# All Questions

100,158 questions

**2**

votes

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40 views

### example in $L^p_{s}-$Sobolev spaces

We define $L^p-$
Sobolev spaces as follows:
$$L^p_s(\mathbb R^d)=\{f\in \mathcal{S}'(\mathbb R^d): \mathcal{F}^{-1} [\langle \cdot \rangle^s \mathcal{F}(f)] \in L^p(\mathbb R^d) \}$$
where $\langle \...

**0**

votes

**1**answer

29 views

### Minimizing the set of “faulty” edges in a map between the vertex sets of $2$ graphs

The starting point of this question is the fact that for some simple, undirected graphs $G, H$ there is no graph homomorphism $f:G\to H$. This is the case for instance if $\chi(G)>\chi(H)$.
...

**6**

votes

**1**answer

281 views

### A question about Poincare duality

Let $k$ be a field. Let $C$ be a small category and assume that for every $i\geq 0$ we have a functor $H^i:C\rightarrow FinDimVect_k$. Assume that there is a function $dim:Obj(C)\rightarrow \mathbb{Z}...

**-6**

votes

**0**answers

34 views

### Trigonometry Functions Help! [on hold]

I'm having some trouble trying to figure out the amplitude, period, phase shift, and vertical displacement of the trigonometric function: f(x)=3sin[2(x+2pi/3)].

**0**

votes

**0**answers

59 views

### How many lattices require exactly 3 elements to generate them?

This question by Moshe Newman:
How many different lattices are there on n points, that require
exactly 3 elements to generate them? This sequence seems to start
0,0,1,0,4,3 (for n = 1 to 6) and seems ...

**5**

votes

**0**answers

117 views

### Can one use forcing as a step to prove the Keisler-Shelah isomorphism theorem?

Can one use forcing (perhaps at the expense of using larger ultrafilters) to prove the Keisler-Shelah isomorphism theorem? My idea is to use an ultrafilter $U$ on a set $I$ such that if $M=V^{I}/U$, ...

**0**

votes

**0**answers

60 views

### What matrix has only negative or zero real part for all the eigenvalues?

Say $X \in \mathbb{R}^{m\times m}$,
Is it possible to have a constraint on $X$, such that all the eigenvalues has negative or zero real part?
What I conjecture
The following $X$ has only negative ...

**2**

votes

**1**answer

112 views

### Leray-Serre spectral sequence for projective bundles

Let $\mathcal{E} \rightarrow X$ be a complex vector bundle of rank $r+1$ and let $F=\mathbb{P}^r \rightarrow E = \mathbb{P}\mathcal{E}\rightarrow X$ be the associated projective bundle. We know that ...

**6**

votes

**0**answers

62 views

### Morita equivalence for graded von Neumann algebras

I am interested in understanding Morita equivalence of $Z_2$-graded von Neumann algebras. In the ungraded case, Rieffel showed that all Type I factors are Morita-equivalent, while for Type III factors ...

**0**

votes

**0**answers

45 views

### switching the order of composition of two functions [on hold]

Let $f_a(x)=x+\exp(-ax)/a$ be a function, defined on $R_+$ for $a$ positive.
Fix $a$ and $b$ positive, can we show that the sign of $f_a\circ f_b - f_b\circ f_a$ does not change on $R_+$, with $\circ$ ...

**8**

votes

**0**answers

120 views

### Does there exist a non-trivial elementary embedding from an ultrapower $V^{I}/U$ to $V^{I}/U$?

Does there exist a set $I$ and an ultrafilter $U$ on $I$ and a non-trivial elementary embedding $j:V^{I}/U\rightarrow V^{I}/U$?
So the Kunen inconsistency result states that there does not exist a ...

**3**

votes

**1**answer

186 views

### Hochschild Homology and Formal Geometry

My question concerns the degeneration of the spectral sequence computing Hochschild homology of differential operators on a smooth affine variety $X$.
The spectral sequence arises from the ...

**1**

vote

**0**answers

81 views

### questions about a finite solvable group

These questions are by Moshe Newman
Let G be a finite solvable group of derived length d, with the
property that every proper subgroup and every proper quotient of G has
derived length less than d.
...

**1**

vote

**1**answer

118 views

### Does $\delta$-invariant give a sufficient condition for flatness for plane curve singularities?

Let $\pi:\mathcal{C}\to S$ be a morphism of schemes such that $\mathcal{C} \subset \mathbb{C}^2 \times S$ with the inclusion map commuting with the natural projection to $S$ and for all $s \in S$, $\...

**3**

votes

**1**answer

81 views

### Group cohomology with coefficients in a chain complex

Let us suppose that I'm in the following situation: I have a chain complex $(C,\partial)$ and say a finite group $G$ acting over $C$ up to homotopy, meaning that for each $g \in G$ I have a self ...

**11**

votes

**1**answer

342 views

### Are Hausdorff measures on the real line Haar measures for some locally compact topology?

For $0\leq d\leq 1$, let $\lambda_d$ be the $d$-dimensional Hausdorff measure on $\mathbb{R}$. Note that it is translation-invariant. Does there exist a locally compact topology $\mathscr{T}_d$ on $\...

**2**

votes

**0**answers

98 views

### Berthelot’s comparison theorem and functoriality

Let $A$ be a noetherian $p$-adically complete ring with an ideal $I$ equipped with a PD structure and such that $p$ is nilpotent on $A/I$.
Let $S = \text{Spec}(A)$, $S_0 = \text{Spec}(A/I)$, $Y\to S$ ...

**3**

votes

**1**answer

211 views

### Is the integral closure of a valuation ring in a finite separable extension of its fraction field étale?

Let $K$ be a field endowed with a rank (height) one valuation with completion $\hat{K}$, which is not discrete. Let $R$ be the valuation ring of $K$.
Let $L \subset \hat{K}$ be a separable finite ...

**1**

vote

**1**answer

112 views

### Principal Symbol for the Ricci-DeTurck Flow

I am following some lecture notes on Ricci flow and reached the section where we linearize the Ricci tensor and obtain the principal symbol for the resulting operator. We have $T \in \: \Gamma(Sym^2 ...

**0**

votes

**0**answers

167 views

### Parity of number of partitions of $n!/6$ and $n!/2$

The parities of the number of partitions of $n!/6$ and $n!/2$ appear to be non-random initially, as follows — is there an explanation for this other than chance? With $p$ being the partition ...

**1**

vote

**0**answers

27 views

### Convergence estimates for approximation with Gaussians / radial basis functions

tl;dr: Are there known convergence estimates for approximating a function with a radial basis family?
Details: Let $\mathcal{G}$ be a family of radial basis functions, e.g. $\mathcal{G}=\{\exp(-\...

**1**

vote

**0**answers

35 views

### Homeomorphism type of the horofunction boundary for nilpotent Lie groups

Consider a metric space $(X,d)$ and fix a base point $w$. A horofunction is a function of the form
$$\beta_y(x)=d(x,y)-d(w,y).$$
The map $y\mapsto \beta_y$ is an embedding of $X$ into the space of $1$-...

**1**

vote

**1**answer

49 views

### Good UPPER bounds for $\log(\sum_{i=1}^n p_ie^{z_i})-\sum_{i=1}^np_iz_i$ where $(p_i)_i$ is a probability vector

Let $x=(z_1,\ldots,z_n)$ be real vector and $(p_1,\ldots,p_n)$ be a probability vector.
Question
$\log(\sum_{i=1}^n p_ie^{z_i})-\sum_{i=1}^np_iz_i \le ???$
Observation
This paper allows us to ...

**15**

votes

**0**answers

268 views

+100

### Maximizing the expectation of a polynomial function of iid random variables

Let $f \colon \mathbb R^N \to \mathbb R$ be a smooth function. Let $\mu$ be a probability measure on $[0,1]$ and $X_1, \ldots , X_N$ be i.i.d. random variables on $\mathbb R$.
Question 1. What is ...

**1**

vote

**0**answers

69 views

### Requirement for weak pullback to be a Lie groupoid (Moerdijk)

Let $\phi:\mathcal{G}\rightarrow \mathcal{K}$ and $\psi:\mathcal{H}\rightarrow \mathcal{K}$ be morphisms of Lie groupoids.
Is it necessary for $\phi_1:\mathcal{G}_1\rightarrow \mathcal{H}_1, \...

**3**

votes

**2**answers

150 views

### Packing vertices on a hypercube graph?

Imagine a graph where the vertices and edges model an n dimensional hypercube (a line, a square, a cube and so on). A red vertex must have a minimum distance of 3 from every other red vertex. The ...

**1**

vote

**0**answers

88 views

### Doubts related Shifting from Pure to Applied math [on hold]

I am a second year (Pure) Math and (Theoretical) Physics undergraduate in India. I want to do a masters in Applied/Computational Science or Math, for which I have apply after next 7 months.
I have ...

**0**

votes

**0**answers

72 views

### Bound of size $X\subset \mathbb{Z}/N\mathbb{Z}$ which satisfies $X+X=\mathbb{Z}/N\mathbb{Z}$

(Sorry for my poor english skill..)
Let $N$ be a large integer and the set $X$ be the subset of $\mathbb{Z}/N\mathbb{Z}$. For two sets $A$ and $B$, we define
\begin{equation}
A+B:=\{a+b : a\in A, b\...

**-3**

votes

**0**answers

32 views

### Low rank integral equations [on hold]

My question is about how to prove
k(x,t)=i(x-t) is symmetric
also k(x,t)=i(x+t) is not symmetric

**5**

votes

**1**answer

150 views

### Multiple mirrors phenomenon from SYZ and HMS perspective

There is a set of ideas called mirror symmetry which, roughly speaking, relates symplectic and complex geometry of Calabi--Yau manifolds. There are also extensions to Fano and general type varieties ...

**7**

votes

**0**answers

216 views

### Is it true that $\sum_{k=1}^\infty\frac{\binom{2k}k^2}{k16^k}(H_{2k}-H_k)=\frac23\sum_{k=1}^\infty\frac{\binom{2k}k^2H_{2k}}{(2k+1)16^k}$?

On Jan. 27, 2012, I conjectured the identity
$$\sum_{k=1}^\infty\frac{\binom{2k}k^2}{k16^k}(H_{2k}-H_k)=\frac23\sum_{k=1}^\infty\frac{\binom{2k}k^2H_{2k}}{(2k+1)16^k},\tag{$*$}$$
where $H_n$ denotes ...

**1**

vote

**0**answers

43 views

### Differences of $\omega$-plurisubharmonic functions

Let $X$ be a complex manifold, and $\omega$ a Kähler form on $X$.
A smooth function $\phi$ on $X$ is $\omega$-plurisubharmonic ($\omega$-psh for short) if the form $\omega+\sqrt{-1}\partial\bar{\...

**-1**

votes

**0**answers

20 views

### Independence of events [on hold]

I have a question about probability. Imagine we have a deck of 40 cards with 4 different suits of ten cards. Define two events:
$A \equiv $ We take a card and its an ace $\Rightarrow P(A)=\frac{1}{10}...

**0**

votes

**0**answers

117 views

### Normal subgroups of $p$-groups

I was reading Professor Yukov Berkovich' paper "On Subgroups of Finite $p$-groups" when I stumled upon the following theorem:
Let $G$ be a nonabelian $p$-group with cyclic Frattini subgroup, $|\Phi(...

**-1**

votes

**1**answer

50 views

### On spectral multiplicity of left shift operators

Let $U$ be an operator defined on $l^{2}(\mathbb{Z})$ by $U(e_{n})=e_{n-1}$, where $e_{n}$ is an orthonormal basis of $l^{2}(\mathbb{Z})$. $U$ is a left shift operator. Since $U$ is unitary operator ...

**0**

votes

**0**answers

100 views

### Definition of the surface measure in some books

I am studying PDEs and in some books (Folland, Introduction to Partial Differential Equations and Evans, Partial Differential Equations), I found an integral integrated by the surface measure on a $C^...

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vote

**0**answers

37 views

### Name for a pair of lattices one of which having theta series with coefficients a subsequence of another lattice's theta series coefficients

Is there a name for a pair of lattices which have the property given in the title? The following example of a pair captures the property mentioned above:
$$(i)\ 1 + 80q^3 + 270q^4 + 432q^5 + 960q^6 + ...

**7**

votes

**1**answer

280 views

### Do any finite predictions of Quantum Mechanics depend on the set theoretic axioms used?

I was wondering if any of the finite predictions of Quantum Mechanics depend on what set theoretic axioms are used.
We will say that Quantum Mechanics makes a finite prediction about an experiment if,...

**1**

vote

**1**answer

138 views

### On the 2002 paper “Dynamics of polynomial automorphisms of $\mathbb{C}^k$” by Guedj and Sibony

I desperately need to read the paper [1] before meeting a would-be supervisor, but with limited undergraduate knowledge that I have like Aluffi's Algebra and Churchill's Complex Analysis, not even one ...

**2**

votes

**0**answers

176 views

### Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorphic vector bundle $E$?

Please let me know whether this question is suitable for Mathoverflow.
Let $E$ be a finite holomorphic vector bundle (or more generally a coherent analytic sheaf) on a compact complex manifold $X$. ...

**0**

votes

**0**answers

17 views

### Find local coordinates of end points of a time varying line (w.r.t. two other objects) to minimize line-length variance

Line A'A rotates cyclically around point A' in a fixed time varying pattern and coordinates of the point A' are fixed (i.e. line A'A has only one degree of freedom).
Line BB' can move along x-axis and ...

**16**

votes

**2**answers

509 views

### Motivation behind Analytic Number Theory

I am an undergraduate student of mathematics and recently took an introductory course in analytic number theory, where the instructor roughly followed Apostol's first text on the subject. I have now ...

**7**

votes

**2**answers

172 views

### Measure of the numbers with length of $n$ for a nonstandard number $n$

Is there any nonstandard model of $PA$ with the following properties?
There exists a nonstandard number $n\in M$ such that $M\upharpoonright n$ is countable,
Let $|x|=\lceil\log_2x\rceil$, ...

**1**

vote

**3**answers

59 views

### Is there a process for finding an implicit representation for an approximation to an arbitrary plane curve?

There are a number of plane curves listed on mathworld, described by implicit algebraic equations, including the butterfly curve, ampersand curve, and bow curve. These all loosely resemble ...

**2**

votes

**2**answers

159 views

### What do the eigenvectors of the $n$th roots of $I_n$ look like?

This was asked at math stackexchange a long time ago with no answers but some upvotes.
Let $A^n=I,$ where $A$ is $n\times n,$ and assume that $A^k\neq I,$ for all $1\leq k<n.$ Since its ...

**16**

votes

**1**answer

432 views

### Commutative rings : Topoi = Fields :?

The following is probably a bad question, but hopefully, it might have a very good answer.
In category theory there is a quite famous analogy between topoi and commutative rings, I was never ...

**-2**

votes

**0**answers

37 views

### Decompose geometric mean [on hold]

Sorry if this is a super-dumb question. I have three data series: organic growth, volume growth and price growth. Organic growth = volume growth + price growth. I have converted them into indices and ...

**2**

votes

**0**answers

117 views

### Taylor Expansion on a Riemannian Manifold in Normal Coordinates

Let $\phi: (M,g)\hookrightarrow (N,\tilde{g})$ be an isometric embedding of a Riemannian manifold $M$ of dimension $m$ into a Riemannian manifold $N$ of dimension $n$. I am interested in trying to do ...

**1**

vote

**1**answer

61 views

### Does every uncountably categorical theory have a $\varnothing$-definable strongly minimal imaginary?

An uncountably categorical theory always has a strongly minimal set definable over its prime model, but sometimes this set needs parameters to define.
By a $\varnothing$-definable imaginary I mean ...

**4**

votes

**1**answer

122 views

### Decidability: Presentations vs. Groups

This question is just a curiosity for me as a non-expert. Quite often we ask about decidability of various properties in a group. Often the answer is that the property is undecidable in general. ...