0
votes
0answers
12 views

Are fibers at points of morphism of schemes closed subschemes?

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 $X,Y$ ...
-5
votes
0answers
25 views

Are these conjectures true? how important they are? [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 ...
0
votes
1answer
19 views

Criteria for Compactness of a Closed in $L^2$ Spaces

$(X, \mathcal{B}, \mu)$ 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 ...
0
votes
1answer
15 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 ...
-4
votes
0answers
83 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
13 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. ...
4
votes
0answers
77 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 ...
3
votes
1answer
95 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
79 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
19 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 ...
1
vote
0answers
30 views

The automorphism groups of smallest grammars of a language string are isomorphic

Let $s \in \Sigma^*$ be a formal language string. Consider the automorphism group of $s$, defined to be the set of all permutations of positions of $s$ that leave $s$ fixed. For instance $G(abab) = ...
0
votes
0answers
48 views

Can anyone comment on uniformizing parameters and uniformizing coordinates?

Let $V$ be an algebraic variety ($\dim V = r$) over an algebraically closed field $k$, $U \subseteq V$ an open subset (in Zariski topology), and W a prime divisor of V, that is, the closed subvariety ...
0
votes
0answers
25 views

How local is the exponent in the definition of a function with analytic/algebraic singularities?

In Demailly's Analytic Methods in Algebraic Geometry (available on his web page), the definition of a (plurisubharmonic) "function with analytic singularities" is a (plurisubharmonic) function $ u: ...
0
votes
1answer
59 views

A $C^{*}$ algebra associated to a group

Let $G$ be a compact group which act on a Hilbert space $H$. We define a linear map $T$ on the dual space $H^{*}$ with $$T(\phi)(x)=\int_{G} \phi(g.x)$$ The integration is based on the Haar ...
0
votes
0answers
58 views

Average probability that a random cosine polynomial with bernoulli coefficients is small

Let $P_{n}(t)=\sum_{k=0}^{n}\varepsilon_{k}\cos(kt)$ where $\varepsilon_{i}$ are independent random variables taking values in $\left\{-1,1\right\}$ with equal probability. Is is true that for any ...
3
votes
4answers
336 views

number theory which is close to analysis

I have basic training in Fourier and Harmonic analysis. And wanting to enter and work in area of number theory(and which is of some interest for current researcher) which is close to analysis. ...
1
vote
0answers
74 views

Functor of points of a tensor triangulated category

Is there is a functor of points approach to tensor triangulated categories parallel to Balmer's theory of prime ideal spectra? Given a tensor triangulated category $\mathcal{T}$ an $R$-point can be ...
0
votes
0answers
7 views

dual basis of cohomology algebra [migrated]

Let $H^*(M)$ be the cohomology algebra of oriented manifold $M$ with rational coefficients. Let $\{b_i\}$ be a basis of $H^*(M)$ as a vector space over $\mathbb{Q}$. Let the dual basis be ...
-3
votes
0answers
34 views

shortest line segment that equally divide a triangle? [on hold]

Given the coordinates of all three vertexes of a triangle, what's the length of the shortest line segment that divide a triangle into two equal-area halves? This is a problem that a friend gave to ...
17
votes
1answer
273 views

Interplay between Loop Quantum Gravity and Mathematics

It is known that there are many interesting connections between String Theory and modern Mathematics, with a rich feedback going on in both directions: there have been advances in mathematics thanks ...
4
votes
0answers
40 views

Thales Style Level Sets

Encouraged by Joseph O'Rourke ( and inspired by the discussion at Thales' semicircle theorem in higher dimensions ), I ask about level sets in three dimensional space occuring from considering ...
1
vote
1answer
32 views

Probable direction of deviations from the expected value in binomial and hypergeometric cases

Suppose I have an urn with N marbles, with frequencies p and q for red and black marbles, and with p > 0,5. I take a sample of r marbles. It sounds intuitive to say that deviations from the mean ...
3
votes
0answers
54 views

Is there any counterpart to Thales' semicircle theorem in higher dimensions?

It was established by TMA, @WillSawin, and @DouglasZare, in their responses to the MO question, "Thales' semicircle theorem in higher dimensions," that the natural generalization of Thales' semicircle ...
2
votes
0answers
90 views

Classifying spaces of topological groups whose underlying spaces are homotopy equivalent

Let $G$, $H$ be topological groups and $f:G\rightarrow H$ a continuous group homomorphism which happens to be a homotopy equivalence of the underlying topological spaces. Let us assume that $G$, $H$ ...
4
votes
1answer
52 views

A decision problem for clones

E. Post proved that there are only countably many clones on a two-element set (classes of operations closed under superposition and containing all projections). All these clones are finitely ...
0
votes
0answers
24 views

Relation eccentricity/diameter in undirected tree [on hold]

I know in my mind that it's very obvious, but I just can't seem to prove the following statement: Let $G$ be an undirected non-trivial tree with at least $3$ vertices. Let $u$ be an arbitrary vertex ...
0
votes
0answers
52 views

Why $C^0$ - Convergence gives Gromov-Hausdorff convergence?

Let $(M,\omega (t)) $ be a family of kahler forms , why $C^0$ - Convergence gives Gromov-Hausdorff convergence?
2
votes
0answers
40 views

Intersecting balls with convex regions and a bisector thereof

This question is related to my previous posting Angle subtended by the shortest segment that bisects the area of a convex polygon Let $C$ be a convex region in the plane and let $s$ be the shortest ...
1
vote
0answers
49 views

freedom in choosing a smooth function of compact support [migrated]

Suppose $\Omega$ represents a bounded domain in $\mathbb{R}^n$. For ease, let $\Omega$ be a ball around the origin. Let $\varphi$ be a smooth radial function defined on $\Omega$. I am trying to ...
1
vote
0answers
48 views

Exterior product

I have asked this question in the Mathematics forum but I received no answer. Let $E$ be an algebraic vector bundle of rank $r$ and degree $d$, Then $\Lambda^2 E$ is of rank $r'=r(r-1)/2$, but is of ...
0
votes
1answer
101 views

homological invariant of the “universal elliptic curve” over the punctured $j$-line

My question considers the curve $E$ over the affine $j$-line $S$ given by $$Y^2 - (j-1728)XY = X^3 - 36(j-1728)^3X - (j-1728)^5$$ This curve has the property that it's $j$-invariant is $j$ (see ...
-4
votes
0answers
100 views

How does a mathematician sees the numbers? [on hold]

When I look at a tree - I see the tree. I feel the tree in my head, it's shape, it's presence - everything about it. When I look at a number or a math expression I see only the expression and the ink ...
1
vote
0answers
44 views

Obtaining graphics of functions in non-standard analysis

In the context of $R(\varepsilon)$ or more broad fields, Levi-Civita field or $No(\omega_1)$, how can we obtain the graphics of functions on the infinitesimal range? For instance, it is alleged that ...
2
votes
1answer
132 views

Glueing a property via homotopy colimits

I have a problem concerning a fact which is stated without proof in this Rezk's draft: http://www.math.uiuc.edu/~rezk/i-hate-the-pi-star-kan-condition.pdf . In the proof of Lemma 2.11, we are given a ...
-4
votes
0answers
54 views

Math mobile Apps [on hold]

Are there any interactive apps, which you can use your phone camera and point at things in your environment and the app regognizes the shapes of objects etc?
9
votes
1answer
132 views

Relative Picard functor for the Zariski topology

I'm trying to understand better the relative Picard functor, as defined, for example, in Kleiman's article. Let $X \to S$ be a smooth projective morphism of schemes whose geometric fibres are ...
0
votes
1answer
131 views

When is finding an explicit inverse of an isomorphism not possible

My question is about Shapiro's lemma. Consider the isomorphism $\phi: H^n(G, Hom_{ZH}(ZG, A))\cong H^n(H,A)$ of shapiro's lemma. I would like to describe this via cochains. So the obvious map is ...
-2
votes
0answers
49 views

the special value in a L-funtion [on hold]

how to calculate the value of series The Gamma function satisfying $\Gamma(n) = (n-1)!\quad\forall n\in\mathbb N$ is via through the Euler integral $$ \Gamma(z) = \int_0^\infty t^{z-1}e^{-t}dt\,. $$ ...
1
vote
0answers
31 views

About the space of function used in the harmonic extensions for elliptic problems involving the fractional laplacian

recently i am studying the following paper: A concave–convex elliptic problem involving the fractional Laplacian - C. Brandle, E. Colorado, A. de Pablo and U. Sánchez. At the Pgs 41, 42, the ...
0
votes
0answers
17 views

How to character the norm of elemental units in a quadratic number field [on hold]

if a prime number P≡1 mod 4,why the equation x^2-py^2=-4 has solutions in integer
4
votes
1answer
128 views

Coherent sheaves on $\mathbb C^2$ and commuting matrices

Let $V$ be an $n$-dimensional complex vector space. The stack $Coh^n(\mathbb C^2)$ of coherent sheaves on $\mathbb C^2$ supported on $n$ points (not necessarily distinct) is equivalent to the stack ...
0
votes
0answers
28 views

How to use persistence of regularity to obtain global well posedness result in $H^{s}(\mathbb R), (0<s<1)$?

[This question occurs to by the answer given by W. W ;and may be trivial for MO; But I am keen to understand the process:"local existence and persistence of regularity implies global well posedness" ] ...
3
votes
2answers
134 views

How can dimension depend on the point?

Let $M$ be a metric space. For any subset $A\subset M$ let $\dim(A)$ denote its Hausdorff dimension. For $x\in M$, define the dimension of $M$ at $x$ by $\dim(x)=\lim_{r\to0}\dim(B(x,r))$; this limit ...
2
votes
2answers
66 views

Polynomial invariants for unoriented links

I have seen that usually one finds polynomial invariants for oriented links (for example the Jones polynomial, the Hompfly polynomial). Does anyone know what polynomial invariants exist for ...
0
votes
0answers
20 views

SVD of sum of a symmetric matrix and a banded matrix [on hold]

The SVD of the sum of a symmetric square matrix and an appropriately sized identity matrix can be written as following: $A^TA + \lambda I = V(\Sigma + \lambda I)V^T$ where $\Sigma$ contains the ...
0
votes
0answers
34 views

How to prove that the set of maximal elements of a set of prime ideals is finite

Let $A$ be a subset of ${\rm Spec}(R)$ with $R$ noetherian Are there any techniques to prove that ${\rm max}(A)$ (ie the set of maximal elements of $A$) is finite? I'm looking for equivalent ...
-1
votes
0answers
11 views

What is the most efficient algorithmic implementation of maximum overlap discrete wavelet transform?

What is the most efficient algorithmic implementation of maximum overlap discrete wavelet transform (MODWT)?
5
votes
0answers
86 views

A generalization of SOCA

Roughly speaking, SOCA (Semi Open Coloring Axiom) says that for an open coloring of the unordered pairs over an uncountable separable metric space you can always find an uncountable homogeneous subset ...
2
votes
1answer
69 views

Weak convergence in $W^{1,p}_0$

Note from the answerer : this question stems from this article. I ask this question in http://math.stackexchange.com/questions/1206617 I have a bounded sequence $(u_n)$ from $W^{1,p}_0(\Omega)$ so ...
-1
votes
0answers
55 views

Is a perfectoid algebra over a perfectoid ring flat?

Let $S/R$ be a perfectoid rings, in what conditions $S^\circ/R^\circ$ must be flat? Like $R^\circ$ a valuation ring.

15 30 50 per page