# All Questions

**2**

votes

**0**answers

51 views

### A specific mollified functions in the Sobolev space H^1(R)

Let $u>0$ be in $H^{1}(\mathbb{R})=W^{1,2}(\mathbb{R})$, we know that the set of $C^{\infty}$ functions with compact support are dense in the Sobolev space $H^{1}(\mathbb{R})$. Hence, we have a ...

**5**

votes

**2**answers

115 views

### Do character tables determine association schemes up to isomorphism?

I am interested in commutative, but not-necessarily-symmetric association schemes. I noticed that the conjugacy class scheme of the dihedral group of order 8 has the same character table as the one ...

**1**

vote

**1**answer

140 views

### Do we know an upper bound for the number of possible real parts of the non trivial zeroes of $\zeta$?

Let $n_{\zeta}$ denote the number of possible real parts for the non trivial zeroes of the Riemann Zeta function. RH is equivalent to $n_{\zeta}=1$, and the symmetry arising from the functional ...

**2**

votes

**1**answer

104 views

### Can you reconstruct a simplicial set from an $\infty$-groupoid?

In some categories of things with interesting structure, said structure can be recovered from the category.
For example, in the category of chain complexes of abelian groups, if you're given a chain ...

**6**

votes

**0**answers

101 views

### Variants of the Angel problem

The original Angel problem, first proposed by Conway, Berlekamp, and Guy has two players: the devil and the angel. The angel is placed at the origin of an infinite $2$-D chessboard. The angel's ...

**2**

votes

**1**answer

80 views

### Can this equality hold for a nonzero $b$?

Please may you kindly assist me on this integration exercise: For real $a, b$ with $a \neq 0$, consider the equality
$$\int_1^\infty f(x)\sin(a\log \sqrt x)x^b \mathrm{d}x = \int_1^\infty f(x)\sin(a\...

**7**

votes

**3**answers

384 views

### Homotopy type of some lattices with top and bottom removed

The only reaction to this question on math.SE was 21 views in 4 days, so I decided to repost it here. I am not changing anything.
There was an interesting question on MO which OP removed by some ...

**2**

votes

**1**answer

115 views

### GCD for two Cullen numbers

The $n$'th Cullen number is $C_n = n\cdot2^n+1$.
If $m$ and $n$ are natural numbers, what can one say about $\gcd(C_n,C_m)$, where $m$ and $n$ are different positive integers?

**3**

votes

**1**answer

45 views

### Cluster algebra structure compatible with Poisson brackets

Let $X$ be a Poisson variety. There is a concept "cluster algebra structure compatible with Poisson structure" introduced in the paper.
Suppose that we construct a maximal independent set of ...

**1**

vote

**0**answers

30 views

### Mersenne number with small Carmichael function

Let $\lambda(\cdot)$ be the Carmichael function. I'm trying to understand the magnitude of the smallest values of $\lambda(2^n - 1)$, when $n$ runs over the positive integers. Precisely my question is:...

**-2**

votes

**0**answers

36 views

### I can't derive the integrating factor of this first order linear Equation [on hold]

I can't derive the integrating factor of this first order linear Equation
(x2 - y2 - y) dx - (x2 - y2 - x) dy = O.
the answer is: integrating factor = 1/(x2 - y2)

**0**

votes

**0**answers

26 views

### Jordan curve in $C^2$ [migrated]

Can we find a Jordan curve $\gamma$ in $\mathbf{C}^2$ of class $C^1$ such that the projection to the first coordinate plane divides the plane into infinite components of connectivity.

**2**

votes

**2**answers

87 views

### Asymptotic Growth of Markov Chain

I asked the following question one week ago at math.stackexchange but didn't receive a response, so I want to give it here another try:
I'm interested in the following problem: We have got a time-...

**3**

votes

**2**answers

63 views

### Is there a full-rank map with connected graph and simply connected image that is not injective?

I want to find a continuously differentiable function $F:X\to Y$, where $X\subseteq\mathbb{R}^n$, $Y\subseteq\mathbb{R}^m$ are open ($n\le m$) with
${\rm rk}\, \frac{\partial F}{\partial x}(x) = ...

**2**

votes

**0**answers

100 views

### The uses of the polar topology in topological vector spaces

The polar topology originates from the $S$-topology and is used in duality pairs. Due to the connection between the original topology and the weak topology, we can rephrase the original topology in ...

**2**

votes

**0**answers

18 views

### Connectedness of the space of symplectic embeddings into a higher dimensional manifold

Suppose $M$ and $N$ are symplectic manifolds, $N$ is compact, $\dim_{\mathbb R}(N) \leq \dim_{\mathbb R}(M) -4$. Suppose there are embeddings $f_i:N \to M$, $i=0,1$ such that $f_i^*\omega_M$ is non-...

**11**

votes

**1**answer

887 views

### What should I cite for the Poincaré conjecture?

I'm writing a paper that, rather unexpectedly, needs the Poincaré conjecture for one of the results. (The paper has almost nothing to do with differential geometry!)
The conjecture was famously ...

**-4**

votes

**0**answers

15 views

### Exam FM Study Material [on hold]

This is a math question from an Exam FM study textbook that I've been looking over that I need an explanation for:
A fund is earning 5% simple interest. Calculate the effective
interest rate in the ...

**5**

votes

**1**answer

95 views

### On certain solutions of a quadratic form equation

This is a continuation of this question: A class of quadratic equations
Let $f(x,y) = ax^2 + bxy + cy^2$ be an irreducible and indefinite binary quadratic form. Consider the equation
$$\displaystyle ...

**0**

votes

**0**answers

22 views

### $H$ self-adjoint with mass gap, $P≥0,Ω∈D(P),H+λP$ self-adjoint $⟹$ for $λ$ small, $H+λP$ has gap?

Suppose $H$ is a self-adjoint operator on a Hilbert space having a simple isolated least eigenvalue $0$ with gap $1$ ( $H\Omega = 0$, $\Vert \Omega\Vert = 1$ ), $P$ is a non-negative symmetric ...

**6**

votes

**0**answers

179 views

### A conjecture generalization of Karamata inequality

Fist I observe function $f(x)=x^2$ in the figure as following
I found that when $x_1 \ge y_1$ and $x_2 \le y_2$ $\Rightarrow$ $AB \ge CD$
$\Rightarrow$ $$\frac{f(x_1)+f(x_2)}{2}-f(\frac{x_1+...

**1**

vote

**0**answers

39 views

### What are the rank 3 boolean intervals [H,G], with G simple group?

The rank $n$ boolean lattice $B_{n}$ is the subset lattice of $\{1,2, \dots , n\}$.
The lattice $B_{3}$ is the following:
Question: What are the rank $3$ boolean intervals of the form $[H,G]$, ...

**3**

votes

**0**answers

87 views

### Generalization of de Rham cohomology, or cohomology for non-smooth case

Let $\Omega\subseteq \mathbb{R}^{3}$ be a contractible region and $f:\Omega\to \mathbb{R}^{3}$ be a vector field on $f$. If $f$ is smooth vector field and $\nabla\cdot f=0$, then $f=\nabla\times g$ ...

**1**

vote

**1**answer

169 views

### What is a universal tree?

I came across some slides talking about the Hrushovski construction. One of the examples was the construction of a "universal tree".
I was curious because the collection of finite trees does not ...

**5**

votes

**0**answers

66 views

### Integral basis of an extension of complete fields

Let $\mathcal{O}_K$ be a complete discrete valuation ring with quotient field $K = \text{Quot}(A)$.
Let $L | K$ be an arbitrary finite field extension. Because $K$ is henselian, the integral closure $\...

**5**

votes

**0**answers

110 views

### When is a given polynomial a square of another polynomial?

I meet a problem in which I hope to show a special polynomial is not a square of another polynomial. More precisely, let's consider the polynomial
$f(x):= 1-x+2bx^n-2bx^{n+1}-b^2x^{2n-1}+2b^2x^{2n}-b^...

**4**

votes

**0**answers

59 views

### Coming up with a represenation for sum of functions in the Fourier algebra

This is my first overflow question, so let me apologize in advance if this belongs on http://math.stackexchange.com.
Let $G$ be a discrete group.
Let $\lambda:G\to B(\ell^{2}(G))$ be the left ...

**1**

vote

**0**answers

52 views

### Non-negative Polynomials from Polynomial Ideal?

Related to the thread Nonnegativity conditions for a polynomial in two variables? but on more than two variables. Suppose a probability vector $p$ belongs to a compact polytope where for each entry $...

**4**

votes

**0**answers

77 views

### Automorphisms of unipotent groups

I start with a hopelessly broad question: what is known about the structure of the automorphism group of a (smooth, connected) unipotent group (over a field), and particularly about the structure of ...

**-1**

votes

**0**answers

31 views

### Probability - transformation [on hold]

I've just come across this derivation (it's only a fragment I'm interested in):
$$
\int p(x | \theta) \frac{\nabla_\theta p(x | \theta)}{p(x | \theta)} f(x) dx = \int p(x | \theta) \nabla_\theta \log ...

**8**

votes

**2**answers

165 views

### An identity related to partitions into $n$ parts and Schur polynomials

While working with Schur polynomials I found what seems like a nice identity, and I wonder if it has a simple proof.
Notation: Suppose $d,n\in\mathbb{N}$, and $\lambda =(\lambda_1,\dots,\lambda_n)$ ...

**-2**

votes

**0**answers

76 views

### Where to publish paper in mathematical physiology? [on hold]

Recently I discovered one applied area of Mathematics, and that is Mathematical Physiology. I would like to know mathematical journal where it can be publish something from that area of research. This ...

**2**

votes

**0**answers

119 views

### Another quesion about J.H. Conway's Surreal Numbers

Let CF be Conway's real closed field of Surreal Numbers and let ACF be the algebraic closure of CF. Is there an Extension E of ZFC that provides for the existence of "proper classes", in which ACF can ...

**3**

votes

**1**answer

139 views

### Euler characteristic of a surface in $\mathbb{R}^3.$

Suppose I have a (smooth) surface in $\mathbb{R}^3,$ given as (a component of) a real algebraic hypersurface. Is there a good algorithm (assuming, for example, we can compute intersections with lines ...

**2**

votes

**0**answers

32 views

### A List-Like Frobenius Monad

Has anyone ever seen a Monad that is very much like the List Monad but is also a co-monad, and hence a Frobenius monad. I was reading a paper that, I think, suggested zipper as an example. I think ...

**-1**

votes

**0**answers

45 views

### Closure property of completely monotone functions [on hold]

A $C^{\infty}$ function $f(x_1, \dots, x_n)$ defined on $(0,\infty)^n$ is said to be completely monotone if
$$
(-1)^{k}\frac{\partial^k f}{\partial x_{i_1} \cdots \partial x_{i_k}} \geq 0
$$
...

**1**

vote

**0**answers

105 views

### The Lie algebra of Harmonic functions

Is there a Riemannian metric $g$ on $\mathbb{R}^{2}$ with corresponding volume form $\omega= \sqrt{det(g_{ij})} dx \wedge dy$ and the corresponding Laplace operator $\Delta$ such that the space ...

**-1**

votes

**0**answers

28 views

### Relation between Independent variables in an Equation [on hold]

Description: We define index as an indicator, sign, or measure of something.
Let, $A_{i}$ is an index, that measures the benefits of choosing a network station $i$ among other existing network ...

**3**

votes

**1**answer

61 views

### Restricted Lie algebras with a $p$-nilpotent basis

Let $L$ be a finite-dimensional restricted Lie algebra over a field of characteristic $p>0$. An element $x$ of $L$ is called $p$-nilpotent if $x^{[p]^k}=0$ for some positive integer $k$. If $L$ is ...

**2**

votes

**0**answers

25 views

### continuous injective extension of a map defined on a hemisphere

Let $S^2 = \{x\in \mathbf R^3\colon |x|=1\}$ be the unit sphere, $S^2_+ = S^2 \cap \{x_3 \ge 0\}$ be the upper hemisphere and $S^1 = S^2 \cap \{x_3 = 0\}$ be the unit circle. Let $u\colon S^2_+\to \...

**3**

votes

**0**answers

79 views

### How can I describe explicitely a nonsingular model of the elliptic surface?

Consider the surface $\mathcal{E} = Q_1 \cap Q_2 \subset \mathbb{P}_k^3\times \mathbb{P}_k^1$ with homogenous coordinates $x$, $x^\prime$, $y$, $z$ and $t$, $s$ respectively and a field $k$ of even ...

**8**

votes

**0**answers

92 views

### Trouble with Stable Equivariant Profinite Homotopy Theory

I've heard that there are some problems in developing a good formalism for stable equivariant homotopy theory (either from the spectral mackey functors perspective or from the orthogonal spectra ...

**-1**

votes

**0**answers

12 views

### Rigorious formulation of approximation of integral as area of a square and its radius of convergence [migrated]

We know that the taylor expansion of
$$\left(\int_{t}^{t+\Delta t}a(t')dt'\right) = a(t)\Delta t + \frac{1}{2}\frac{da}{dt}(t) \Delta t^2 + \frac{1}{3!}\frac{d^2a}{dt^2}(t) \Delta t^3 + \frac{1}{4!}\...

**0**

votes

**0**answers

86 views

### Join of $G$-CW-Complexes

I want to understand the CW-structure on the join of $G$- CW complexes for my master's thesis.
Let $G$ be a discrete group and $X$ and $Y$ $G$-CW-complexes. Furtheremore, let $X*Y$ denote the join
$$[...

**1**

vote

**1**answer

118 views

### Lift Lie group action on a small neighborhood

Suppose a manifold $M$ admits a smooth Lie Group action $G$, and $N$ is a closed sub-manifold of $M$ such that $G$ action freely on $N$.
Q: Why in a small neighborhood of $N$, $G$ also action ...

**4**

votes

**1**answer

83 views

### Is there a known criterion for a compact complex analytic space to be projective?

It is known when a compact complex analytic space $X$ is the analytification of a complex projective variety? If $X$ is a manifold, then Kodaira's embedding theorem and Chow's theorem says that $X$ is ...

**5**

votes

**1**answer

153 views

### A two-point inequality

Let $M(p,q) = (2p-\sqrt{p^{2}+q^{2}})\sqrt{p+\sqrt{p^{2}+q^{2}}}$ and set $B(t) = M(x+t, \sqrt{t^{2}+(y+bt)^{2}})$. Given any real $x,y,b$ is it true that $\varphi(t) = B(t)+B(-t)$ is decreasing in $...

**0**

votes

**0**answers

46 views

### interpolation inequalities and embeddings

When $Z$ is an interpolation space between two Banach spaces $X$ and $Y$ (say real / complex method), we have a norm inequality
$$
\| x \|_Z \le C \| x \|_X^\theta \| x \|_Y^{1-\theta}
$$
My question ...

**4**

votes

**0**answers

59 views

### Is this map representable? what is the fiber?

Consider the following map of stacks:
Let $S$ be the stack whose $A$ points are diagrams of the form
\begin{array}{ccccc}
{} & {} & U & {} \\
{} & {} & \downarrow & \searrow \\...

**-1**

votes

**0**answers

57 views

### Applications of computing the averages of arithmetical functions

I often read many papers in which the authors compute the average of certain arithmetical functions like 'On the distribution of the Euler function of shifted smooth numbers' of Shparlinski and al. ...