# All Questions

**-5**

votes

**0**answers

112 views

**8**

votes

**1**answer

179 views

### How do I check that this is a Frobenius algebra?

Let $f_1,f_2,\ldots,f_n\in \mathbb C[z_1,\ldots, z_n]$ be such that the quotient ring
$$A:=\mathbb C[z_1,\ldots, z_n]/(f_1,f_2,\ldots,f_n)$$
is finite dimensional (in other words, it's a ...

**1**

vote

**1**answer

51 views

### Special retraction from a metric space onto an arc

Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ ...

**0**

votes

**0**answers

47 views

### Sequence from count [on hold]

I need to generate a formula for a programming project. The formula will assist in the positioning of elements on screen.
I would like a formula that produces the following sequence indefinitely:
1, ...

**0**

votes

**1**answer

72 views

### Braids, pure braids and Dehn twists

Consider the braid group with $n$ strands $B_n$. Each braid can be drawn (say) from bottom to top as $n$-intertwining strictly monotonic strands. Moreover, the group $B_n$ is generated by $n-1$ ...

**10**

votes

**1**answer

177 views

### Diffeomorphisms and homotopy equivalences sliced over BO(n)

There are some classical results stating sufficient conditions on a manifold $\Sigma$ such that every homotopy equivalence $\Pi(\Sigma) \stackrel{\simeq}{\longrightarrow} \Pi(\Sigma)$ is homotopic to ...

**-2**

votes

**0**answers

78 views

### Prove irrationality for the supplied exercise [on hold]

How can I prove that the product of cube root of 2 and the cube root of 4 is irrational ?
3 sqrt(2) * 3 sqrt(4) = irrational.
Thanks!

**3**

votes

**0**answers

63 views

### Annihillator of the highest weight vector in a finite-dimensional representation

Let $\mathfrak g$ be a simple complex Lie algebra and let $V(\lambda)$ be a finite-dimensional representation with highest weight $\lambda$. Let $v$ be the highest weight vector. Then the action of ...

**1**

vote

**2**answers

122 views

### Question on Posets and open sets

i'm sorry if my question is really trivial but this one is really bugging me out..
So let's have a partially ordered set $I$ with the topology in which the open sets are the increasing ones: $i\in U$ ...

**4**

votes

**1**answer

105 views

### Intersections in almost complex manifolds

Question: Suppose $(M,J)$ is an almost complex manifold, and $X$ and $Y$ are two almost complex submanifolds (i.e. $J(T(X)) \subset T(X)$ and $J(T(Y)) \subset T(Y)$). Then must $X \cap Y$ also be an ...

**0**

votes

**0**answers

37 views

### decomposition of polynomials over a field [on hold]

$K|F$ has this property that every polynomial $f(x)∈F[x]$ has a root in $K$.is it true that every polynomial $f(x)∈F[x]$ can be completely decomposed on $K$?
i think it is false,because if we write ...

**-5**

votes

**0**answers

30 views

### How to find secret key and public key for ECC cryptosystem? [on hold]

Develop an ECC cryptosystem based on E31(1;1),
point G = (0,1) which has order 32.
nA value of 6.
What is the secret key?
What is the public key?

**0**

votes

**3**answers

64 views

### On the existence of compactly supported functions whose its Fourier transform satisfies a given condition

My question is concerned with the existence of compactly supported functions whose its Fourier transform satisfies a given condition: For $\gamma\ge 1$, one can prove that there is no compactly ...

**-3**

votes

**0**answers

37 views

### How to compute 3P from elliptic curve where P is (28, 8) [on hold]

Consider the elliptic curve E31(1,1):
Calculate 3P, where P = (28,8).

**3**

votes

**0**answers

120 views

### Is the ISC kaput [on hold]

The very useful Inverse Symbolic Calculator is showing me this
What's up? multiple choice
(a) No, it's fine at that address: idiot Edgar did something wrong...
(b) It is off-line at that ...

**1**

vote

**1**answer

173 views

### Disruptive innovations in mathematical notations [on hold]

I am wondering whether there are examples of mathematical notations that, once introduced, have drastically changed or simplified the way to address a problem or a mathematical area, or that have ...

**-2**

votes

**0**answers

74 views

### Complexity Dick Word in Turing Machine single tape [on hold]

(I precise I don't have a good level in english so I can rewrite if you want)
The probleme :
I just have two symbols O(open) for "(" and C(close) for ")"
The probleme consist to implement an ...

**0**

votes

**0**answers

37 views

### Connectedness of the symplectic automorphism of the 2-sphere $S^2$

The 2-sphere, endowed with the round Riemann metric with constant curvature 1, is a symplectic manifolds.
My question is:
Is the group of symplectic automorphisms
of $S^2$ with respect to this ...

**1**

vote

**1**answer

105 views

### trigonometric sum and inequalities

let $x\in\mathbb{R}-\mathbb{Z}$ and $e(x)=e^{2\pi ix}$. If we have this sum $$\left|\overset{q}{\underset{h=1}{\sum}^{*}}e\left(h\, x\right)\underset{\underset{p\equiv h\,\textrm{mod}\, q}{p\leq ...

**0**

votes

**0**answers

48 views

### Studies of Specific Kinds of Beurling Primes?

I know that Beurling developed a notion of generalized primes (and integers.
However, does anyone know if Beurling, or anyone else, studied subclasses of the broader class of Beurling primes that ...

**-3**

votes

**0**answers

103 views

### About Gödel's incompleteness theorems [on hold]

I think maybe I found the mistake of Gödel's incompleteness theorems
first,these are something I suppose
1、the content of Proof must be able to be transformed to
formal logic
So my point is ...

**0**

votes

**0**answers

11 views

### Rearranging a sequence to minimize a series function on its subsequences

Given an arbitrary nonempty sequence of integers $Q$ with $p$ elements:
Let $R$ be a rearrangement of $Q$.
Let $A$ be the solution set of $1\leq n\lt m\leq p$, where $n,m\in \mathbb{Z}$.
$F(n,m) = ...

**2**

votes

**0**answers

14 views

### Second order term of the Fedosov quantised product

In Fedosov's version of quantisation of functions on a symplectic manifold, the product is given in terms of a symplectic connection. I have looked through Fedosov's book in deformation quantisation, ...

**0**

votes

**1**answer

51 views

### What is the expression of first eigen function of Laplacian on Hyperbolic plane?

Let $\Delta$ be the Laplacian (a positive operator) on $H^2$ the hyperbolic plane. My question is what is the expression of the eigenfunction $\Delta f= f/4$? (say in the ploar coordiante)

**0**

votes

**0**answers

30 views

### algorithms math help [on hold]

I can't understand the basic math behind algorithms. For example, here's a question:
If f(n) = O(g(n)) is ...

**3**

votes

**1**answer

87 views

### The sixth power integral moment of automorphic L-function attached to Maass Forms

It is known that the sixth power integral moment of automorphic L-function attached to Cusp Forms has been proved by M. Jutila, that is $\int_{0}^{T}|L(1/2+it,f)|^{6}dt \ll T^{2+\varepsilon}$.
And ...

**-1**

votes

**0**answers

66 views

### Galois group of equation [on hold]

Let the equation $5x^6-12x^5-12x^4+204x^3+81x^2-792x+414=0$
The Galois group of $P(x)=5x^6-12x^5-12x^4+204x^3+81x^2-792x+414$ have solvable to be or not?

**-3**

votes

**0**answers

46 views

### How to verify a vector has a steady gradual increase mathematically? [on hold]

I rank the values inside my vector then look to verify the values have a gradual but steady increase. Ideally if I had 10 numbers the smallest would occur first and the second smallest would rank ...

**5**

votes

**0**answers

105 views

### Hyperbolicity of Deligne-Mumford stacks

Let $X$ be a smooth finite type separated connected Deligne-Mumford stack over $\mathbb C$ (with trivial generic stabilizer if necessary).
This question is about "hyperbolicity" and it is motivated ...

**6**

votes

**1**answer

78 views

### Universality with respect to quotients

Is there an infinite cardinal $\kappa$ for which the following statement (S) true?
(S) : There is a topology $\tau_\kappa$ on $\kappa$ such that for all topological spaces $(X,\tau)$ with $|X|\leq ...

**-2**

votes

**0**answers

55 views

### Identification of Hilbert space with dual follows from another identification? [on hold]

Let $X$ be a Hilbert space with inner product $(\cdot,\cdot)_X$, and let $Y$ be another Hilbert space with inner product $(\cdot,\cdot)_Y$. Suppose there is a bijective continuous linear operator $F:X ...

**24**

votes

**0**answers

394 views

### Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section?

Possibly this has already been asked, but it came up again in this question of Daniel Litt. Does every smooth, projective morphism $f:Y\to \mathbb{C}P^1$ admit a section, i.e., a morphism ...

**12**

votes

**3**answers

457 views

### Characterize the category of rings

(Sub)categories of many well-studied mathematical objects have been characterized purely in terms of their morphisms. Some (famous) examples:
Sets and functions, due to Lawvere.
Modules over some ...

**0**

votes

**0**answers

94 views

### A question on the Euclidean domain $\mathbb{Z}[\omega]$ [on hold]

Let $\omega=\frac{-1+i\sqrt{3}}{2}=e^{\frac{2 \pi i}{3}}$ be a complex cube root of unity, and $\mathbb{Z}[\omega]$ the Euclidean domain. In view of that $\int_0^\infty e^{ix} ...

**-2**

votes

**0**answers

45 views

### Existence of minimizer in Sobolev space $H^{1,2}(\Omega)$ [on hold]

I am looking at a functional $$\frac{\int_{\partial \Omega} u^2 \mathrm{dx}}{ \left(\int_{\Omega} u^q \mathrm{dx} \right)^{2/q} }$$
And i want to know if the minimizer exists in the space ...

**8**

votes

**1**answer

187 views

### A linear category with objects of infinite length but which is otherwise finite?

Fix a ground field $k$. By a linear category I will mean an Abelian category which is compatibly enriched over $k$-vector spaces. A linear category is called finite if it satisfies the following four ...

**0**

votes

**1**answer

47 views

### Computing row-sum scaled unsigned Stirling nos. of the 1st kind

As the title suggests, I would like to compute probability vectors with elements proportional to (unsigned) Stirling numbers of the first kind by row. For easy reference, here is the Wiki page.
For ...

**2**

votes

**0**answers

79 views

### Semigroup nilpotents and compostional inversion

The integer coefficients of a general partition formula for the compositional inverse of a function are a refined version of the coefficients of the generating series for the number of nilpotents in a ...

**0**

votes

**0**answers

86 views

### Is holomorphic 2-form on Moduli of Higgs bundle in Biswas' paper is non-degenerate

In Biswas' paper, Geometry of moduli of Higgs bundles, he defined a holomorphic 2-form on moduli of stable Higgs bundles, using Kodaira-Spencer map and Petersson-Weil metric.
I want to know whether ...

**3**

votes

**1**answer

88 views

### Probability that a sum of intependent random variables hits a point

Let $X_1,\ldots,X_n$ be independent random elements of a normed space $X$. Suppose that $\sup_{x\in X}\mathbb{P}(X_i=x)=p_i$. What is the best known upper bound for
$$\sup_{x\in X} ...

**-2**

votes

**0**answers

176 views

### Conjecture Reference Request

If Second Hardy-Littlewood Conjecture is true then we can claim that $\pi(x)-\pi(y)\leq \pi(x-y)$. Thus the conjecture gives an upper bound for the number of primes between $x$ and $y$. I have found ...

**4**

votes

**1**answer

100 views

### a question about minimal non-abelian groups

Let $G$ be a minimal non-abelian group with cyclic Sylow $p$-subgroup $P$ and normal Sylow $q$-subgroup $Q$ , see [ Huppert, Endlich Gruppen I, Aufgaben III, 5.14].
My quesion is, if there is another ...

**15**

votes

**2**answers

695 views

### Is a group uniquely determined by the sets $\{ab,ba\}$ for each pair of elements a and b?

This is a cross-posted question, originally active here on math.stackexchange.
For a given group $G=(S,\cdot)$ with underlying set $S$, consider the function
$$
F_G:S\times ...

**0**

votes

**0**answers

77 views

### Is the parallelogram rule an axiom or a theorem in euclidean geometry? [on hold]

I am aware of the proof of the rule in inner product spaces. Excluding the geometry of Descartes, is it possible to prove parallelogram rule or is it an axiom?

**2**

votes

**1**answer

43 views

### lower bound of a trace quadratic form [on hold]

i want to find a lower bound on the following expression:
$tr(AXA^T)$ in terms of $tr(X)$
where A is real $n\times n$ matrix and $X>0$ is positive symmetric. It seems that the following bound is ...

**0**

votes

**1**answer

197 views

### Is there any algorithm to decide whether a series with integral coefficiens is a algebraic function? [on hold]

Given a series with integral coefficiens as following:
$$F(x)=\sum_0^i a_i x^i,\text{where }a_i\in \mathbb{N}\bigcup 0 $$$$\text{and there is a computable function $\psi$ such that } \forall i ...

**5**

votes

**0**answers

99 views

### Does $\mathsf{fReR}_0$ prove the existence of the cartesian product of two sets

$\mathsf{fReR}_0$ is the set-theoretical system whose axioms consist of:
(1) Axiom of extensionality: $\forall z\in x\ (z\in y)\wedge\forall z\in y\ (z\in x)\rightarrow x=y$
(2) Axiom of empty set: ...

**1**

vote

**0**answers

101 views

### Equations over $\mathbb{Z}[[T]]$ vs. equations over $\mathbb{Z}_p$

This question might be deemed totally unanswerable, unless there is an obvious counterexample. Answers to either effect would be welcome.
Question. Let $X$ be a finite-type scheme over ...

**1**

vote

**0**answers

37 views

### Cohomological dimension of transcendental p-adic extensions

Let $k = \mathbb{Q}_p$ for any prime $p$ and set
$L = k(t_1,..,t_n)$.
The u-invariant of a field $u(k)$ is defined by $u(k):=\{ max (\mathrm{rank}(q)) $ | $ q $ is anisotropic over $k\}$.
It is ...

**2**

votes

**2**answers

169 views

### A metric associated with a continuous surjective map $f:X\to Y$

Assume that $f:(X,d_{1})\to (Y,d_{2})$ is a continuous surjective map between compact metric spaces. We define another
metric $d_{f}$ on $Y$ With $$ d_{f}(a,b)=Hd(f^{-1}(x), f^{-1}(y))$$ ...