All Questions

0answers
11 views

How do you generate orthogonal Rotations in d-dimensions?

I know that matrices that satisfy $\mathbf{x^TMx} > 0$ for all $\mathbf{x} \in \mathbb{R}^d$ are called positive definite matrices. It seems to me that a matrix that represents an $90^{\circ}$ ...
0answers
10 views

Realizing algebraic curves as complete intersections

I have two related questions about smooth complete algebraic curves (over $\mathbb{C}$). Does there exist a smooth complete algebraic curve $X$ that cannot be embedded as a complete intersection in ...
0answers
31 views

Map from real numbers to real numbers as abelian groups [on hold]

What is an example of an abelian group homomorphism from $\mathbb{R}$ to $\mathbb{R}$ that is NOT a linear transformation?
0answers
31 views

reference on aperiodicity and cluster

From this image: I believe there is a message relating those clusters drawn in picture and aperiodic tiling. Does anyone have some reference on this? Thank you:)
1answer
64 views

Proof of the Dunford-Pettis theorem

I would like to know where to find a complete proof of the Dunford-Pettis theorem: A sequence $(f_n)_{n\geq 0} \subset L^1$ is uniformly integrable if and only if it is relatively compact for the weak ...
1answer
40 views

Software producing complex trees

Does anyone know any kind of graph software that could produce graphs like this for publication? Those links and crosses and numbers actually needs to be presented…. Thank you:) One small update, ...
0answers
51 views

How to find generators to Mordell weil groups of elliptic curves using Sage software? [on hold]

I am new to sage.I want to find generators to Mordell Weil group of the Elliptic Curve $y^2=x^3-6321363052$. While using sage it gives error as increase decent and then make use of same command but I ...
0answers
46 views

Complex conjugation of positive roots

I have a simple question about root systems. Suppose that $G$ is a connected reductive group over the reals $\mathbb{R}$, and $T\subset G$ is a maximal torus (by this I mean that $T_{\mathbb{C}}$ is a ...
0answers
23 views

0answers
39 views

Image of the typenorm contains the squares

I am having a look at the paper Explicit CM-theory for level 2-structures on abelian surfaces by Bröker, Gruenewald and Lauter, and there is an argument which I don't understand. The main reason being ...
0answers
68 views

Is there an example of an SDE that has no weak solution? [on hold]

So far I couldn't find an example for an SDE for which there exists no weak solution. Do you know one?
1answer
107 views

Tensor product of certain Sobolev spaces on non-compact manifolds

Let $M$ be a non-compact Riemannian manifold of bounded geometry (i.e., its injectivity radius is uniformly positive and the curvature tensor and all its covariant derivatives are bounded in ...
0answers
66 views

Existence of affine hulls

(This question is inspired by Matthieu Romagny's answer to my previous question about base change properties of affine hulls.) Given a scheme $S$, it is well-known (cf. EGA I.9.1.21) that the ...
1answer
35 views

Parallel transport along a reparametrized geodesic

Let $M$ denote a Riemannian manifold, $\gamma$ a geodesic of $M$ defined on $\mathbb{R}$. Let $t_{0} \in \mathbb{R}$ and $(\alpha,\beta) \in \mathbb{R}^{2}$. I define the reparametrized geodesic ...
0answers
52 views

Cover a set with balls centered at smooth functions (Ascoli theorem)

Assume $M$ to be a compact $n$-dimensional manifold, endowed with a complete metric. Let us consider the space $C^\infty(M)$ endowed with the standard $C^\infty$ topology, i.e. generated by the ...
0answers
81 views

A variant of Chang's model with choice

Let $M_n$, $n < \omega$, be a models of $ZFC$ with the same ordinals, closed under countable sequences. Let $\alpha_n$ be an ordinal which is a regular cardinal in $M_n$. Question: Is it possible ...
0answers
35 views

Good Intermediate text on ODEs for self-study (meaning solved problems) [on hold]

So I am just about to finish Tenenbaum and Pollard's introductory text on ODEs and I wanted to go to the next level. I am doing this as a self-study, so I really appreciate the fact that T&P have ...
0answers
28 views

Properties of rearrangement maps

I have the following question to ask, concerning some properties of Schwarz radially decreasing rearrangements. It is well known that the map $u\rightarrow u^{\ast}$, being $u^{\ast}$ the Schwarz ...
1answer
81 views

Decay rate of the convolution of two functions

Let $f(x)=e^{-\frac{x^2}{2}}$ ($x\in\mathbb{R}$), and $g\in C^{\infty}(\mathbb{R})$ with $|g(x)|=O(e^{-k|x|^{\gamma}})$ as $|x|\to\infty$, for $k>0$, $\gamma>0$. Let $h=f*g$, the convolution of ...
0answers
71 views

Sums of $n$ powers [on hold]

I managed to resolve that $s(n) = 1^2+2^2+3^2...+n^2 = \dfrac {n(n+1)(2n+1)}{6}$ where $n$ is integer But I'm a bit confused how to resolve: $s(n,p) = 1^p+2^p+3^p...+n^p$ where $n$, $p$ are ...
0answers
188 views

Artin L-function and Zeta function of twisted Dirac operator

If one thinks of a Frobenius as an element in the fundamental group of an arithmetic curve and of a Galois representation $\sigma$ as a flat connection on the curve, then the definition of the Artin ...
0answers
52 views

Coloring summands of given n-partition with given weights of colors

Let $\lambda$ and $\sigma$ be n-partitions $\lambda_1+\lambda_2+\cdots+\lambda_l=n$ and $\sigma_1+\sigma_2+\cdots+\sigma_s=n$ Then let $M_{\lambda \sigma}$ be the number of ways to colour blocks of ...

15 30 50 per page