# All Questions

**0**

votes

**0**answers

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**

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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**

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**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**1**answer

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

**2**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

27 views

### Journals on stochastic approximation/control theory [on hold]

What are some good journals on stochastic approximation/control theory?
Thanks

**1**

vote

**0**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**2**answers

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

**0**answers

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

**1**answer

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

**0**answers

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

**2**answers

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

**0**answers

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) ...