0
votes
0answers
2 views

Embeddings of subshifts

Consider $(X,\sigma_X)$ and $(Y, \sigma_{Y})$ be subshifts of the one sided shift in two symbols. Assume that $(X,\sigma_X)$ is a transitive subshift of finite type and $(Y, \sigma_{Y})$ is a ...
0
votes
0answers
2 views

How can I calculate the global log canonical threshold?

Let $X$ be a normal variety and let $D$ be a $\mathbb{Q}$-divisor. The log canonical threshold of a pair $(X,D)$ is $lct(X,D)=sup\{c|(X,cD)$ is log canonical$\}$. If $X$ is $\mathbb{Q}$-Fano ...
1
vote
0answers
11 views

A strange condition on containment of special complex numbers in cyclotomic fields

In a recent theorem we have naturally come across this condition, that seems to be important, but rarely satisfied: $\sqrt{\frac 1 4 + a^m} \in \mathbb Q(\zeta_m, a)$ where $a\in\mathbb C^*$ and ...
2
votes
0answers
15 views

Is there a maximal connected Hausdorff space?

We call a space $(X,\tau)$ maximal connected, if it is connected, and for any topology $\sigma \supseteq \tau$ with $\sigma\neq \tau$, the space $(X,\sigma)$ is not connected. Is there a maximal ...
1
vote
0answers
10 views

Maximal connected topologies

We call a space $(X,\tau)$ maximal connected, if it is connected, and for any topology $\sigma \supseteq \tau$ with $\sigma\neq \tau$, the space $(X,\sigma)$ is not connected. If $(X,\tau)$ is ...
-2
votes
0answers
14 views

log(n) vs n^f - formal prove

It's clear to see that log(n)=O(n^f) when f>0 I'm wondering what's the easiest and the best way to prove this? Thanks!
0
votes
0answers
9 views

Defining a brownian bridge indexed by angle

I have a random closed curve of the form $(\theta,r_\theta)$, where $\theta\in [0,2\pi]$, is the counter clockwise angle from the x-axis and $r_\theta$ is the radial distance from the origin ...
-5
votes
0answers
19 views

LyX preamble to auto add space before and after math (CTRL+M) [migrated]

I tried everything, but nothing works. How can I make auto space bofore and after math formulas in the same line? Thank you.
1
vote
1answer
16 views

Null tetrad transformation

I have been going through the Chandrasekhar's "The Mathematical Theory of Black holes", in particular the chapter on Newman Penrose formalism. I have a question about what he calls a "class III ...
1
vote
0answers
46 views

Irreducibility of a general fibre

Let $A\subseteq B$ be an inclusion of affine domains over an algebraically closed field $k$ of characteristic $0$. Can someone give me a reference for the following fact? If $A$ is algebraically ...
2
votes
0answers
38 views

Relating different topologies on $C^{\infty}_c(M)$

This is somehow connected to this question. I can think of at least four topologies to put on $C_c(M)$: Topologize $C^{\infty}_c(M)\subseteq C^{\infty}(M)$ as a subspace with the weak Whitney ...
7
votes
1answer
92 views

(Non)existence of mirrors with more than two foci

Do there exist any mirrors $M$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ for which there exist three different points $x_1$, $x_2$, $x_3 \in \mathbb{R}^d$ such that if any ray of light passes ...
-2
votes
0answers
27 views

How to estimate some combinatorial expression? [on hold]

How to estimate (or explicitly compute) the following sum $\sum_{j=1}^{k}\left|\binom{x}{j}\binom{k-1}{j-1}\right|$ from above? The most convenient estimation ...
0
votes
0answers
25 views

Minimal dimension of a Lie algebra of matrices, with a restrictive property

Let $\mathfrak{g}$ be a sub-Lie-algebra of $\mathfrak{gl}_n(\mathbb{C})$, the Lie algebra of complex $n\times n$ square matrices. Let us call $(H)$ the hypothesis: for all $x, y\in\mathbb{C}^n$, ...
0
votes
1answer
24 views

Monoidal structure on simplicial sheaves

Let $\mathcal{C}$ be a site and let $sPh(\mathcal{C})_{proj}$ be the category of simplicial presheaves equipped with the projective model structure. This category is a closed monoidal model category ...
-2
votes
0answers
21 views

Deriving sequence of number added after sum of the number [on hold]

I just want to know , is there any mathematics operation by which we can achieve the below mentioned task: 1> I will sum up a sequence of number, it could be any number(For the task I am free to ...
1
vote
0answers
25 views

Hyperellptic curve defined by a set of rational points

If we fix a field $\mathbb{F}$ of positive characteristic, and a a genus $g$ , how many rational points are enough to build a unique hyperelliptic curve of genus $g$ over $\mathbb{F}$?. The thing is ...
1
vote
0answers
26 views

Weak topology on subsets of a Hilbert Space

I have few questions about the subsets of a (for example) Hilbert Space endowed with the weak topology. Let $E$ be such subset. When is the norm a continuous function on $E$? This happens for ...
1
vote
0answers
27 views

The number of $k$-free integers not exceeding $x$

We say that an integer $n\in\mathbb{N}$ is $k$-free if for each prime $p\mid n$, one has $p^k \nmid n$. Let $\mu_k(n)$ be the characteristic function of $k$-free numbers, where $k\ge 2$. Let ...
0
votes
0answers
20 views

Approximation property of Fréchet if range is restricted to an embedded Hilbert space

Let $W$ be a separable Fréchet space, and $H\subset W$ be a separable Hilbert space that is continuously embedded (equivalently, the topology of $H$ is stronger than the subspace topology generated by ...
2
votes
0answers
62 views

Constructing normal crossing varieites

Let $X_i$ be a smooth projective variety with a smooth divior $D_i$ for $i=1,2$. Suppose that $D_1$ is isomorphic to $D_2$. Then does it make sense to construct a normal crossing variety $X=X_1 ...
1
vote
0answers
37 views

If $R$ is generated by idempotents, then $\text{Ann}(R)=0$?

Let $R$ be a ring (not necessarily commutative or unital) that is generated by idempotents. I'd like to know if $\text{Ann}(R)=0$ must hold. Here I use $\text{Ann}(R)$ to denote the set of all ...
5
votes
1answer
80 views

Notions of infinity in $\mathsf{ZF}$ without choice

Consider the following statements about a given set $X$ in in $\mathsf{ZF}$: (1) There is $x_0\in X$ such that there is a surjective map $\varphi: X\setminus\{x_0\}\to X$. (2) There is an injective ...
0
votes
0answers
52 views

Degree of compositeness of integer

Given $N\in\Bbb N$, call a number $(t,d,c)-$composite with respect to $N$ if there is there a $2t$ bit number $R$ such that number of distinct factor pairs $r_1,r_2$ of size $t\pm c$ bits such that ...
0
votes
0answers
25 views

How to prove Butler's inequality for the maximal slope of the kernel bundle?

In Butler' paper "Normal generation of vector bundles over a curve" (J.d.g.,1994). Proposition 1.4 said that $$prop^+(M_E)\leq \max\left\{-2,\frac{-prop^+(E)}{prop^+(E)-g}\right\}$$ where $E$ is a ...
3
votes
0answers
34 views

Concentration of measure for uniform distribution on Stiefel manifolds

This is my first post on MO, so I hope the question is suitable. I am looking at the uniform distribution on the Stiefel manifold, but more specifically, at the uniform distribution on the ...
0
votes
0answers
183 views

On 'Riemann Hypothesis' in Geometric Complexity Theory using Algebraic Geometry

In http://ramakrishnadas.cs.uchicago.edu/gctriemann.ps it is stated that there is an unknown non-standard riemann hypothesis. AFAIK riemann hypothesis in AG was shown using Etale cohomology by Artin, ...
2
votes
1answer
68 views

Classification of Hopf-Galois Extensions as Torsors

Faithfully flat Hopf-Galois extensions of rings: $A\to B$, with $H$ coacting on $B$ such that $B\otimes_AB\simeq B\otimes H$, are often thought of as being accessible substitutes for $G$-torsors in ...
3
votes
0answers
120 views

Have topographs been studied before?

This is my first post on MO so I hope this question is suitable. I have quite a few definitions which I will need to state before my questions at the end of this post. Please let me know if anything ...
-1
votes
0answers
92 views

About “covering” subgroups

Let $H$ be a subgroup of $S_n$ (the symmetric group with n elements). In the paper I read (cf. Thm 3.17 there), the authors define $H$ to be a covering if the following condition holds: for all ...
10
votes
1answer
198 views

What's an example of 2 elliptic curves with the same ground ring s.t. their associated cohomology theories detect different things?

My understanding is that a complex-oriented spectrum is a ring spectrum $E$ with a map $MU \to E$. Analogously, a ring with a formal group law is a ring $R$ with a map $L \to R$ (where $L$ is the ...
-7
votes
0answers
52 views

taylor-series condition [on hold]

I think it is interesting, if we have the formula $\frac{n^m - (n - 1)^ m }{m}$ ~ ${n ^ {m-1}}$ for example $\frac{100^3 - (100-1) ^ 3 }{3} $ = $9900$ ~ ${100 ^ 2}$, if the difference (I'll ...
8
votes
5answers
689 views

Proof that no differentiable space-filling curve exists

Could someone provide a reference or a sketch of a proof that no differentiable space-filling curve exists? Or piecewise differentiable? Must every continuous space-filling curve be nowhere ...
1
vote
0answers
75 views

When does an algebraic space that is a torsor over a scheme have to be a scheme?

In Group actions on stacks and applications (Section 4 of part A), M.Romagny gives a definition of $G$-torsor over a scheme $S$ in which the total space need not be a scheme, just an algebraic space. ...
1
vote
0answers
54 views

Curvature of a principal bundle and the exterior covariant derivative

I am sorry if this is too elementary; I had posted it on math.stack but no one answered. Let $P\to M$ a principal fibre bundle with fibre $G$, and let $A\in \Omega^{1}(P)\otimes\mathfrak{g}$ be a ...
7
votes
1answer
112 views

Tauberian theorem with better error term

This is a fairly vague question. Suppose we have a sequence of positive numbers $(c_n)_n$ and we want to find an asymptotic formula for $S(x) = \sum_{n \leq X} c_n$. In favorable circumstances, ...
0
votes
0answers
27 views

Is the minimal solution of a Pell equation a positive integral power of the fundamental unit? [migrated]

Let $k=\mathbb{Q}(\sqrt{d})$ -- $d$ is a positive square-free integer -- be a real quadratic field, and let $\varepsilon_k$ be its fundamental unit. Let $(x,y)$ be the minimal solution to the Pell ...
6
votes
1answer
125 views

Example of a ring $R$ such that $\dim(R[[X]])<\dim(R[X])$

Dimension refers to the Krull dimension of a commutative ring. In the paper "Prime ideals in power series rings" J. Arnold gives an example of such a ring: Let $k$ be a field and $K=k(t)$ a ...
19
votes
0answers
196 views

Identities for power series like $\sum_n z^{n^3}$

Probably, one of the first power series that every mathematician encounter is the geometric series $$\sum_{n=0}^\infty z^n = \frac1{1-z}, \quad z \in \mathbb{C},\; |z| < 1 .$$ Also, a particular ...
0
votes
0answers
63 views

Are fibers at points of morphism of schemes closed subschemes? [on hold]

Is $X \rightarrow Y$ is a morphism of schemes and $y \in Y$, is the fiber of $y$ a closed subscheme of $X$? Is is true that the fibers of the projection $X \times_S Y \rightarrow Y$ (with $X,Y$ ...
-7
votes
0answers
51 views

Closed configuration of prime numbers and composed numbers [on hold]

Conjecture 1. Being P the product of the multiplication of several different prime numbers, and being Np ˂ P any prime number not being prime factor of P; being NL ˂ │P^(1/2)│ any prime number not ...
2
votes
1answer
64 views

Criteria for Compactness of a Closed in $L^2$ Spaces [on hold]

$(X, \mathcal{B}, \mu)$ is a measure space. Is there any well-known criteria for compactness of a closed set in $L^2(X, \mu)$? If the answer is negative what about $L^2(\mathbb{R}^n,\mu)$(in this ...
4
votes
1answer
137 views

Hausdorff measure of the graph

Is there any example of a real valued function on the real line whose domain has Lebesgue measure zero but the graph (in the plane) has positive one dimensional Hausdorff measure? Of course if such ...
-5
votes
0answers
158 views

Are numbers fundamental mathematical entities? [on hold]

This question came to my mind after seeing Vi Hart's video on YouTube about the "number" Wau and the answer I gave there to the question "what is the number Wau?". As far as I know, numbers have ...
0
votes
0answers
22 views

Is there a term for “ranked distance” matrices?

In a n by n "ranked distance matrix" each element has a rank $r_{ij}$ between 1 and n that indicates it is the $r_{ij}$th smallest element in column $i$ of a corresponding Euclidean distance matrix. ...
5
votes
0answers
113 views

Is there a higher, “orientalish” version of geometric realisation?

Geometric realisation of simplicial sets can be roughly thought of like this: In some category $\mathcal{C}$, we choose an object for every abstract $n$-simplex. In topological spaces, we would ...
4
votes
1answer
147 views

Representability of morphism of stacks

A morphism of Artin stacks $f:X\to Y$ over $\mathbb Q$ is representable by algebraic spaces if and only if its geometric fibres are algebraic spaces. I would like to know if one can use this to prove ...
1
vote
0answers
110 views

Generalization of Little Fermat Theorem for a particular $a$ and perfect shuffles

I'm looking for the smallest $n\in \mathbb{N}$ that solves the following equation: $$2^n=1 \mod m$$ For an odd $m$. I know that Little Fermat Theorem and Euler Totient give me a solution but they ...
0
votes
0answers
111 views

What is the status on questions related to Bhargava's factorial function?

In Manjul Bhargava's The Factorial Function and Generalizations he motivates a new type of factorial $n!_S$ using by generalizing a few theorems like: For $k, l \in \mathbb{Z}$, we have $k! \times ...
0
votes
0answers
30 views

Relation between Chebyshev Interpolation and Expansion

I am seeking connections between pointwise Lagrange interpolation (using Chebyshev-Gauss nodes) and generalized series approximation approach using Chebyshev polynomials. Pointwise Lagrange ...

15 30 50 per page