All Questions

Filter by
Sorted by
Tagged with
1
vote
1answer
108 views

$0$-“norm” minimization with least-squares regularization

I have the following optimization problem in $\mathbf{x} \in \mathbb{R}^{K \times 1}$ $$\min_{\mathbf{x}>0} \quad \|\mathbf{A}\mathbf{x}\|_0 + \alpha \|\mathbf{B}\mathbf{x}-\mathbf{c}\|_2^2$$ ...
6
votes
1answer
122 views

Point distributions in unit square which minimize E[1 / distance]

Choose $n$ points $p_1,\ldots,p_n$ in the unit square $[0,1]^2\subset\mathbb{R}^2$ such that $D:=\mathop{\sum}\limits_{1\le i<j\le n}\frac{1}{dist(p_i,p_j)}$ is minimized, where $dist(p_i,p_j)$ is ...
10
votes
0answers
263 views

A purely algebraic argument for existence of a section of a smooth projective morphism to the projective line

If I am reading this post correctly, any smooth projective $\mathbb{C}$-morphism of schemes $X\rightarrow \mathbb{P}^1$ admits a section. I am afraid of the topological argument presented there. Is ...
1
vote
0answers
26 views

Lattices with no roots and spread out shells

I am looking for lattices with the following properties: The lattice has no roots. The norm (squared length) of the second shortest vectors should be at least twice as large as the norm of the ...
3
votes
0answers
56 views

Weight spaces of modules over Lie algebras

I know that an irreducible infinite-dimensional weight module over the Virasoro algebra in which it has a non-zero finite-dimensional weight space, then all its weight spaces have finite dimension. ...
2
votes
0answers
83 views

A non-Kaehler manifold complex and symplectic in exactly one way

Does there exist a closed connected smooth manifold that admits exactly one (up to biholomorphism) integrable complex structure and exactly one (up to symplectomorphism and rescaling) symplectic ...
0
votes
1answer
140 views

Solution of nonlinear second-order ODE $y''+\frac{(y'+2ax)^2+4b^2}{2y}+\frac{10}{3}a=0$

Is there any way of solving the following second-order ODE $$y''+\frac{(y'+2ax)^2+4b^2}{2y}+\frac{10}{3}a=0,$$ where $a$ and $b$ are some constant? If we know that one solution exists, how would it ...
1
vote
0answers
93 views

Question about Local Henselian Rings

I have a question regarding properties/characterizations of local Henselian rings exploited in M. Artin's article "On Isolated Rational Singularities of Surfaces": Here the relevant excerpt: Remark: ...
3
votes
0answers
157 views

reductive groups in algebraic geometry

presumably this is a quite broad question but up to now I haven't found a discussion treating following question: in a lot of fields in algebraic geometry (e.g. GIT or topics on etale cohomology) ...
-2
votes
0answers
32 views

Stationary Points Possible Values [on hold]

I am having trouble with part d) of this question. It follows on with other parts of a question which I have attached. I have written that 'p' can indeed have stationary points but am not sure what ...
5
votes
0answers
409 views

Theorem from Deformation Theory

My question refers to some steps it the proof of Theorem 3.3 part (b) in Christensen's paper treating Deformation theory (see pages 9-11): https://mathematics.stanford.edu/wp.../A.-Christensen-Draft....
5
votes
0answers
82 views

CoCartesian vs. locally CoCartesian fibrations

Say $\pi: C\to J$ is an inner fibration of $\infty$-categories. Then "morally", $\pi$ corresponds to a diagram indexed by $J$ in the "category of categories with correspondences", and if $\pi$ is ...
7
votes
3answers
233 views

Wildness of codimension 1 submanifolds of euclidean space

This question arose out of this stack exchange post. I am wirting a thesis about the $s$-cobordism theorem and Siebenmann's work about end obstructions. Combined they give a quick proof of the ...
-3
votes
0answers
117 views

Does the strong multiplicity one theorem imply the isomorphy of these two automorphism groups?

Defining the notion of "Galois class of L-functions" as a set of automorphic L-functions belonging to the Selberg class closed under the usual product and the Rankin-Selberg convolution and containing ...
5
votes
1answer
163 views

De Rham cohomology of Lie groupoid

Let $G$ be a Lie group acting on a manifold $M$. Consider the transformation groupoid $\mathcal{G}=(G\times M\rightrightarrows M)$. We have the notion of de Rham cohomology of a Lie groupoid by ...
2
votes
1answer
426 views

Have new conjectures generated by the Ramanujan machine been proven?

Recently the following preprint was published with new automatically generated conjectures on generalizes continuous fractions, e.g., for the Euler constant: Raayoni, Pisha, Manor, Mendlovic, Haviv, ...
-1
votes
0answers
49 views

Infinitely generated PID algebra with infinitely many prime ideals

Given a field, is there a functorial construction of a PID algebra over it that has infinitely many prime ideals and is not finitely generated? This excludes the ring of univariate polynomials and the ...
0
votes
0answers
25 views

Integral of exponential + limit [closed]

Let $f:\mathbb{R} - \{-5\}->\mathbb{R}$, $f(x)=(x-1)e^{-(1/(x+5))}$. I have to calculate $lim_{(n->\infty)}=n^2\int_{0}^{1}x^nf(x)dx$. I've tried using integration by parts, but i'm still stuck....
2
votes
2answers
260 views

Domain of definition of Laplace Operator on $L^2$

I'm trying to combine two ways of looking at the Laplacian $\Delta$ on $\mathbb R^n$ (and on other domains). Firstly, it is well known that this operator is essentially self-adjoint on $C_c^\infty(\...
1
vote
0answers
117 views

On a map between Riemann surfaces of genus $1$

Let $C$ be a compact Riemann surface of genus $1$, and $p\in C$, and $w$ be a local holomorphic coordinate on $C$ near $p$ with $w=0$ at $p$. As usual, for a divisor $D$ denote by $L(D)$ the vector ...
4
votes
2answers
182 views

Comparing two limsup's

Let $f\in L^2(0,\infty)$ be a positive, decreasing function. Is it then true that $$ \limsup_{x\to\infty} xf(x) = \limsup_{x\to\infty} \frac{1}{f(x)}\int_x^{\infty} f^2(t)\, dt $$ (and similarly for $\...
2
votes
0answers
49 views

Finding a cover of the Hilbert functor, that corresponds to a cover of the Grassmannian

Let $\mathrm{Grass}_{k+1,n+1}:\mathrm{Sch}^{\circ}\rightarrow\mathrm{Set}$ be the Grassmann functor, which maps a scheme $S$ to the set: $$\left\{\mathscr{U}\subseteq\mathscr{O}_S^{n+1}:\,\,\mathscr{...
2
votes
0answers
68 views

When is $C\text-\mathsf{dg\text-mod}$ determined by the connective base changes?

I'm using cohomological gradings. For $C\in k\text-\mathsf{cdga}$ (where $k$ can be taken of characteristic 0), a morphism $C\to A$ to a connective dg-algebra $A\in k\text-\mathsf{cdga}_{\leq0}$ ...
0
votes
0answers
38 views

Strichartz estimates for the inhomogeneous wave equation

In the Blair, Smith and Sogge's paper Strichartz estimates for the wave equation on manifolds with boundary, the authors study integrability estimates for solution of the following problem: \begin{...
2
votes
0answers
69 views

A class of Grothendieck categories

Is there a name and some work on Grothendieck categories in which each non-zero object has a simple subquotient? Every locally finitely generated Grothendieck category has this property, but I guess ...
7
votes
1answer
381 views

Reference request: The unit of an adjunction of $\infty$-categories in the sense of Riehl-Verity is a unit in the sense of Lurie

I'm looking for a reference (or proof) for the statement given in the title: that when we have an adjunction between quasicategories in the sense of Riehl and Verity (defined e.g. in Section 4 of ...
5
votes
1answer
177 views
+100

Symmetric monoidal category with trivial switch morphisms

Is there a specific terminology for a symmetric monoidal category in which for any object $x$ the switch map $x\otimes x\to x\otimes x$ is the identity ? (Or alternatively the action of the symmetric ...
2
votes
1answer
76 views

are spectral measures characterized by their moments?

On a Hilbert space $\cal H$, consider an essentially self-adjoint operator $A\colon Dom(A)\to {\cal H}$, and a vector $\psi\in\bigcap_{n=1}^\infty Dom(A^n)$. Without further assumptions, can we say ...
1
vote
1answer
76 views

Embedding a graph in $\mathbb{R}^3$ with partial geometric information

I have a connected, sparse, graph (a molecule to be specific) and I'm interested in associating 3D coordinates with the vertices. Here's the kicker: I already have coordinates for none/some/all ...
2
votes
0answers
34 views

Pullback of homogeneous twisted differential operators

Let $X,Y$ be smooth complex varieties and let $G$ be an smooth affine algebraic group acting on $X$ and $Y$ such that $X,Y$ are $G$-homogeneous spaces (the $G$ action is transitive). We also let $f:Y \...
4
votes
2answers
354 views

When does glueing affine schemes produce affine/separated schemes?

Let $X$ be an affine scheme with an open affine subscheme $U\subset X$. Given an automorphism of $U$, we can glue $X$ with itself along $U$ to get a new scheme. Is there a description in terms of ...
0
votes
0answers
27 views

What can one say about a subscheme of a Hilbert scheme, which is covered by lines?

k= complex numbers, X/k closed subscheme of a Grassmannian, which is Plücker embedded in a projective space. a)X is simply connected b) the first Chow group (rational coefficients)of X is generated by ...
-1
votes
0answers
83 views

A problem in asymptotic coding theory?

Denote $\mathcal T_n$ to be all 'unique minimum weight' $[n,k]$ binary linear codes. Is there any evidence that this set has cardinality $\omega(\operatorname{poly}(n))$?
0
votes
0answers
133 views

Proper curve over any base is projective?

Is it true that any proper morphism of relative dimension$\leq 1$ is projective (no additional assumptions whatsoever)? Is it true that any such morphism is $H$-projective (https://stacks.math....
2
votes
0answers
60 views

Monodromy operators on hyperkähler varieties

Let $X$ be a hyperkähler variety. In an article (Conjecture 2.1) from some years ago, Markman conjectured that any monodromy operator acting trivially on $H^2(X,\mathbb Z)$ is the identity operator, ...
4
votes
1answer
174 views

Confusion about complex differential forms

I follow Kobayashi "Differential Geometry of Complex Vector Bundles", pages 11-12, prop. 4.9. Given a rank-$r$ Hermitian holomorphic vector bundle $(E,h)$ over a complex manifold $M$, there exists a ...
1
vote
0answers
111 views

Morphisms whose reduction is projective

IIUC Remark 5.3.5 in EGA II says that there exist proper non-projective morphisms $X\rightarrow Y$ where $Y$ is the spectrum of a finite-dimensional $\mathbb{C}$-algebra such that the induced morphism ...
1
vote
2answers
80 views

Question on Parabolic PDEs: Improvement of the bound ${\vert \vert v(\cdot,t)-v_0(\cdot) \vert \vert}_{L^p}\le \hat C t^{1/q}$

Let $M$ be a $C^3-$compact manifold and $v \in W^{2,1}_p(M\times [0,T])$ ($1\le p<\infty$) be the solution of: $\begin{cases} \partial_t v-\Delta_{M} v=f(v), \quad M\times [0,T]\\ v(x,0)=v_0,...
2
votes
0answers
241 views

Is ZFC interpretable in a kind of an extended form of second order arithmetic?

Informally the following theory is a kind of extension of second order arithmetic, where numbers are not limited to naturals, instead here we have formation of further numbers by setting limits on ...
4
votes
1answer
88 views

Kuenneth short exact sequence for K-homology

Atiyah proved a Kuenneth short exact sequence for K-theory. I need one for K-homology, but can not find any reference in the literature. Do you know one? Using general spectra stuff, one gets a ...
2
votes
0answers
72 views

On semicontinuity of Hilbert function for a zero dimensional scheme

Let, $X$ be a zero dimensional subscheme of $\Bbb P^n$ and let us define a function as follows: $h_{\Bbb P^n}(X ,d) = \binom {n+d}{n}$ - dim $I_{X}(d)$ , where dim $I_{X}(d)$ = the dimension of ...
2
votes
0answers
40 views

Second order non-instantaneous impulsive evolution equations

The first order linear non-instantaneous impulsive evolution equations is given as; $u'(t)=Au(t)~~ t\in[s_i,t_{i+1}],\,i\in\mathbb{N_0}:=\{0,1,2,...\}$ $u(t_i^+)=(E+B_i)u(t_i^-),\,\,i\in\mathbb{N}:=...
6
votes
1answer
256 views

To find a point in Teichmüller space or measured foliation, how many lengths of curves do you need?

To parametrize Teichmüller space, it suffices to measure the hyperbolic lengths of a finite number of curves. It is well-known that $9g-9$ curves suffice, by a standard pair-of-pants argument given in,...
0
votes
1answer
73 views

The mean E(X) of negative binomial distribution [closed]

What I know about the mean of the negative binomial distribution is E(x)=r(1-p)/p. but there are some questions use E(x)=r/p as the mean. Very confusing and I don't understand at all. For example: ...
5
votes
1answer
63 views

Coloring in Combinatorial Design Generalizing Latin Square

I have a question about a combinatorial design very similar to a Latin Square, which is arising out of an open problem in graph theory. The design is an $n \times n$ matrix whose entries we want to ...
0
votes
1answer
137 views

Stochastic Calculus vs Stochastic Processes in Finance [on hold]

I'm a second year student, interested in financial mathematics, who's trying to plan out his degree path currently. There's a stochastic processes unit offered in year 3 and a stochastic calculus unit ...
2
votes
1answer
145 views

For $G$ an adjoint Chevalley group, are all of $G(\mathbb Z)$'s finite-index subgroups congruence subgroups?

Let $G$ be an adjoint Chevalley group. Are all of $G(\mathbb Z)$'s finite-index subgroups congruence subgroups? I read a theorem that states: When $G$ is the universal Chevalley group and it's not of ...
2
votes
0answers
52 views

Stable m-Calabi Yau property for Frobenius categories

Let $C$ be a Frobenius category. The stable category $\underline{C}$ is called $m$-Calabi Yau in case it is Hom-finite and there is a functorial duality $D \underline{Hom}(X,Y)=\underline{Hom}(Y,\...
5
votes
2answers
230 views

Hopf structure on the universal enveloping of a super Hopf algebra

The universal enveloping algebra of a Lie algebra has a canonically defined Hopf algebra structure. Is the same true of the universal enveloping of a super Lie algebra? A presentation in terms of the ...
4
votes
0answers
139 views

Reference request: A knot is tame if and only if it has a tubular neighbourhood

Definitions: A knot is an embedding $\kappa:S^1\hookrightarrow S^3$ (we do not require smooth or polygonal). Two knots $\kappa,\,\lambda:S^1\hookrightarrow S^3$ are equivalent if one of the following ...

15 30 50 per page