All Questions
-1
votes
0answers
19 views
How can this statement of the link between Hamiltonian and symplectic matrices be made more rigorous?
I quote the a textbook, which says the following:
It is easily checked that the exponential of a Hamiltonian matrix
$$
g=exp(\phi\cdot\mathbf{T})
$$
is a symplectic matrix; Lie group ...
1
vote
1answer
36 views
the existence of a real polynomial satisfying the following property
It is easy to verify that
$$ \frac{t}{2}\leq \frac{1}{4}+\frac{1}{4}t^2\leq \frac{t}{1-(1-t^2)^2}-\frac{t}{2}
\quad \quad 0<t\leq1$$
I want to ask if there exist a real polynomial $h(t)$ such ...
0
votes
0answers
6 views
presence of turbulent phenomena in systems of linear pde?
Are there linear systems of PDE that are known to have solutions which exhibit turbulence, or can turbulence be firmly classified as a fundamentally non-linear phenomenon, similar to solitons or shock ...
1
vote
0answers
12 views
Measure on hyperspace of compact subsets
For a Polish space $X$, let $K(X)$ be the set of compact subsets of $X$. Given the topology with basis $\{K\in K(X):K\subset U_0, K\cap U_1\neq\emptyset,\ldots,K\cap U_n\neq\emptyset\}$ for open sets ...
2
votes
1answer
53 views
Sites for seeking possible collaborations
As a material scientist, I have recently constructed algorithms for solving ground state of arbitrary cluster interactions models and prepared publications in the field of physics and material ...
1
vote
0answers
52 views
Category of modules over commutative monoid in symmetric monoidal category
Let $\left(\cal{C},\otimes ,I\right)$ be a symmetric monoidal category (not necessarily closed) and $A$ a commutative monoid in $\cal{C}$. In his DAG III (page 95), Lurie writes:
In many cases, ...
1
vote
1answer
41 views
Question on the number of equilibria
Let $f: C \to C$ be a smooth function and $C$ be a compact set, subset of $\mathbb{R}^n$.
We assume that all the fixed points are hyperbolic. Is it true that the number of fixed points is finite or ...
3
votes
0answers
63 views
Totally disconnected subspaces
This question is motivated by this one, where no simple solution within ZFC seems to exist. Let me ask a weaker question then.
Suppose that $K$ is a compact, Hausdorff, non-metrizable space. Does it ...
1
vote
0answers
49 views
which sections of elliptic curves are conjugate?
Suppose you have a relative elliptic curves $f : E\rightarrow S$ (say $S$ is connected). Then suppose you have two sections $g,g' : S\rightarrow E$, corresponding to two sections $g_*,g'_*$ to the map ...
0
votes
0answers
59 views
Characterization convex function [on hold]
Let be $f:[0,1]\rightarrow\mathbb{R}$ a continuous function such that far all $a,b\in [0,1]$ with $a<b$
$$f\left(\frac{a+b}{2}\right)\leq\frac{1}{b-a}\int_a^b f(x)\,dx.$$
How to prove that $f$ is ...
8
votes
1answer
73 views
Flag complexes that are shellable but not vertex decomposable
As the title suggests, I was wondering if anyone can point me to any examples in the literature to flag complexes that are shellable but not vertex decomposable.
It is well-known that if a ...
10
votes
0answers
95 views
Is every elementary absolute geometry Euclidean or hyperbolic?
Absolute geometry is any one that satisfies Hilbert's axioms of plane geometry without the axiom of parallels. It is well-known that it is either the Euclidean or a hyperbolic plane. For an elementary ...
-3
votes
0answers
63 views
Tripet prime reciprocals series [on hold]
Does any body know if the series of reciprocals of triplet primes of form
p,p+2,p+6 or p, p+4,p+6 converges or diverges. Could this be used as a proof of infinity of twin primes
0
votes
0answers
21 views
Which Hyperspace Topologies Yield Topological Lattices?
At least on a continuum, the binary operations of intersection and union are Vietoris-continuous. But the Vietoris topology only applies the the collection of NONEMPTY closed subsets, and this means ...
-1
votes
0answers
24 views
Mean exit time / first passage time for a general symmetric Markov chain [on hold]
Suppose I have a Markov chain as depicted in the following figure:
where $N$ is even. State 0 and $N$ are the two sinks of the chain. The transition probabilities have the following property: ...
7
votes
1answer
253 views
Can a division algebra have degree divisible by its characteristic?
I apologize in advance if this is easy, but I've tried Googling, and had no luck.
I'm currently working on a proof, and I realized in the course of writing that this proof will break if out there ...
2
votes
0answers
64 views
Morse theory Vs degree theory
I asked this question on http://math.stackexchange.com but no unswers!
I have this paragraph from K.C. Chang Infinite dimensional Morse theory
In comparison with degree theory, which has proved ...
1
vote
0answers
55 views
Distributivity of group topologies on $\Bbb Z$
Let $\mathcal L(\Bbb Z)$ be the set of all group topologies on $\Bbb Z$.
It is known that $(\mathcal L(\Bbb Z),\subseteq)$ is a modular complete lattice.
Is $(\mathcal L(\Bbb Z),\subseteq)$ ...
0
votes
1answer
64 views
Estimates on gamma- functions [on hold]
I need a special inequality related to a fractional derivative problem.
Let k∈ℕ ,0<α<1 , 0<β<1.Consider :
A=[Γ(1-α)Γ(1+k-β)/Γ(2-β-α+k)].(1-α)
On what conditions (on k ,β and α) A is less ...
0
votes
0answers
20 views
Beta distribution - changes in multiple time points
Let's say I have a set of daily data (assume iid) that I know is beta distributed (between 0 and 1). I can estimate the parameters of the distribution and calculate the tails etc. This would tell me ...
-1
votes
0answers
54 views
I need help in understanding O(nlogn) question [on hold]
I wish I could think of a better way to word my question. Maybe some one here could offer s suggestion for that, as well.
On to my question. Before I do, this is a class question that has been asked, ...
0
votes
0answers
30 views
construction of four dimensional regular convex polytopes
Could anybody give me a reference book about the explicit construction of the 6 regular four dimensional convex polytopes. I cannot easily find Schläfli's original paper so I am looking for a modern ...
1
vote
1answer
104 views
Distribution of a random walk on a directed line
Is there a closed formula for the distribution of $x_t$ in the following random process, describing a random walk on a directed line?
$x_0 = n$
$x_t$ is a uniformly random integer between 1 and ...
1
vote
0answers
27 views
Does the following measurable Halmilton-Jacobian equation admit a Lipschitz solution?
I have the following question:
Let $F:\Omega\times \mathbb{R}^n\to [0,\infty)$ be a convex Finsler norm, which means that
$F(x,\cdot)$ is convex with respect to the second variable.
$F(\cdot,v)$ ...
10
votes
2answers
298 views
(co)homology of symmetric groups
Let $S_n=\{\text{bijections }[n]\to[n]\}$ be the n-th symmetric group. Its (co)homology will be understood with trivial action. What are the $\mathbb{Z}$-modules $H_k(S_n;\mathbb{Z})$? Using GAP, we ...
3
votes
0answers
52 views
The action of Steenrod squares on the indeterminate in Bullett-Macdonald identities
The Bullet-Macdonald identity (c.f. On the Adem relations)is the following:
$$P(s^2+st)P(t^2)=P(t^2+st)P(s^2).$$
where we have $P(s)=\Sigma _s s^iSq^i$. This is known to be equivalent to the
Adem ...
1
vote
0answers
28 views
All all hypo-multiplicative functions linear combinations of quasi-multiplicative functions?
A function is called quasi-multiplicative by many authors if $f(m)f(n)=f(1)f(mn)$, a slight generalization of multiplicativity. (Basically a multiplicative function times a constant is a ...
0
votes
1answer
42 views
Depth formula in CM-ring involving canonical module
In this article by Iyama and Wemyss there is the following formula:
Let $R$ be a Cohen-Macaulay ring with canonical module $\omega$, let $X$ be a finitely generated $R$-module. Then
...
1
vote
0answers
98 views
Searching for surprising equation connecting distant mathematical fields [on hold]
I hope this is not too off topic on this site, if so i excuse myself.
Some time ago i read an article about important equations (as most lists feature prominent unequations) in math and the unsolved ...
2
votes
0answers
48 views
Logarithms in an algebraic differential field
I have this problem: let $Y_1,\dots,Y_n$ be real analytic functions $\mathbb{R}^+\to\mathbb{R}^+$ such that all the $Y_1,\dots,Y_n$ and all their derivatives are algebraically independent over ...
0
votes
0answers
46 views
Mean distance between two points in a disk [on hold]
Two points are uniformly distributed in a disk(say disk1) of radius 2r with origin as center. I need to get mean distance of the two points from origin, with the following conditions satisfied.
One ...
7
votes
1answer
99 views
When is a continous $\epsilon$-isometry of the sphere surjective?
Equip $\mathbb S^n$ with the standard round metric. Let $f : \mathbb S^n \to \mathbb S^n$ be a continous map satisfying $\vert d(f(x),f(y)) - d(x,y)\vert \leq \epsilon$.
Is $f$ is surjective for all ...
2
votes
3answers
114 views
Reference on representations of knot groups
Recently, I was studying the knot group and I want to learn some more material about it (e.g. its representations).
"Knots" by Burde and Zieschang discusses some material but it is not entirely ...
0
votes
0answers
15 views
Pseudo-random number generation on top of the countable grid
Is it possible to generate many streams of pseudo-random numbers given one (or several) natural number as an argument in the way that they are not correlated?
As a minimal goal I want to have some ...
4
votes
1answer
148 views
Higher coherent multiplicative structures on S-algebras
In their book, Elmendorf, Kriz, May and Mandell describe a useful category of spectra, called S-modules, where S is the sphere spectrum. Ring objects in this category can be identified with spectra ...
0
votes
0answers
19 views
Find relationships between events
I have a set of Events $(E_i)_i$ which have a probability $(P_i)_i$.
I am able to write each event as a sum of distinct events that form a partition of the space.
My goal is to find all the ...
1
vote
1answer
83 views
Checking the intersection of two sets
Let $E\subset{\mathbb R}^n$ be a set of the type $I_1\times \dots \times I_n$, where $I_k$ are real intervals, and $X$ be and $n\times p$ real matrix. Suppose also that $rank(X)=p$ and $n>p$. Is ...
-3
votes
0answers
50 views
Eigenvalues of a Symmetric Block Tridiagonal Matrix [on hold]
Does anyone have any idea on how to get the analytical answer for a symmtrical block tridiagonal matrix ??
Given that the the Block Matrices on the super and subdiagonals are Identity matrices.
it is ...
-1
votes
0answers
27 views
find all path segments in an undirected graph [on hold]
I am not a mathematician. I am planning to write some python code to do this task, and I thought that mathematicians could help me come up with the most efficient way to do it. :)
I have an ...
6
votes
2answers
308 views
How did height in algeb. number theory/elliptic curves started?
Maybe this is obvious but it isn't to me yet. What is the history of heights used in say points of the project plane over a number field or of elliptic curve over a number field? I would guess people ...
2
votes
0answers
37 views
A result on absolute mean of a stopped supermartingale
The reason of posting the following problem here is that I heard that it is a result from some paper.
Let $(X_n, \mathscr{F_n}), n \geq 0$ be a super martingale and $T$ an $\{F_n\}$-stopping time ...
0
votes
1answer
112 views
Knot is an unknot iff [on hold]
Is it true that a knot in 3-sphere is an unknot if and only if the fundamental group of its complement is $Z$? If so, references would be nice.
-3
votes
0answers
33 views
Can I describe the motion of Helicopter in limit cycles? [on hold]
I know that the basic equation of the motion of helicopter is based on Euler's laws of motion,or multibody system dynamics.The force on a helicopter is complex and it is related to motion of air.It is ...
4
votes
1answer
127 views
Harish-Chandra isomorphism for compact symmetric spaces
I would be interested to have an explicit description of the algebra of invariant differential operators on functions on a compact symmetric space $G/K$. A reference would be especially useful.
...
6
votes
1answer
233 views
Are bounds known for the maximum determinant of a (0,1)-matrix of specified size and with a specifed number of 1s?
The problems of determining the maximum determinant of an $n \times n$ $(0,1)$-matrix and the spectral problem of determining exactly which other determinants can possibly occur are both reasonably ...
0
votes
0answers
23 views
Does there exist a method which is similar to striping in network coding [on hold]
In distributed storage system, one way to reduce repair bandwidth is to look the data file at higher granularity, in other words, view a symbol as several smaller symbols. In this paper, Dimakis et al ...
4
votes
0answers
45 views
Subgraphs of planar trivalent graphs
Let's think about planar trivalent graphs. (Or you can dualize and think about triangulations if you prefer.) It's easy to come up with a list of 'planar trivalent graphs with boundary' such that at ...
3
votes
0answers
129 views
What is the density of the reciprocal of the set of cubes?
In his MathOverflow question "How thick is the reciprocal of the squares?" Kevin O'Bryant asks if a certain set, the reciprocal of the set of squares (identifying sets with power series in ...
0
votes
0answers
141 views
Covering a finite subset of $\mathbb{N}$ with prime arithmetic progressions
Because of a problem I ran into I am trying to get a quick start in covering with arithmetic progressions.
First I want to say I am aware of this previously asked question:
Covering $\mathbb{N}$ with ...
0
votes
0answers
48 views
Definition of a monomial [on hold]
Why is "A function M:{1,2,...,n}->N is called a monomial"? (Page 9 of Lie Groups: An Approach through Invariants and Representations) I thought a monomial is just a one-term polynomial over a general ...
