Questions tagged [tag-removed]
This tag is to be used only when re-tagging highly(!) off-topic questions where none of the actual tags would make sense; all actual tags the questioner has used are removed and something is needed to have some tag, which is enforced by the software, so this tag is used. However note that this tag is also used in the process of moderators deleting tags. Thus a question having this tag does most of the time not mean that somebody found it off-topic.
50
questions with no upvoted or accepted answers
36
votes
0
answers
1k
views
Two-convexity ⇒ Lefschetz?
Assume that
$\Omega$ is an open simply connected set in $\mathbb R^n$
(two-convexity) if 3 faces of a 3-simplex belong to $\Omega$ then whole simplex in $\Omega$.
Is it true that any component of ...
- 43.7k
20
votes
0
answers
2k
views
Can the similarity between the Riesz representation theorem and the Yoneda embedding lemma be given a formal undergirding?
For example, by viewing Hilbert spaces as enriched categories in some fashion? (I suppose the same idea of considering the inner product of a Hilbert space as a generalized Hom-set has also been ...
- 5,652
16
votes
0
answers
644
views
Codimension Two Embeddings in Goodwillie-Weiss Manifold Calculus, and the Difficulty of Fundamental Groups
In manifold calculus, there are various analyticity estimates which run into trouble for codimension two embeddings. For instance, the functor $\operatorname{Emb}(M,N)$ is analytic in $M$ if $\dim M \...
- 3,301
10
votes
0
answers
350
views
Krull dimension and Morley rank
Definition : A Topological space $\mathcal{D}$ is called noetherian if it satisfies the descending chain condition for closed subsets. We define the dimension of $\mathcal{D}$ to be the supremum of ...
- 1,882
8
votes
0
answers
3k
views
elementary exact sequence of normal sheaves
Let $Z \subset Y \subset \mathbb{A^n}$ be a smooth subvarieties of $\mathbb{A^n}$.
I'm trying to show that there is an exact sequence of normal bundles.
$0 \rightarrow N_{Z/Y} \rightarrow N_{Z} \...
- 327
8
votes
0
answers
2k
views
Homotopy groups of a Bouquet of n-spheres
Let $$X=\vee_{\alpha\in A} S_{\alpha}^n$$ be a bouquet of $n$-spheres.
Q: How does one compute the homotopy groups $\pi_k(X)$?
- 7,521
7
votes
0
answers
313
views
Other applications of the 'increment' approach
I would like to hear about other instances of the so-called 'increments' approach, first used by Roth to prove that a subset of $\mathbb{N}$ of positive upper density contained infinitely many ...
- 25.5k
6
votes
0
answers
476
views
Symmetric matrices with $\rho(A)\gg\|A\|_\infty$
For a symmetric real matrix $A$, denote by $\rho(A)$ the spectral radius of $A$, and by $\sigma(A)$ the largest absolute row sum of $A$; that is, $\sigma(A)=\max_i \sum_j |a_{ij}|$, where $a_{ij}$ are ...
- 22.8k
6
votes
0
answers
1k
views
Why is mechanical differentiation so hard to get right?
This question is related to this question on differentiation/integration which asks why differentiation is mechanical but integration is an art. The answers given all make a huge assumption: that one ...
- 11.7k
5
votes
0
answers
396
views
Azimuthal and polar integration of a 3D Gaussian
Numerical evaluation of the following integral of a 3D gaussian $G$ seems to result in a 1D Gaussian $g$:
$$\int_{0}^{2\pi}\int_{0}^{\pi}G(R,\phi,\theta)\sin\theta\ \text{d}\theta \ \text{d}\phi= g(R)$...
- 347
5
votes
0
answers
228
views
Does every stack with a connection admit an atlas with a connection?
Dear all,
Let $S$ be a scheme in characteristic $0$,
and let $\mathscr{X}/S$ mean a crystal in Artin stacks over $S$ in the sense of this handout, page 4, Definition 0.5, where we replace the scheme $...
- 2,230
4
votes
0
answers
386
views
A question on an intuitive way to look at stacks
I am reading the chapter "Introducing Algebraic Stacks" in The Stacks Projects to get a feeling for them. There is a small point that throws me off. They denote $\mathcal{M}_{1, 1}$ the moduli stack ...
- 805
4
votes
0
answers
282
views
Easy to find roots
Is there a smooth function $f:\mathbb{R} \to \mathbb{R}_{\geq 0}$ such that:
1) $\lim_{x \to \infty} = \lim_{x \to -\infty} = 0$
2) $\forall x > 0$, $f'(x) < 0$
3) $\forall x < 0$, $f'(x) &...
- 3,125
3
votes
0
answers
1k
views
What is the inverse kernel of this integral transform?
I am looking for the associated inverse kernel to the integral transform $T$ defined by
$(Tf)(u) = \int_{-\infty}^{+\infty} K(u,t)f(t) \ dt,\ \ u \in \mathbb{R^+}$
whose kernel is $K(u,t) = \frac{...
- 31
3
votes
0
answers
145
views
P-adic Weierstrass Lemma for several variables
The p-adic Weiestrass lemma asserts that a power series $f(z)$ with coefficients in the ring of integers of a local field can be factored as $π^n·u(z)·p(z)$ where u(z) is a unit in the ring of power ...
- 31
3
votes
0
answers
370
views
Extension divergence-free, curl-converging vector field
Hi.
Consider a smooth open Set $\Omega\subset\mathbb{R}^3$ and a bounded sequence of vector fields $(u_n)_n \in L^2(\Omega)$ having $0$ divergence. I know how to extend this sequence to the whole ...
- 2,710
3
votes
0
answers
154
views
Topology of K3 as a sum of two abelian fibrations.
Let $E$ be a blow-up of $\mathbb{P}^2$ at 9-points in the bases locus of a pencil of elliptic curves (A $T^2$ fibration over $S^2$).
K3 surfaces is obtained by removing a fiber from two copies of $E$ ...
3
votes
0
answers
796
views
Tamagawa number for functional fields
Let $G$ be a split semi-simple simply connected group over a global field $F$ and let
$\omega$ be a top-degree differential form on $G$ without zeroes (defined over $F$). It is well
known that $\omega$...
- 6,957
3
votes
0
answers
379
views
Systems of linear octonionic equations
Is there theory of determinants, rank of matrices and systems of linear equations with octonionic coefficients? Does anybody could indicate references? I want to know mainly does there exist a ...
- 75
3
votes
0
answers
301
views
functions on intervals with endpoints
Would most analysts say that $(2/3) x^{3/2}$ is an antiderivative of $x^{1/2}$ on $[0,\infty)$, or
just on $(0,\infty)$?
More generally, is there a standard interpretation of the assertion "$F$ is an ...
- 19.4k
3
votes
0
answers
401
views
Statistic of cubic Irreducible polynomial with cyclic Galois group
Van der Waerden proved for monic irreducible polynomials $f$ of degree $n$ with bounded height $X$:
$$
|\{ f(x)\in \mathbb{Z}[x]: Gal(f)\neq S_n \}|=o(X)
$$
Where height of $f$ is defined by maximum ...
- 2,468
3
votes
0
answers
315
views
Drawing a combinatorial 3-configuration of points and lines with pseudolines
This question is related to the question of drawing a combinatorial 3-configuration of points and lines with straight lines. We only relax the condition and admit drawings with pseudolines. Let us ...
- 784
2
votes
0
answers
291
views
Prime divisors of the difference set
Fix $c\in(0,1)$, and let $N$ be a (large) positive integer. Given a set $A=\{0=a_1<\dots<a_n=N\}$ of density $\alpha:=n/N>c$ with $\gcd(A)=1$, I want to find a prime dividing as few ...
- 22.8k
2
votes
0
answers
189
views
open orbits and invariant distributions
Suppose $G$ is a p-adic algebraic group, $P=MN$ a parabolic subgroup of $G$ with its Levi decomposition, $\sigma$ be a irreducible representation of $M$, we use $I(\sigma)$ to denote the unique ...
- 2,679
2
votes
0
answers
298
views
volume under induced metric of preimage set of a regular value under a polynomial map
I am interested in the following kind of polynomial map:
$$ f: \mathbb{T}^k \to \mathbb{R}^n$$
where $f$ is a polynomial map of a certain maximum degree $d$, in the sense that if we imbed $\mathbb{T}^...
- 4,354
2
votes
0
answers
684
views
Vector bundles on some non-projective surfaces
Let $X$ be a smooth projective curve over a field $k$ and let $L$ be a line bundle on $X$.
I will denote by $S$ the total space of $L$ -- this is a smooth surface over $k$ containing
$X$ (as the zero ...
- 6,957
2
votes
0
answers
77
views
Characterizing local homeomorphisms into an exponent
Let $X$,$Y$, and $Z$ be (compactly generated) spaces. Suppose $f:Z \to Y^X$ is a local homeomorphism. How can we tell this from its adjoint $\tilde f:Z \times X \to Y$? I.e., I want a property $P$ ...
- 15.3k
2
votes
0
answers
677
views
Strong Bezout's Identity?
Let $\{ a_i \}_{i=1}^N $ be a set of elements of the ring of integers, $\mathbb{Z}_D$ and define $g = \text{gcd}(a_1, a_2,\ldots, a_N, D)$. Then Bezout's Identity states that there exists another set $...
- 133
1
vote
0
answers
1k
views
Properties of a rational function of multiple variables
Suppose you are given a multivariable rational function f(x0,x1,x2,x3,..,xn), so the only four operation are +,-,*,/.
Assume that all constants and exponents are integers within certain range.
I ...
1
vote
0
answers
121
views
Existence of open dense subset in a Lie group
Let $G=S\cdot R$ be a Levi-Malcev decomposition of a connected complex Lie group
and $\Gamma$ a discrete subgroup of $G$ such that the subgroups
$\Gamma_g := \Gamma\cap (gSg^{-1})$ are finite for all ...
- 645
1
vote
0
answers
263
views
Average weighted value of a linear functional over increasing bounded subsets of Z^n
Say you're working within the finite-dimensional free Z-module $\mathbb{Z}^n$, and you want to impose a "norm" on this module. By a "norm" I mean a function $\|·\|: \mathbb{Z}^n \to \mathbb{R}$ which ...
- 4,525
1
vote
0
answers
389
views
The used symbols for equality and equivalence
Background: I am currently developing a general purpose programming language which allows formal verification (i.e. correctness proofs) of programs. During the development it came out that a lot of ...
- 165
1
vote
0
answers
115
views
A question about smoothness
$f$ is a smooth function on $[0,+\infty)$ and $f(x)>0$ for all $x>0$. Then does the following equivalence hold :
$\phi(x,y)=f(\sqrt{x^2+y^2})$ is smooth if and only if $f^{(k)}(0)=0$ for all ...
- 1,361
1
vote
0
answers
243
views
Evaluating the integral $\int_{a}^{+\infty} \frac{\exp(-bx)}{x+c} Ei(x) dx$
I'm trying to evaluate or simplify this integral:
$$I_{a,b,c} = \int_{a}^{+\infty} \frac{\exp(-bx)}{x+c} Ei(x) dx $$
with $a,b,c \in \mathbb{R}_+^*$.
and $ Ei(x) =\int_{-\infty}^{x} \frac{\exp(t)}{t}...
- 11
1
vote
0
answers
283
views
Monge Ampere and Calculus
[ I posted the question on Math StackExchange but didn't get any reply nor comment, so I'm trying here ]
I am learning about mass transportation theory and the Monge-Ampere equation, to transport a ...
- 481
1
vote
0
answers
256
views
Fractional Radon - Nikodym derivative
Given $f$ a function measurable in $[0,\infty]$ defined as $$\frac{d\mu}{d\nu}$$
such that, for every measurable set $A$ we have:
$$\mu(A)=\int_A{}fd\nu$$
the function $f$ is called $Radon - Nikodym\...
- 399
1
vote
0
answers
287
views
Homotopy-Fibre Sequence of Classifying Spaces
Let $G$ be a topological group and $H$ be a normal subgroup of $G$ (I think $H$ is required to be admissible in the sense that the quotient map $G\to G/H$ is a principal $H$-bundle, am I right?). Then ...
- 1,108
1
vote
0
answers
148
views
Morphisms, inducing isomorphisms on global functions
Let $f:X\to Y$ be a surjective morphism of complex varieties with $Y$ affine. Assume that every fiber of this morphism has the property that all the global functions are constant.
What else do I need ...
- 1,550
1
vote
0
answers
323
views
Some help with differential operators
Hello
I am trying to follow the derivation of the Generalized Cornish Fisher Expansion from this paper.
I dont see how the author goes from equation (21) to (22).
For one to be able to do this ...
- 569
1
vote
0
answers
417
views
Recursive algorithm for integration of complex functions
Integrals of the form $\int_{0}^{\pi} d\theta \sin\theta f(r(\theta)) j_{\ell_{1}} (a r(\theta))y_{\ell_{2}}(br(\theta))P_{\ell_{3}} ^{m} (\cos(\theta))P_{\ell_{4}} ^{m}(\cos(\theta))$, where $f$ is a ...
1
vote
0
answers
148
views
Do higher dimensional maxima of a real valued multivariable function form a cell complex?
Suppose $f: R^n \rightarrow R$ is a positive real valued function. Let $\lambda_1, \ldots , \lambda_i$ be the first $i$ ordered eigenvalues of the Hessian $Hess(f)$. Let $v_1, \ldots, v_i$ be the ...
- 11
1
vote
0
answers
545
views
A transformation of infinite series
Suppose I have a convergent infinite series $\sum_{n=0}^\infty (-1)^n a_n = S_0$ and $0 < S_0 < 1$. Write $s_n$ for the $n$-th partial sum. ($s_n = \sum_{k=0}^n (-1)^k a_k$) Now consider the ...
- 1,424
0
votes
0
answers
243
views
Checking whether this would be bounded
It may be better to post this question here. Assume that $M$ is an $m$ by $m$ ($m$ is an even number) symmetric
positive-semi-definite matrix with exactly $m/2$ positive eigenvalues
and every entry of ...
- 1
0
votes
0
answers
187
views
Matrix Maximization.
Hi everyone,
I'm trying to solve/define the following optimization problem:
$\max_M f(M)$
s.t.
$M \theta = b$
$\sum_j \theta_j = 1$
When:
M is an m*n real matrix
$\theta$ and $b$ are n*1 column ...
- 101
0
votes
0
answers
1k
views
"closed form" finite sum
If a finite sum has a definite integral representation, for which it can be proved the underlying indefinite integral is not an elementary function, then does this imply the original finite sum can ...
- 1
0
votes
0
answers
329
views
Properties of morphisms induced by divisors on curves
There are a few properties from Hartshorne IV on curves that I am trying to verify. Let $D$ be an effective divisor on a curve (integral scheme of dimension 1, proper over $k$, regular) $X$, $\dim |D|...
- 419
0
votes
0
answers
308
views
Is there an intuition for the exterior calculus identity dd = 0
Considering an exterior derivative $d$, which may be discretized as the transpose of the boundary operator on a simplicial mesh, I have read and seen that $dd = 0$, but I have not seen an intuitive ...
- 193
0
votes
0
answers
808
views
covariant derivative complex manifold
Assume we have $X$ a complex manifold and $Y = Y^{\alpha} \frac{\partial}{\partial z^{\alpha}}$ and $Z = Z^{\alpha} \frac{\partial}{\partial z^{\alpha}}$ two vector fields on $X$. Let $\nabla$ be the ...
- 23
0
votes
0
answers
499
views
Integrating the product of two functions one of which has a positive non-integer power
I'm looking to integrate several functions having the form
$\int_0^T \frac{ sin(\omega \tau) }{\omega} \tau^{2H} d\tau$
where $2H \ge 0$ but may not be an integer. I'd like to know if the machinery ...
- 661
0
votes
0
answers
189
views
Packing Icons Onto A screen
You are trying to pack icons onto a screen that is divided into n horizontal rows of uniformly varying size. The rows narrow by a fixed ratio as one goes up the screen from the bottom. Since the icons ...
