5
votes
0answers
41 views
Definitions of ordinal besides von Neumann & Frege-Russel?
So my Google-fu didn't show any references on this. I'm studying an obscure set theory (ML, a variation on NF with proper classes) and it seems to not deal well with the standard definitions of ...
0
votes
1answer
16 views
taut foliations and the existence of total transversals
A codimension one foliation $\cal F$ on a smooth manifold $M$ is taut if every leaf of $\cal F$ meets a closed transversal (i.e., a simple closed curve that is everywhere transversal to the leaves of ...
0
votes
0answers
63 views
Can I conclude that a morphism of vector bundles is zero if it is so fiberwise?
Let $f: X \rightarrow Y$ be a flat morphism of locally noetherian schemes and $\varphi: \mathcal U \rightarrow \mathcal V$ a map of vector bundles (locally free sheaves of finite rank) on $X$.
I want ...
1
vote
0answers
28 views
When does Bogomolov's inequality become an equality?
The Bogomolov theorem says if $V$ is a rank 2 vector bundle on an algebriac surfaces $S$ is $H$-stable (in the sense of Mumford-Takemoto) for some ample divisor $H$, then $c_1^2(V) \leq 4c_2(V)$ ...
4
votes
1answer
57 views
Fixed points on boundary of hyperbolic group
Let G be a word-hyperbolic group with torsion and let ∂G be its boundary. Do there exist criteria that imply that all non-trivial finite order elements of G act fixed-point freely on ∂G?
2
votes
0answers
35 views
Probability that a random edge coloring of the complete graph is proper
This is a repost of this math.se question that I am posting here since it received no attention there.
What is the probability that a random edge coloring of $K_n$ with
$m \geq n$ colors ...
4
votes
3answers
118 views
Good reference for studying operads?
Can you, please, recommend a good text about algebraic operads?
I know the main one, namely, Loday-Vallette "Algebraic operads". But it is very big and there is no way you can read it fast. Also ...
2
votes
1answer
57 views
Is the localisation of a product of categories the product of the localisation?
Let $\cal C, \cal D$ be model categories. Hovey says in his monograph "Model Categories" that the homotopy category $\operatorname{Ho}(\cal C \times D)$ is isomorphic to $\operatorname{Ho}(\cal C) ...
0
votes
0answers
12 views
On an optimal estimate of a certain pseudo-differential operator
Concerning a pseudo-differential operator of which the symbol is $e^{-i\xi^{m}}/\hat{f}(\xi)$, where $m$ is a positive integer. Can we choose a ceratain $f$ such that there exists an estimate of ...
-3
votes
0answers
95 views
What's difference of Simplicial complex and CW complex? [on hold]
I do not know how simplicial complex can differ from CW complex?
Please give me typical examples.
Is it normal that mathematicians treat non-CW complex?
0
votes
0answers
40 views
point which minimizes the sum of the distances from the sides of a triangle [on hold]
i was wondering for which point P in the plane the sum of the perpendicular distances from the three sides of a regular triangle (PD+PE+PF) is minimized where D,E,F are the feet of the perpendiculars ...
2
votes
0answers
54 views
Relationship between virtual cohomological dimension and tautological rings for moduli spaces of curves
Here's the short version of the question. For $M_{g,n}$, $M_{g,n}^{rt}$, $M_{g,n}^{ct}$ and $\overline M_{g,n}$ it seems that the virtual cohomological dimension is given by the complex dimension plus ...
2
votes
0answers
33 views
Uniform hyperbolicity decay estimate
I have been banging my head against a wall off and on for about a month now trying to understand the proof of the following result, which is considered well-known.
Theorem: Fix a compact metric ...
4
votes
0answers
77 views
Homology of localisations of spectra
Let $H^*$ and $K^*$ be two cohomology theories, and $X$ a reasonable spectrum. Here, I'm thinking that $H^*$ is singular cohomology (and for my purposes, rational cohomology will suffice), and $K$ is ...
1
vote
0answers
41 views
Uniqueness theorems related to Hardy Uncertainty Principle
Uncertainty Principles state that a function and its Fourier transform cannot be simultaneously sharply localised. A well known result due to G.H.Hardy says that
if $f(x)=O(e^{-\alpha^2|x|^2})$, ...
2
votes
0answers
164 views
A prime curiosity [on hold]
$\qquad $ A correspondent of mine, Will Gosnell, has noticed that when the sum of the squares of the digits of the prime 18973 is subtracted from it, the result is the square of 137. Similarly, ...
2
votes
0answers
116 views
Peu or très ramifiée extension
Let $p$ be a prime number. Let $\mathbb{F}$ be a finite extension of $\mathbb{F}_p$. Let $\omega$ be the mod $p$ cyclotomic character and let $V$ be a representation of $G_{p} = Gal(\bar{\mathbb{Q}}_p ...
0
votes
0answers
94 views
A reference about Dolbeault cohomology
I am looking for a reference about Dolbeault cohomology when the line bundle is not supposed to be positive.
2
votes
0answers
46 views
May a globally bounded G-function have a logarithmic branching? (On a conjecture of Ruzsa)
By a "globally bounded $G$-function," I will mean a solution to a (minimal) linear differential equation on $\mathbb{P}^1$ (then necessarily of the Fuchsian type and with rational exponents), which is ...
-4
votes
0answers
25 views
Distance between two disjoint polyhedrons [on hold]
Polyhedron: A subset P⊂Rn is a polyhedron if it is the intersection of a finite number of closed affine halfspaces. I guess the distance between two disjoint polyhedrons is positive. Please give a ...
-7
votes
0answers
44 views
functional analysis Hahn–Banach [on hold]
what By the Hahn–Banach theorem, for every nontrivial Banach space X we can pick an n ∈ N for which there is a continuous
linear T : X →R^n such that T (X) = R^n???
-2
votes
0answers
27 views
how to impliment fractional formula to get range between 0.0 to 3.0 on given range [on hold]
I am implementing one algorithm based on popularity count of website . i have range as follows:
input rating count 0 - 500 = 0.0 - 1.0 output popularity count
input rating count 500 - 2500 ...
-6
votes
0answers
35 views
how did he conclude that?integral(spivak's calculus) [migrated]
So the question is : Find all continious functions such that $\displaystyle \int_{0}^{x} f(t) \, \mathrm{d}t$= ((f(x)^2)+C , what interests me is the way the solutions book presented the solution , ...
-1
votes
0answers
41 views
effective divisors on a curve and upper semi-continuity
Let consider a smooth projective curve over $\mathbb{C}$. We consider the scheme that classifies effective divisors of degree $d$, isomorphic to $X^{d}/S_{d}$ where $S_{d}$ is the symmetric group.
We ...
-1
votes
0answers
37 views
On the commutativity of the relative homotopy groups [migrated]
Can you explain to me why relative homotopy groups $\pi_{n}(X, A; x_0)$ are commutative for $n \geq 3$? It would be great if you will show me explicit homotopy.
2
votes
0answers
49 views
A partition of the unit interval into uncountably dense uncountable subsets [migrated]
The title says it all: Is there a partition of $[0,1]$ into uncountably dense uncountable subsets ?
3
votes
2answers
137 views
zeta(3) in Euler's Section 153
Jeffery Lagarias, in his recent article
Euler's constant: Euler's work and modern developments
in the AMS Bulletin, mentions that Euler obtained $\zeta(3)={{2\pi^3 b(3/2)}\over 3}$ for some "Bernoulli ...
4
votes
0answers
67 views
Who first proved there's an $\omega$-model of $WKL_0$ in which all sets are low?
I am trying to pin down: who first proved that $WKL_0$ has an $\omega$-model in which every set is of low degree? As shown in Simpson's Subsystems of Second Order Arithmetic (Theorem IX.2.17), one ...
4
votes
0answers
37 views
Minimum dilatation pseudo-anosovs on non-orientable surfaces
Is anything known about minimum dilatation pseudo-anosovs on non-orientable surfaces?
More specifically it is known whether the asymptotic behavior for log(minimal dilatation) is 1/genus? (The lower ...
-2
votes
0answers
78 views
The one point compatification [on hold]
The one point compatification of a countable $KC$ space$X$ is $KC$ if and only if $X$ is compact.
proof
sufficiency: an open subspace of a sequential spaces is sequential.
necessity: supposr that ...
2
votes
1answer
63 views
Infinitesimal equivalence of admissible representations
Let $G_0$ be the $\mathbb{R}$-points of a real reductive group with complexified Lie algebra $\mathfrak{g}$ and maximal compact subgroup $K$. What is the precise relation between the category of ...
-3
votes
0answers
104 views
Proof why this sum is equal to 1 [on hold]
This sum is equal to 1 for any 2 integers n and k for which n>k and n>0 and k>=0
...
2
votes
1answer
39 views
model co-isotropic submanifold
Just as the zero section in $T^*\mathbb{R}^N$ (equipped with the standard symplectic form) is the "model" / "quintessential" Lagrangian submanifold, does $T^*\mathbb{R}^N$ have a "model" co-isotropic ...
6
votes
1answer
75 views
Uniqueness up to isometric isomorphism of predual of $(\sum_{\lambda\in\Lambda} H_\lambda)_{l_\infty}$ where $H_\lambda$ are Hilbert spaces
This fact is an easy consequence of results of the paper by Leon Brown and Takashi Ito, but it looks like an overkill. Does anyone know a simpler proof?
9
votes
3answers
230 views
Convergent subsequence of $\sin n$
It is well known (not to me -- ed.) that for every real number $\theta \in [0, 1]$ there exists a sequence $(k_i)$ such that $\lim\sin k_i = \theta,$ but there appear to be no explicit such ...
2
votes
0answers
65 views
Which unordered partition of $n$ gives rise to the largest number of ordered partitions?
A quick look at the wikipedia article on partitions of $n \in \mathbb{N}$ shows that the number of ordered partitions is $2^{n-1}$, and the number of unordered partitions is asymptotically $ \sim ...
-3
votes
0answers
51 views
Spectral Radius of Reduced Matrix [on hold]
Suppose $M$ is an $n\times n$ matrix, and $P$ is an $n\times l$ orthornormal matrix. I would like to show that the spectral radius of $P^TMP$ is smaller than the spectral radius of $M$. Is that ...
2
votes
1answer
61 views
Actions of compact Lie groups on (possibly but hopefully not) non-regular spaces
Suppose $G$ is a compact Lie group acting freely on a topological space $Q$ (about whose separation conditions I make no assumptions) and the qoutient $Q/G$ is known to be completely regular Hausdorff ...
1
vote
0answers
31 views
Reference for a path groupoid being a diffeological groupoid
I am looking for a reference that has a proof that a path groupoid
is a groupoid internal to the category of diffeological spaces. I do know how to prove this fact, and a proof is not hard. My reason ...
2
votes
0answers
30 views
Spherical completions and flatness
Let $k$ be a non-Archimedean field. Does there exist a spherical completion $K$ of $k$ such that for any $k$-Banach space $X$, the natural map $X \to X \widehat{\otimes}K$ is an isometric embedding? ...
2
votes
0answers
63 views
Equivalent paths in graphs
Let $G$ be a finite, planar graph. In this question I consider a path in $G$ to be a finite sequence of vertices $v_1,\dots,v_n$ of $G$, where $v_i$ is adjacent to $v_{i-1}$ for $i=2,\dots,n$. A ...
0
votes
1answer
98 views
Non simply connected HyperKähler 4-manifolds without ALE metrics
In a 1989 paper Peter Kronheimer showed that each simply connected HyperKähler 4-manifold possesses an ALE metric. What do we know about the non-simply connected cases?
2
votes
0answers
59 views
Is the local norm index known for elliptic curves at a place of additive reduction?
Let $K/F$ be a quadratic extension of number fields and let $v$ be a place of $F$ and $w$ a place over $v$. Let $E$ be an elliptic curve, the local norm index is given by $${\rm dim}_{\mathbb{F}_2} ...
2
votes
1answer
75 views
Irreducibility of trinomials
I wonder if the following is known or, not very difficult to see:
Let $K$ be a number field and $A, B \in \mathcal{O}_K$ be nonzero integers of $K$. Does there necessarily exist a positive integer $n ...
2
votes
3answers
194 views
Good Books on the history of Zero
I am looking for books that discuss the origins of the zero, specifically the differences in the use and concept of the zero number among different civilizations (considering also the Mesoamerican ...
6
votes
2answers
92 views
Vanishing of integral on hemispheres implies vanishing of function?
Consider a function $F$ on the half space $\{(x,y,z)|z>0\}$. If $F$ is analytic, it is straightforward to show that
A) The integral of $F$ over the hemisphere $(x-x_0)^2 + (y-y_0)^2 + z^2 = R^2$ ...
4
votes
1answer
161 views
The d-dimensional matrix with columns (1,0,0…), (1/2,1/2,0,…), (1/3,1/3,1/3,0,…),…, (1/d,1/d,…,1/d)
During the course of physics research on nonequilibirum statistical mechanics involving the theory of majorization, I have come across a linear transformation on a d-dimensional vector space that I ...
0
votes
0answers
17 views
What is the tutte polynomial [migrated]
I am really stuck on how to work out the tutte polynomial so any help would be great thanks.
G is a graph with 2 vertices, joined by n edges.
How to you show what the tutte polynomial is?
And what ...
-1
votes
0answers
71 views
Beach Path math problem [on hold]
Anyone who has walked on the beach knows that walking speed is dependent upon how far away from the ocean one walks. If you walk on the wet sand you can walk much more quickly than if you walked on ...
-6
votes
0answers
90 views
please help to find this question [on hold]
In each of the following questions, a number is missing which is indicated by a question mark.
Your task is to find out what will come in place of the question mark (?).
Q. 42 + 73 + 137 = ?
options ...
