Math

### Acceleration via smoothing

Is the following approach to accelerating the rate of convergence of $(1+1/2+\dots+1/n)- \ln n$ (with $n=1,2,3,\dots$), and other sequences like it, in the literature? Let $f(t)=(\sum_{1 \leq n \leq t} 1/n) - \ln t$ for $t \geq 0$, so that $f(t)$ tends to Euler's constant $\gamma$ as $t \rightarrow \infty$. .... Sadie: 12 hours ago

Math

### Analog to the Chinese Remainder Theorem in groups other than Z_n.

The idea hit me when I was in my Elliptic Curve Cryptography class. $Z_n \leftrightarrow Z_{f_1} \times Z_{f_2} \times ...$ where $f_1 \times f_2 \times ... = n$ and $\{f_1, f_2, ...\}$ are pairwise coprime. Applications of this Chinese Remainder Theorem not only include computational speedups (in the case of .... Autumn: 13 hours ago

Math

### Group action: 'Minimal' subgroup generating an orbit

Let $G$ be a symmetric group on a finite set acting on another finite set $X$ through a natural action $\alpha:G \times X \to X$, $\alpha(g,x)=gx$. Let $x \in X$ and consider the orbit $G \cdot x := \{gx: g \in G\}$. Assuming that $|G\cdot x| <|G|$, can we always .... Ryan: 13 hours ago

Math

### An elementary inequality for graph Laplacians

Let $G$ be an arbitrary graph on $n$ vertices and $\mathcal L$ be its Laplacian. I need to show that \begin{equation}\tag{$*$} \langle \mathcal Lx,\mathcal L(|x|^{p-2}x)\rangle_{\mathbb R^n}\ge 0\qquad \hbox{for all }x\in \mathbb R^n \end{equation} and small $p\in (2,\infty)$ (my guess is that $p\approx 3$ will do), where $|x|^{p-2}x$ is the coordinatewise .... Miles: 13 hours ago

Math

### Do the signs in Puppe sequences matter?

A basic construction in homotopy is Puppe sequences (http://en.wikipedia.org/wiki/Puppe_sequence). Given a map $A \stackrel{f}{\to} X$, its homotopy cofiber is the map $X\to X/A=X \cup_f CA$ from $X$ to the mapping cone of $f$. If we then take the cofiber again, something remarkable happens: $(X/A)/X$ is naturally homotopy equivalent to the .... Savannah: 15 hours ago

Math

### Lovasz local lemma for the edge model

In order to successfully apply the Lovasz local lemma, one needs the events to be relatively independent. This (sometimes) works well in the $G(n,p)$ model of random graphs, where the presence or absence of edges doesn't affect the events they are not involved in. However, in the $G(n,m)$ model (where .... Gabriella: 15 hours ago

Math

### examples of Kähler manifolds with trivial Hodge numbers and first Chern classes

Yesterday I asked the following question to which abx has given a positive answer. examples of Kähler manifolds with trivial odd Betti numbers and first Chern classes (https://mathoverflow.net/questions/168029/examples-of-kahler-manifolds-with-trivial-odd-betti-numbers-and-first-chern-clas) But I suddenly realized that those Fano manifolds I mentioned in the quesion above (flag manifolds $G/P$ and Fano contact manifolds) not .... Aurora: 15 hours ago

Math

### $| f_n |^p - | f |^p - | f_n-f |^p$ converges in distribution sense if $f_k$ converges almost everywhere and weakly to $f$?

Let $1<p<\infty$ and $f_n$ be a sequence in $L^p(S^1)$ that converges weakly to some $f$. Here $S^1$ is the circle so we are dealing with periodic functions. Let us see if $| f_n |^p - | f |^p - | f_n-f |^p$ converges to zero in distribution sense. This means .... Amelia: 16 hours ago

Math

### Global sections of determinant bundle of symmetric powers

Let $E$ be a globally generated vector bundle of rank $r$ on a normal irreducible projective variety $X$. Suppose that $E$ induces a finite map $$X \to \mathbb{G}r (H^0(E), r)$$ to the Grassmannian of rank r quotients. Can we say that a symmetric power of $S^mE$ for $m>>0$ induces an .... Jace: 16 hours ago

Math

### Splitting the determinant polynomial into linear factors - a Dedekind problem

Here's the question in a nutshell. For some $n\in\mathbb N$, we consider the polynomial $\det\left(\left(X_{i,j}\right) _ {1\leq i\leq n,\ 1\leq j\leq n}\right)\in\mathbb Z\left$ in $n^2$ indeterminates $X_{i,j}$. This is known to be irreducible over $\mathbb Z$, but is there a "nice" ring in which $\mathbb Z$ embeds and where this .... Amir: 17 hours ago