0
votes
0answers
13 views

Balancing real numbers in one dimension

Given numbers $d_i \leq 1$ for $i=1,\ldots,m$, it is easy to see that you can always find signs $\varepsilon_i \in \{-1,1\}$ such that the partial sums $\sum_{i=1}^k \varepsilon_i d_i/2$, for ...
1
vote
0answers
18 views

If $E(K)=E(L)$ for an elliptic curve $E$ and an algebraic extension $L/K$, what can we say about $Sel(E/K), Sel(E/L), L/K$?

More generally, when $E(K_m)$ is stable as $m$ increases for an extension equence $K_0<K_1<K_2<\cdots<K_m<\cdots$ ? In the case, is $\mathrm{Sel}(E/K_m)$ stable as $m\rightarrow ...
-1
votes
0answers
36 views

Prove $\exists x,y \in A$ st $\mu(A \cap (x,y))>c(x-y)$ [on hold]

Let $\mu$ be the Lebesgue measure on $\Bbb{R}$ and $A$ be a measurable subset of $\Bbb{R}$ with positive measure. Prove for any $c\in (0,1),$ $\exists x,y \in A$ st $\mu(A \cap (x,y))>c(x-y)$. ...
-2
votes
2answers
93 views

Serre's Theorem for Coherent Sheaves

I recently heard a discussion about a certain of Serre which reconstructs the category of coherent sheaves of a variety $V$ as the category of modules over the homogeneous space of $V$ modulo modules ...
1
vote
0answers
17 views

Applications of finite presentation of lie algebra

If you know a finite presentation of say a certain Poisson algebra (finite presentation as a Lie algebra), in what ways might this be useful? Does this allow you to extract information that would ...
0
votes
0answers
12 views

Invariant subalgebra and dual torus for symmetric permutation module

Given permutation module with three generators and corresponding Galois action of symmetric group $\mathfrak S_3$ I am interested in computing corresponding dual torus $T$ (which should be of ...
2
votes
0answers
31 views

Are isometric homorphisms of C* algebras *-homorphisms

Here is my precise question: Let $A$ and $B$ be two $C^*$ algebras. Let $f: A \rightarrow B$ a morphism of algebras which is isometric (on its image). Is $f$ necessary a $*$-homomorphism ? It sounds ...
0
votes
1answer
56 views

Global section of very ample line bundles and its value on stalks

Let $X$ be a projective scheme and $\mathcal{L}$ be a very ample line bundle on $X$ with respect to some projective embedding $X \hookrightarrow \mathbb{P}^n_{\mathbb{C}}$ (for some $n$). Given any ...
10
votes
1answer
76 views

Completed and uncompleted operations for Morava $E$-theory

Let $E = E_n$ be the $n$-th Morava $E$-theory with coefficient ring $$ E_* = \mathbb{W}(\mathbb{F}_{p^n})[\![u_1,\ldots,u_{n-1}]\!][u^{\pm 1}]. $$ It is usual to consider the completed co-operations ...
2
votes
0answers
28 views

Staircase Schur functions squared

Let $\Delta_n$ be the staircase-shaped partition $(n-1,n-2,\dots,1)$. Are there any non-obvious combinatorial objects that index $s_{\Delta_n}^2$? Here, $s_\lambda$ is the Schur function indexed by ...
3
votes
0answers
104 views

Flat Connections on Ring Spectra

So first I'll try to give a really quick reminder of the classical description of these things when one is doing non-commutative descent theory. In the setting of discrete algebra, if we have a ...
0
votes
0answers
22 views

How to put together a set of modified conditional distributions to a joint distribution? [on hold]

I am abstracting my original problem to a simple scenario.Consider a bi-variate multi-modal mixture of gaussian distribution, P(x,y). When we slice through x or y we get a univariate multi-modal ...
0
votes
0answers
12 views

a special case of the Borodin-Kostochka conjecture for $\Delta (G)=4$

The Borodin-Kostochka Conjecture states that if a graph $G$ satisfies $\Delta (G)\geq 9$ and $\omega (G)\leq \Delta (G)-1$, then $\chi (G)\leq \Delta (G)-1$. It is easy to find a counterexamples to ...
2
votes
0answers
69 views

Quasi-disjoint subsets of an infinite cardinal and $\neg \mathsf{AC}$

Is it consistent with $\mathsf{ZF}$ (without $\mathsf{AC}$) that there is an infinite set $X$ and a subset $S\subseteq\mathcal P(X)$ of the same cardinality as $\mathcal P(X)$ with the property that ...
0
votes
0answers
31 views

A Problem on Fixed Point Theory [on hold]

Let $T:\mathbb{R}\rightarrow\mathbb{R}$ be a function satisfying the following conditions: (a) $T$ is continuous, (b) $T(n)=2015n+1$, $\forall{n}\in\mathbb{Z}$, and (c) $|T(x)-T(y)|\geq 2015|x-y|, ...
3
votes
0answers
43 views

When does the canonical model structure on $\mathcal V$-$\mathbf{Cat}$ give a structure of monoidal model category?

Let $\mathcal V$ be a closed symmetric monoidal model category. It is well known that the category $\mathcal V$-$\mathbf{Cat}$ of $\mathcal V$-enriched categories is itself a closed symmetric monoidal ...
1
vote
0answers
113 views

Primes in integral domains

Let $\mathcal O_{\mathbb K}$ be the ring of integers in a number field $\mathbb K$. It is easy to prove that the number of (non-associated) primes in $\mathcal O_{\mathbb K}$ is infinite. On the other ...
1
vote
1answer
41 views

how to find coordinate of unknown point given the distance against N known points

I am meeting with a problem, say I have already know the coordinates of N points (a1,a2,a3....) in 3D space. And I have a new point, say x. I only know the distances from x to the known N points. Is ...
5
votes
2answers
337 views

Publication in proceedings

Why and how publishing a paper in proceedings? What are the difference with a "classical" journal? What's the list of the main proceedings in which one can publish? Do proceedings papers (never, ...
1
vote
0answers
106 views

How rigid can a rigid object be in GR?

Consider a cubic lattice of space probes, with rocket motors and lasers to measure distance, and a clock to measure time. As they more from free space to the vicinity of some black hole, they try to ...
4
votes
0answers
63 views

Infinite simple p-groups with only trivial irreps in characteristic p

Is there a prime $p$ and an infinite simple $p$-group $G$ such that for any field $K$ of characteristic $p$ the only irreducible $KG$-module, whether finite or infinite dimensional, is trivial (that ...
1
vote
0answers
77 views

Characterization of the Riemann curvature tensor

Let $(M^n,g)$ be a Riemannian manifold, $a\in M$ be a fixed point. It it well known that there exists a coordinate system near $a$ (e.g. the normal one) such that $$g_{ij}(x)=\delta_{ij}+O(|x|^2).$$ ...
0
votes
1answer
50 views

Relationship of clique, independence, and chromatic numbers

For any graph $G=(V,E)$ let $\bar{G}$ be the complement graph. Is $$\text{inf}\big\{\frac{\omega(G)+\omega(\bar{G})}{\chi(G)} : G \text{ is a finite graph}\big\}$$ known? If not, what lower bounds are ...
0
votes
0answers
14 views

Probe permutationally matrix extreme properties-II

Call $S_{r}$, collection of $0/1$ matrices of rank atmost $r$ that increase rank if any $1$ is changed to $0$. Given $M\in\{0,1\}^{n\times n}$ of rank $r$, what is probability that $M$ could be ...
1
vote
0answers
50 views

Strichartz estimates for the wave equation

Strichartz estimates for the wave equation $\Box u=F $ with $u(0)=g_0$ and $\partial_t g(0)=g_1$ can be stated as $$\Vert u\Vert_{L^q_tL^r_x}+\Vert u\Vert_{C^0_t\dot{H}_x^s}+\Vert\partial_t ...
1
vote
1answer
106 views

Zeta functions versus Cramer's conjecture

A mathematics professor today asked me if Cramer's conjecture on prime gaps has anything to do with Riemann Zeta function. I did not know but my guess was somehow Cramer's conjecture captures local ...
5
votes
2answers
115 views

Definition of internal field objects

Let $\mathcal{C}$ be a category with finite limits and a strictly initial object $\mathbf{0}$. The final object is denoted by $\mathbf{1}$. I propose the following definition of a field object ...
2
votes
1answer
101 views

For a cross section $\sigma\colon G/N\to G$, how is $\sigma(y)^{-1}\sigma(x)^{-1}\sigma(xy)$ called?

Let $G$ be a locally compact group, let $N$ be a closed normal subgroup of $G$, and let $\sigma\colon G/N\to G$ be a cross section. Let us define $\alpha\colon G/N\times G/N \to N$ by the formula $$ ...
1
vote
1answer
32 views

regular polyhedra (and polytopes) in hyperbolic geometry, and generalisations

While there exist regular tesselations of the hyperbolic plane with arbitrary regular polygons, there are no new regular polyhedra in hyperbolic (3D) space. This being quite trivial, it is probably ...
1
vote
0answers
26 views

Polynomial functions of degree 3

Can a homeomorphic harmonic mapping $f=(u,v,w):\Omega\to \Omega'$ have isolated singular points. Here $\Delta f =0$, and singular point is a point with zero Jacobian.
2
votes
0answers
81 views

A lower-dimensional algebraic topology problem between homology group and fundamental group

Let \begin{equation} A\stackrel{\alpha}{\longrightarrow}B\stackrel{\beta}{\longrightarrow}C\quad\quad (1) \end{equation} be a short sequence of abelian groups and homomorphisms. We say that the ...
10
votes
2answers
1k views

Do the real numbers “know” that they are countable in a larger model?

(This was first posted to math.stackexchange but had no answers there after several days): Let ${\mathbb R}$ be the set of real numbers in whatever is your favorite model of $ZFC$. Then (by Levy ...
0
votes
0answers
13 views

Whats the difference between math.SE and mathoverflow? [migrated]

i wanted to know that : Whats the difference between math.SE and mathoverflow ? Are they of SE community or different ?
-3
votes
0answers
36 views

How to solve this using trig idenities [on hold]

(sin(x) + sin(-x))(cos(x) + cos(-x)) I am confused how you get 0 for the answer, can someone explain how my book go to that answer. Like the steps you did. Thanks :)
-1
votes
0answers
40 views

Zeros of a Real Analytic Function [on hold]

Let $f:[0,1] \rightarrow \mathbb{R}$ be a non-zero real analytic function. Consider $Z(f) \subseteq [0,1]$ as the set where $f$ vanishes. What can we say about $Z(f)$? This is (i) finite, (ii) ...
0
votes
0answers
27 views

Journals on stochastic approximation/control theory [on hold]

What are some good journals on stochastic approximation/control theory? Thanks
1
vote
0answers
29 views

Uniqueness of solution of elliptic equation with exponential nonlinearity

Consider the following equation $$\Delta v + p(r)e^v = 0$$ on $\mathbb{R}^n$ where $p(r)$ is a polynomial in $r = |(x_1,..., x_n)|$. I want to understand when equations like these have unique ...
1
vote
0answers
76 views

Does the ring of invariants inherit normality?

Let $A$ be a normal ring (in the sense that its localizations at prime ideals are normal domains), and suppose that a finite group $G$ acts on $A$ by ring automorphisms. Form the subring $A^G \subset ...
3
votes
2answers
207 views

Etale local fibrations in the Grothendieck ring of varieties

Let $k$ be a field and $K_0(Var_k)$ the Grothendieck ring of varieties over $k$. This is the ring generated by isomorphism classes of varieties over $k$ with multiplication given by $$ [X \times_k Y] ...
1
vote
0answers
14 views

Finding the bound of a mixture model percentile [on hold]

I could do with some help on the following issue. I'm trying to obtain $\alpha$ from: $\beta = \int_{\alpha}^{\infty} \sum_{i=1}^{n} p_i f_i(x) dx$ I have that: $0 \leq p_i \leq 1$, $\sum_{i=1}^{n} ...
2
votes
0answers
55 views

degenerate points in the moduli space of flat principal $G$-bundle with respect to a linear representation on a complex

Let $(A^\bullet,\partial)$ be a complexe of $\mathbb{C}$-vector spaces. We suppose that this complex is of finite length, and all $A^\bullet$ are finite dimensional. Let $H^\bullet$ be the cohomology ...
1
vote
0answers
26 views

Select n vectors from k vectors (in 3D) such that each component of the resultant vector >= each component of a given vector M

this was left unanswered for 1 week on MStackExchange, so I thought MOverflow would be more appropriate. Thanks :) Let $R = (R_x, R_y, R_z)$ be the resultant vector of the n vectors and $M = (M_x, ...
0
votes
1answer
76 views

generalization of highest weight theorem for semisimple lie algebras

Let $\mathfrak g$ be a real semisimple Lie algebra (without compact factors) with Iwasawa decomposition $\mathfrak g=\mathfrak k\oplus \mathfrak a\oplus \mathfrak u$. Let $\mathfrak p$ be a ...
6
votes
0answers
50 views

Vanishing of Dolbeault cohomologies and Steinness

That Stein manifolds have all $(p,q), p \geq 0, q \geq 1$ vanishing Dolbeault cohomology groups is more or less standard. I am a little bit confused about the reverse implication: whether the ...
1
vote
2answers
66 views

Ascending chain condition on radical ideals

There is a basic theorem in the geometry of schemes saying that the Spec of a Noetherian ring is a Noetherian topological space. It can be formulated as the ACC condition implies the ACCR condition ...
4
votes
0answers
140 views

Is there a citeable reference for star-shaped open subsets of R^n being diffeomorphic to R^n?

A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n. Is there a citeable reference for this result? For the sake of being definite, let's say that “citeable” means ...
1
vote
1answer
40 views

Division methods for divergent continued fractions

I hadn't even noticed before entering the subject above the parellel with the title of an earlier question posted here titled Summation methods for divergent series. And it's just mutatis mutandis as ...
3
votes
0answers
96 views

Frequency of a representation of SO(3)

When generalizing the basic tenets of Fourier Theory to the symmetric group $S_n$, we can define a notion of the frequency of a basis function (i.e. an irreducible representation of $S_n$). In ...
4
votes
2answers
151 views

A balls and urns model for a hashing problem

Fix $N \in \mathbb{N}$. Suppose we throw $N$ numbered balls into $N$ numbered urns, so that for each $b \in \{1,\ldots,N\}$, ball $b$ lands in urn $j$ with equal probability $1/N$. Choose a number $c ...
4
votes
0answers
61 views

Approximation of convex body by polytopes

In a recent survey paper, Approximation of convex sets by polytopes, Bronstein claims that under Hausdorff distance $\rho_H$, for every convex body $U$, $$\rho_H(U,\mathcal{P}_n)\leq c(U) ...

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