of p(X)=$d*r^{(d-1)}$assuming the pdf given inMLE(A MAXIMUM LIKELIHOOD APPROACH TO CORRELATION DIMENSION AND ENTROPY ... 1answer 417 views ### Counting 2m X 2m 0-1 matrices with m ones in each row and each column. Given$m>1$, what is the number of$2m\times 2m$matrices, made of$0$and$1$, such that each row has exactly$m$ones, and each column has exactly$m\$ zeros. I am not sure if this is a ...

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