# All Questions

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3 views

### Defining Reinhardt Cardinals in Choiceless Models of $ZF$

Can Reinhardt cardinals be defined in choiceless models of $ZF$? This question is motivated by the following remark by Prof. Hamkins in his comment to me regarding Andrea Nespola's question ...

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7 views

### Two equivalent descriptions of a physical system yielding a non-trivial mathematical formula

First I would like to admit that this question may not be entirely appropriate for this site, but I will give it a go none the less.
One often hears stories about how string dualities lead to highly ...

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5 views

### Angle subtended by the shortest segment that bisects the area of a convex polygon

Let $C$ be a convex polygon in the plane and let $s$ be the shortest line segment (I believe this is called a "chord") that divides the area of $C$ in half. What is the smallest angle that $s$ could ...

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**1**answer

13 views

### Mathematical statistical qm book-recommendation

I feel that there are quite a few good and rigorous books on the mathematical foundations of quantum mechanics, but I am currently looking for a book that covers mathematical statistical quantum ...

**4**

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21 views

### Anything known about the Grundy Ordinal of Sylver's Coinage

Sylver's coinage is an example of an unbounded finite (if slightly modified) combinatorial impartial game. Quoth wikipedia:
The two players take turns naming positive integers that are not the
...

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7 views

### Pascal and Brianchon's theorems generalized for hyperbolic paraboloid

I know that giving a general version of these two theorems for quadrics can be quite tricky, but if we restrict ourselves to a verssion that holds for the hyperbolic paraboloid only it should be ...

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15 views

### One question about iteration on groups

Let $G$ be a finite generated group, $H$ is a subgroup of $G$ of index $n$,$G=\displaystyle\bigcup_{i=1}^nH_{a_i}$. Let $\phi:H\rightarrow G$ be a homomorphism. We define a map $\psi:G\rightarrow G$ ...

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16 views

### Beilinson-Bernstein localization: $\mathfrak{g}$ action on $G$-equivariant sheaf

I have a few elementary questions related to Beilinson-Bernstein localization.
Let $G$ be a semisimple algebraic group over $\mathbb{C}$ with Lie algebra $\mathfrak{g}$. Consider the setup of ...

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36 views

### A property of the Frechet filter and every ultrafilter

(Joint question with Piotr Szewczak.)
By filter we mean a filter on $\omega$ containing the cofinite sets at least.
For a filter $\mathcal{F}$, let $\mathcal{F}^+:=\{A\subseteq\omega : A^c\notin ...

**6**

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53 views

### A classic cardinal characteristic of the continuum in disguise?

We believe the answer to the following question, that is relevant to a joint research project with Piotr Szewczak, should be known. We would appreciate any help or pointer.
Needed definitions may be ...

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183 views

### Are there any Algebraic Geometry Theorems that was proved using Combinatorics?

I'm collaborating with some algebraic geometers in a paper, and when writing the introduction I mentioned the interaction of Combinatorics and Algebraic Geometry, and gave some examples like the ...

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37 views

### About structure of the set of perfect matchings of $K_{n,n}$

Are there any special properties known about the set of perfect matchings of $K_{n,n}$? Like any global structure of this set? Some natural way to partition it? Like is there some algebraic structure ...

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28 views

### absolutely continuous of two probability measures

Suppose $X_t$ satisfies
$$X_t=\int_0^t b(X_s)ds+ L_t,\quad t\in[0,1]$$ where $L_t, t\in[0,1]$ is a $\alpha-$stable process. Let $P_L$ be the law of $L$, $P_X$ be the law of $X$. ($P_L, P_X$ are ...

**-4**

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44 views

### Probability- My homework is confusing me [on hold]

The question is that there is a game, it has 38 congruent pieces, 18 are orange, 18 are blue, and 2 are white. To win you have to get either orange or blue and you get 2$, to play you pay 1 dollar, ...

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63 views

### Poincare-Lefschetz duality, universal coefficients, and middle cohomology

Sorry if the question is too simple, algebraic topology is not my strong suit. Let $(M,\partial M)$ be a $2n$-dimensional manifold with boundary, with one-dimensional middle cohomology. By ...

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44 views

### Is there a universal straightedge and compass construction of a segment incommensurable to a given one in the hyperbolic plane?

"Universal" means that the construction steps are independent of the length of the given segment. In the Euclidean plane one can take the diagonal of a square built on it. Without the "universal" the ...

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**1**answer

36 views

### Injecting premises into two implicational premises connected by a tensor (multiplicative conjunction) in linear logic

I have another question regarding linear logic: I want to get to the proof E, using the premises in (1-4). Is this at all possible?
1: $A$
2: $C$
3: $(A\multimap B)\otimes(C\multimap D)$
4: ...

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66 views

### Schoenflies and symplectic topology

The final report from a workshop on Morse theory in low-dimensional and symplectic topology includes the following question, posed by Michael Hutchings: Can we apply symplectic geometry to solve the ...

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**1**answer

95 views

### Proving that (e^x+1)^(1/3) has no elementary antiderivative [on hold]

How should one prove that $\int (e^x + 1)^\frac{1}{3}dx$ is non-elementary? (In case that is really is)

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75 views

### Non-embeddable varieties

Suppose that $k$ is a perfect field of characteristic $p>0$, $\mathcal{V}$ is a complete discrete valuation ring with residue field $k$ and quotient field $K$, of characteristic $0$.
Then when ...

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35 views

### probability distribution of balls in an urn [on hold]

So I have the following question in "probability":
An urn contains three balls: white, blue and red. At each stage a ball is picked up randomly and, if it is not red, it is returned to the urn. The ...

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63 views

### A relative version of Urysohn's Lemma?

Let $f:Y\to X$ be a continuous surjective map between locally compact Hausdorff spaces. Assume there is a continuous section $s:X\to Y$ which has closed image and is a homeomorphism to the image.
I ...

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112 views

### How far is it to extend the results of SGA III Exp. VIB from group schemes to group spaces?

How far is it to extend the results of SGA III Exp. VIB from group schemes to group spaces?
In particular, does Corollary 4.4 from SGA III Exp. VIB hold for G/S being merely a group space? Here the ...

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75 views

### sequences and series [on hold]

I think it is interesting, if we have the formula
$$\frac{n (n + 1) (2 n + 1)}{6} = 1^2 + 2^2 + \cdots + n^2 .$$
If the difference between the closest numbers is smaller (let's call is a) we ...

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**1**answer

34 views

### About trigonometric series of the Lip $\alpha$ class

Assume we have a trigonometric series
$$
f(x)=\sum_{n=1}^{\infty} a_n\sin nx \in \text{Lip }\alpha, \, 0<\alpha <1.
$$
Is there anything we can say about the series
$$
g(x)=\sum_{n=1}^{\infty} ...

**2**

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32 views

### Localized eigenfunctions of drift Laplacians

I am looking for literature which discusses localization of eigenfunctions of drift Laplacians, i.e. $L\underline u=-\Delta \underline u+\underline{v}.\nabla \underline u$ in 2D/3D domains with ...

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**1**answer

92 views

### Arbitrary chains of prime ideals in $R[X]$

For a commutative ring $S$ of finite Krull dimension $d$, we have $1+d\leq \dim(S[X])\leq 2d+1$. One proof of this uses the fact that if $Q_1\subset Q_2\subset Q_3$ is a chain of prime ideals of ...

**-3**

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32 views

### Divide 4D cube into tetrahedrons/simplices [on hold]

I am trying to figure out how can I possibly divide a 4D cube into 16 tetrahedrons/simplices.
Thanks.

**7**

votes

**2**answers

452 views

### How to pack 3D boxes into a bigger box?

Given a box of given size $L\times M\times N$ and a list of smaller boxes of given sizes $(l_i,m_i,n_i)$, decide whether the smaller boxes altogether fit into the big box (and produce such a packing ...

**6**

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141 views

### Mass Transportation Through Wonderful Roller

There is a wonderful ruller that transports mass from A to B and there is a pile of sand with weight $W$ in point A and we want to transport it to B.
Wonderfulness of ruller comes from this property ...

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31 views

### Differentiability and the Maximum Theorem [on hold]

Suppose that in Berge's Maximum Theorem the argmax correspondence happens to be single-valued. Are there assumptions that will guarantee that this argmax function will be smooth (e.g., continuously ...

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vote

**1**answer

58 views

### A differential inequality and a special value

Let $G \colon [0,1] \to [0,1]$ be a monotonically decreasing function with $G(0) = 1$ and $G(1) = 0$. Suppose that $G$ is differentiable infinitely many times, and that: $$G(x)G''(X) \leq ...

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**3**answers

244 views

### How singular can the Stein factorization of a proper map between smooth varieties be?

A little bit of motivation (the question starts below the line): I am studying a proper, generically finite map of varieties $X \to Y$, with $X$ and $Y$ smooth. Since the map is proper, we can use the ...

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**1**answer

47 views

### Existence of functions on finite sets with specific propertise

Let $\Omega$ be an universal set and $|\Omega|=N$, denote $\mathcal{F}$ to be the family of all subsets $\subset \Omega$ with cardinal $n$. We now define a function $f:\mathcal{F}\rightarrow \Omega$, ...

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**1**answer

86 views

### How to prove that $(1-x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1-\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case

After multiple plots I noticed that function $h(x)= (1-x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1-\alpha x$ (with $\alpha \approx 1$), for $x\ll 1$ (specifically $0<x<0.1$) and ...

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46 views

### On conductors, levels and traces on quaternion algebras

I am currently working on conductor and level issues in the division central simple algebra case, say $D$ over $F$. I would like to verify some well-known relations between the conductor or the level ...

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37 views

### Cyclic structure on a balanced (or ribbon) monoidal category

As it is well known, a balanced (and in particular ribbon) monoidal category is an algebra over the framed little 2-discs operad. The latter is homotopy equivalent to the operad of moduli space of ...

**5**

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**1**answer

166 views

### When does the Borel construction have the homotopy type of a CW-complex?

Suppose that $G$ is a Lie group acting smoothly on a manifold $M,$ does the Borel $M \times_G EG$ construction have the homotopy type of a CW-complex? If not, under what conditions would this be true? ...

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32 views

### Teaser: What is $e^{i\mathbb{Q}}$? [migrated]

What are its properties as a topological group? It is not $\mathbb{Q}/\mathbb{Z}$ but resembles it, it contains the subgroups $e^{i\mathbb{Z}}\supseteq e^{ip\mathbb{Z}}\supseteq ...

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52 views

### holomorphic curves invariant by lattices

Suppose I have an entire function $f : \mathbb{C} \longrightarrow \mathbb{C}^n$ for
$n \geq 1$.
Let $C$ be the curve $f(\mathbb{C})$ in $\mathbb{C}^n$.
Let $\Lambda$ be a lattice in $\mathbb{C}^n$ ...

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83 views

### Is Frobenius on $R^\circ/p$ surjective for general perfectoid rings $R$?

In [1], Propisition 6.1.9(2), it said that if $R$ is a perfectoid ring such that $pR^\circ$ is closed in $R^\circ$ (this includes the case if $R$ is of character $p$, or if $p$ is invertible in $R$, ...

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15 views

### Approximate point spectrum is complement of set of points of regular type [migrated]

I have a question concerning the approximate point spectrum of a closed linear operator. I need to show that the approximate point spectrum is the complement of the set of points of regular type, ...

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25 views

### Intertwining Operators Associated to Simple Reflections

Let $G$ be a quasi-split reductive group, over a local field, with a Borel subgroup $B=T\cdot N$ and the associated Weyl group $W$. Given a family of induced representations $\pi_s = Ind_B^G \chi\cdot ...

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41 views

### Online Envelope Calculator

Are there any websites that provide a "one shot" calculation of envelope curves, ideally symbolically and with graphical output?
By "one shot" I mean that one only has to enter the ...

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103 views

### Lovasz's Path removal conjecture

The Lovász Path Removal Conjecture states:
For any positive integer $k$, there exists a minimum positive integer $f(k)$ such that, for any two vertices $x$, $y$ in any $f(k)$-vertex-connected ...

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16 views

### Is the union of strongly base-orderable matroids strongly base-orderable?

A matroid is said to be strongly base-orderable if for any two bases $B_1,B_2$ there is a bijection $f:B_1 \to B_2$ such that for any $S\subseteq B_1$ set $(B_1 \setminus S) \cup f(S)$ is also a base.
...

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19 views

### Closed Form Solutions To Simple Iterated Polynomial Building Blocks [migrated]

I've been doing some work on fractals and simple iterated polynomials lately. I admit, I've only taken classes up through Calc 2, although I've done a decent bit of reading on many topics over the ...

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43 views

### Proof : Limit of a sequence [on hold]

Prove from the definition of the limit of a sequence that $$\lim_{n\to\infty} \frac{2n^2+\cos(n)} {n^2+1} = 2 $$
(that is, for a given $\epsilon > 0$, find an explicit $N_\epsilon$)
Please ...

**2**

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42 views

### Oscillation aspects of two-way infinite alternating series (a followup from the MO-question “functions that eventually oscillate”)

In the recent question on "eventually oscillating function" I had a heuristic for the function $d(x)$ that its amplitude is constant, but could not further describe that function. I just found a ...

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50 views

### Hadamard / matrix product adjoint

First of all I would like to thank everyone over here at mathoverflow for their amazing generosity and help (for both pros and newbies like myself).
I apologize if this question seems dumb; I'm a new ...