# All Questions

**-1**

votes

**0**answers

17 views

### How to get the normal vector to a plane that only knows 3 points coordination?

I have three points Pi(xi,yi,zi),i=0,1,2, I want to get the normal vector to the plane that is decided by these three points which I will write code to realize it. Can any one give any advice? Thank ...

**2**

votes

**0**answers

9 views

### Ordering subsets of the cyclic group to give distinct partial sums

Suppose that you are given a set $S$ of $k$ nonzero elements from $\mathbb{Z}_n$. Is it always possible to order the elements of $S$, say $a_1,a_2,\dots,a_k$ in such a way that the partial sums ...

**0**

votes

**0**answers

16 views

### Continuity of Kan extension along the Yoneda embedding

Let $\mathcal{C}$ be a category and $h_-: \mathcal{C} \to \mathrm{Set}^{\mathcal{C}^{op}}$ be the Yoneda embedding. Let $\mathcal{A}$ be a cocomplete category and $F: \mathcal{C} \to \mathcal{A}$ a ...

**0**

votes

**0**answers

12 views

### Soft Question: What does periodic cyclic theory measure?

The cyclic homology of $\mathbb{C}[X,Y]$ and that of the algebra of functions on the sphere $S^2$ have the same periodic cyclic homology, clearly however these objects are topologically very different ...

**0**

votes

**1**answer

82 views

### What “force” us to accept large cardinal axioms?

Large cardinal axioms are not provable using usual mathematical tools (developed in $\text{ZFC}$).
Their non-existence is consistent with axioms of usual mathematics.
It is provable that some of ...

**-2**

votes

**0**answers

20 views

### differential geometry

vector field $X$ on $M$ is said $\pi$-projectable if there is a field $W$ on $M$ such that
$(T_{x}\pi)(X(x))=W(\pi(x))$ for all $x\in M$.
$X$ is said $\pi$-vertical if $\pi$-projectable and $W=0$.
...

**1**

vote

**1**answer

44 views

### generality of the lattice of normal subgroups

Let $(X,\le)$ a (finite) modular lattice. Is there a (finite) group $G$ such that the lattice of all normal subgroups of $G$ is isomorphic to $(X,\le)$?

**0**

votes

**0**answers

53 views

### Maximal “Spot It!” card count

This question was triggered by the game Spot It!.
The game consists of cards, each having $k$ different symbols from an alphabet of $n>k$ symbols, with the property that any 2 cards have at least ...

**1**

vote

**0**answers

23 views

### Central limit theorem for independent random variables, with a Gumbel limit

Consider independent random variables $Y_i$, $i>0$, such that $\mathbb{E}(Y_i)\approx \frac{1}{i}$ and $\text{Var}(Y_i)\approx \frac{1}{i^2}$, where $\approx$ means asymptotically equivalent up to ...

**2**

votes

**0**answers

23 views

### Convergence of Schwartz Kernels

I read this question, and I would like to ask the opposite: Assume that I have a sequence of smoothing operators $(P_n)$ with (hence smooth) kernels $(p_n)$ converging strongly to some smoothing ...

**3**

votes

**0**answers

23 views

### Is any finitely generated nilpotent pro-$p$ group necessarily the pro-$p$ completion of some finitely generated nilpotent group?

While thinking about this question, I was led to the following question:
My question: Let $G$ be a topologically finitely generated pro-$p$ nilpotent group. Does there exist a finitely generated ...

**1**

vote

**0**answers

18 views

### Group action of $G<\mathbb Z^\infty_2$ over the Golden mean shift

I'm am looking for an action of an infinite subgroup of $\mathbb Z^\infty_2$ over the golden mean shift space $$X=\{x\in \{0,1\}^\mathbb N : x_i=1\Rightarrow x_{i+1}=0\}$$ such that any element of $G$ ...

**3**

votes

**1**answer

107 views

### Equivalent definitions of Calabi-Yau manifolds

How do we prove that a compact Kahler manifold whose 1st Chern class vanishes admits a globally defined nowhere vanishing volume form? Thanks.

**0**

votes

**0**answers

16 views

### Sum of Squares Length of a Product

Let $n \geq 2$. Let $g_1, \ldots , g_{n-1} \in \mathbb{R}[x_1,\ldots,x_n]$ such that $q=g_1^2+\ldots +g_{n-1}^2$ is not divisible by $p=x_1^2+\ldots +x_n^2$. Let $m \geq 1$ be the smallest integer ...

**-2**

votes

**0**answers

37 views

### Why the square of ideal in Lie algebra is also ideal? [on hold]

Let $L$ be a Lie algebra over field $F$, $I$ - ideal in this algebra. It's stated that $I^2$ (and so any item of central series) is also ideal in $L$.
1) For any $a, b \in I^2: [a,b] \in I^2$. True, ...

**0**

votes

**0**answers

22 views

### References on law of large numbers, CLT and iterated logarithm laws

Having access to those references, accumulating many results in one domain is always a bless,like Feller's book in probability, Dembo-Zeitoun's large deviation, Grimmett's percolation and recent ...

**4**

votes

**1**answer

78 views

### Weakening simplicial identities

The generators $d_i, s_i$ for morphisms of the simplicial category satisfy simplicial identities:
$d_jd_i = d_id_{jā1}$ for $i < j$
$s_jd_i = d_is_{jā1}$ for $i < j$
$s_jd_i = id$ for $i = ...

**0**

votes

**1**answer

60 views

### A question about sentences in the language of first order ZFC which assert the existence of cardinal numbers

These sentences are usually of two kinds. The first kind are actually theorems of ZFC asserting the existence of various cardinal numbers and their negations are inconsistent with ZFC. The second kind ...

**7**

votes

**3**answers

190 views

### Changing combination lock

Suppose you have a combination lock (n digits, m symbols) that is unlocked by one specific n-digit key sequence. However, trying a wrong key changes it according to an fixed but unknown function: new ...

**0**

votes

**0**answers

29 views

### Relation between kahler potential and Hermitian metric

Let $(M,\omega)$ be a Kaehler manifold and $h$ be its Hermitian form, then in local sense we can write $$\omega=\partial\bar\partial\log h$$ and also if $f$ be the kaehler potential then we can write ...

**6**

votes

**2**answers

114 views

### A looping of algebraic K-theory

Algebraic K-theory of an exact category $\mathcal{C}$ is a certain universal non-connective spectrum $K(\mathcal{C})$. In particular, objects of $\mathcal{C}$ give elements of $K_0(\mathcal{C})$.
...

**2**

votes

**1**answer

70 views

### Bound for a combinatorial sum

I was playing around with a problem and I obtained a certain
combinatorial sum. I was wondering if there was a way to simplify or bound it.
I have a real valued function $f$, which satisfies $|f(x)| ...

**5**

votes

**2**answers

118 views

### Sufficient Condition for Defining $\in$

Consider the first order language $\mathcal{L}=\{\in,\in'\}$ with two binary relational symbols $\in , \in'$ and $ZFC$ as a $\{\in\}$-theory. If we define $\in'$ using $\{\in\}$-formula $\varphi(x,y)$ ...

**1**

vote

**1**answer

80 views

### On infinitesimal neighbourhood of a point in a projective scheme

Let $X, Y$ be irreducible projective schemes over $\mathbb{C}$ and $X \subset Y$. Let $x \in X$ be a closed point. Assume that for any positive integer $n$ and any morphism from $\mathrm{Spec} ...

**-3**

votes

**0**answers

27 views

### Radial neuron teaching [on hold]

Hello i have a task to write programm for teaching radial neuron with 3 inputs, i can't find some information about it, i find a lot of info about teaching netowork. I can't undestand what algorithm i ...

**0**

votes

**0**answers

37 views

### How to join 2 functions into one? [on hold]

is it possible join for example x^2 and (x-2)^2 into one function, so that the graph displays both of them only using one function (relation, to be exact)?
Subsequently, is there a general way to ...

**3**

votes

**3**answers

99 views

### Is it possible to find $h$ hermitian metric such that $Isom_{h}(X) \cong Aut(X)$?

I suspect this is true for some class of analytic manifolds (Riemann surfaces maybe), but my knowledge in differential geometry is very poor, so I could not conclude it. For complex manifolds, is it ...

**1**

vote

**3**answers

83 views

### Modular group modulo $N$

Let $N\geq2$ be a positive integer. Is the canonical homomorphism $\pi$ from $SL_2(\mathbb{Z})$ to $SL_2(\mathbb{Z}/N\mathbb{Z})$ surjective?
What if we ask the same question for $SL_n$?

**-1**

votes

**0**answers

38 views

### Proving the solution of one non-linear first order ODE has value 'e-1' at point 1

Consider the following first order non-linear ODE defined on interval $[0,1]$:
$$F(x)=f(x)\ln\left(\frac{f^2(x)}{f^2(x)-1}\right)$$
where $f(x)=\frac{\partial F(x)}{\partial x}$, and the initial ...

**2**

votes

**0**answers

62 views

### Cohomology of elementary Abelian p-group

Let $E=(\mathbb{Z}/p\mathbb{Z})^n$, an elementary Abelian p-group.
Let $k$ be an algebraically closed field of characteristic 0.
There is a good description of $H^*(E,F^{\times})$ where $F$ is a field ...

**0**

votes

**0**answers

40 views

### Cohomology operations over general rings [duplicate]

If $X$ is a topological space and $R$ is a commutative ring, then the singular cohomology groups $H^*(X,R)$ support cohomology operations coming from the homology of symmetric groups. If $R = ...

**0**

votes

**0**answers

12 views

### The use of wavelets in time series modelling

I have been working on modelling a time series using wavelets for a long time. I am quite familiar with the wavelet theory and all...However, I have a big understanding issue and really appreciate it ...

**2**

votes

**0**answers

41 views

### symmetric monoidal double categories?

Let me preface this by saying that I don't know much category theory.
I am running into a situation where I have a double category and additionally there is a multiplication. Moreover, choosing ...

**1**

vote

**1**answer

120 views

### Number theoretic functions that have an irregular behaviour at primes

Usually, number theoretic functions have "trivial" (or at least easily defined) values for primes. In this thread, I am rather asking for functions which are only defined on primes (well, this ...

**3**

votes

**0**answers

35 views

### Petersson product of newforms to different level

Let $\text{S}_k^{new}(\Gamma_0(N),\chi)$ be the space of newforms. We call $f\in\text{S}_k^{new}(\Gamma_0(N))$ a newform if $f$ is a Hecke eigenform i.e $\text{T}_nf=\lambda_nf$ ($\text{T}_n$ hecke ...

**1**

vote

**0**answers

27 views

### Is semistability of smooth Weil sheaf preserved under tensor product?

Let $X_0$ be a smooth, geometrically connected scheme over $\mathbb{F}_q$. As usual, let $\tau : \bar{\mathbb{Q}}_{\ell} \simeq \mathbb{C}$ be a fixed isomorphism. Let $\mathcal{C}$ be the category of ...

**-3**

votes

**0**answers

104 views

### Math Instructor [on hold]

How do you obtain a disjoint family from an arbitrary family of sets?
This is mentioned in Kelley's book, p. 201, Theorem 35.
It's also been mentioned in this site.
(Arbitrary union of meager open ...

**3**

votes

**2**answers

131 views

### “Degree 3 fields”

I was wondering what was known about fields $k$ having the property that any polynomial
over $k$ of degree $3$ has at least one root in $k$. Does such a field have a special name ?
Is there some kind ...

**1**

vote

**1**answer

62 views

### About embeddings of connected sums

Let $M_1$ and $M_2$ be two soomth manifolds who're already embedded in $\mathbf{R}^k$.
Can one prove that the connected sum of $M_1$ and $M_2$ can also be embedded into $\mathbf{R}^k$ ?

**3**

votes

**1**answer

76 views

### On Neron-Severi group of normal projective surfaces and blow up

Let $X$ be a normal projective surface with at most rational singularites (in finitely many points). Let $\pi:\tilde{X} \to X$ be the blow up of $X$ at finitely many singular points. The question is ...

**1**

vote

**0**answers

25 views

### Efficient evaluation of multidimensional kernel density estimate

Edit I have copied this discussion to the stats community site here, since I feel it is more relevant. Please feel free to close this in due course.
I've seen a reasonable amount of literature about ...

**7**

votes

**0**answers

83 views

### “abstract” description of geometric fixed points functor

I'm sure this must be well known, but I could not find any references.
My basic question is: Are there "abstract" descriptions of the geometric fixed point functors in equivariant stable homotopy ...

**4**

votes

**1**answer

57 views

### Diagonalization for sums of Hermitian matrices

I found an interesting question about diagonalizable matrices,
Let $A,B\in \mathcal{M}_n(\mathbb{C})$ Hermitian, such that $AB\neq BA$.
Do there exist complex numbers $u\neq v$, such that $A+uB$ and ...

**4**

votes

**0**answers

65 views

### Concrete almost-complex structures on $3 \#CP^2$

The connect sum $X:=CP^2\# CP^2 \# CP^2$ supposedly supports almost-complex structures, i.e. endomorphisms $J$ of the tangent bundle such that $J^2=-id$. The existence of these almost-complex ...

**2**

votes

**0**answers

29 views

### Augmentation ideal of the cohomology of an elemntary abelian 2-group [on hold]

Let V be an elemntary abelian 2-group and $R=H^{*}V$ its cohomology.
What is the Augmentation ideal of R and what is the quotient of R by its augmentation ideal ?

**1**

vote

**0**answers

61 views

### Is the “Hilbert scheme of curves” in $\mathbb C^3$ a degeneracy locus?

It is known that the Hilbert scheme of $n$ points in $\mathbb C^2$ is expressible as a degeneracy locus, i.e. the zero locus of $\textrm{d}f$, where $f$ is some regular function on a smooth variety. A ...

**2**

votes

**0**answers

71 views

### Local Systems on Function fields over $\mathbb{F}_p$

Suppose $X$ is a smooth proper curve over $\mathbb{F}_p$ for some prime number $p$. Let $l\neq p$ be a prime, and suppose $L$ is a rank 2 local system over $X$ with coefficients in $\mathbb{Z}_l$ such ...

**2**

votes

**0**answers

39 views

### Explicit descriptions of self-replicating pro-$p$ groups

A group $G$ is called self-replicating, if there exists a finite index subgroup $H$, such that $H\cong G\times\dots\times G$. Maybe the most famous example of a self-replicating group is a subgroup ...

**4**

votes

**1**answer

149 views

### Which finite groups can be characterized by their subgroup orders?

Given a finite group $G$, we denote by $\pi_s(G)$ the set of orders of its subgroups. Which finite groups $G$ can be characterized by the set $\pi_s(G)$, i.e. $\pi_s(H)=\pi_s(G)$ implies $H\cong G$? ...

**1**

vote

**1**answer

85 views

### Groups in which lower central series and upper central series coincide

Let $G$ a finite two-generated $p$-group in which lower and upper central series coincide. Clearly we obtain that the upper central series become strongly central, we have also that at least half of ...