-1
votes
0answers
21 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
0answers
13 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
0answers
17 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
0answers
13 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
1answer
93 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
0answers
24 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
1answer
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
0answers
54 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
0answers
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
0answers
24 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
0answers
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
0answers
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
1answer
109 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
0answers
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
0answers
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
0answers
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
1answer
78 views

Weakening simplicial identities

The generators $d_i, s_i$ for morphisms of the simplicial category satisfy simplicial identities: $d_jd_i = d_id_{jāˆ’1}$ for $i < j$ $s_jd_i = d_is_{jāˆ’1}$ for $i < j$ $s_jd_i = id$ for $i = ...
0
votes
1answer
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
3answers
197 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
0answers
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
2answers
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
1answer
71 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
2answers
119 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
1answer
81 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
0answers
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
0answers
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
3answers
100 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
3answers
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
0answers
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
0answers
63 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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
28 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
0answers
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
2answers
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 ...
2
votes
1answer
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
1answer
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
0answers
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
0answers
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
1answer
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
0answers
66 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
0answers
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
0answers
62 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 ...
3
votes
0answers
73 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
0answers
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
1answer
150 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
1answer
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 ...

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