Trending questions
159,057 questions
0
votes
0
answers
33
views
On the I-method's energy increment calculation in a paper of Dodson
I am currently reading Dodson's Global Well-posedness for the Defocusing, Quintic Nonlinear Schrödinger Equation in One Dimension for Low Regularity Data article and I am trying to understand Theorem ...
- 910
0
votes
0
answers
29
views
How to synthetize a controller $\dot{u} = F x + G u$ which stabilizes $\dot{x} = Ax + Bu$?
$\textbf{Introduction}$: I study linear control theory. Among strategies, we begin with vector field $Ax + Bu$, $A \in M_{n^2}(\mathbb{R})$, $B \in M_{n \times m}(\mathbb{R})$, and synthesize a ...
- 131
0
votes
0
answers
79
views
On the multiplicative group of quotients of polynomial rings
Related to this.
The $p+1$ factorization algorithm works over $\mathbb{Z}/n\mathbb{Z}[x]/f(x)$
and hopes $p+1$ to be smooth.
We are trying to generalize this to multivariate case
and also try to find ...
- 25.4k
0
votes
0
answers
16
views
Complexity of finding single source paths with capacity constraints and length constraints
Let $G=(V,A)$ be a directed graph with distinguished vertex $s\in V$ and let $c:A\rightarrow{\mathbb N}$ denote arc capacities. For any $t\in V,t\not=s$ we are given two numbers: $C_{t},L_{t}$. Let $...
- 21
0
votes
0
answers
50
views
Kirszbraun-like extension of periodic functions
Let $\Lambda \subset \Lambda' \subset \mathbb{R}^n$ be lattices. Let $f : \Lambda' \rightarrow \mathcal{H}$ be a $a$-Lipschitz function, where $\mathcal{H}$ is a finite-dimensional Hilbert Space. ...
- 1
0
votes
0
answers
37
views
Telling if matrix is contractive from the spectrum of its Choi-Jamiołkowski isomorphism?
Suppose $T$ is a ${d^2}\times {d^2}$ completely positive matrix, and $M$ is ${d^2}\times {d^2}$ matrix obtained by taking Choi-Jamiołkowski isomorphism of $T$. Is it possible to tell if $T$ is ...
- 2,252
0
votes
0
answers
44
views
How to solve recurrences of the form $T(i,n) = \min_{x} f(x) + \max\{T(i,x),T(x,n)\}$?
I am interested in solving a recurrence of the form:
$$T(i,n) = \begin{cases}\min_{x\in\{i+1,\ldots,n-1\}} f(x) + \max\{T(i,x),T(x,n)\} & \mbox{If $i<n-1$}\\ 1 & \mbox{otherwise}\end{cases}\...
- 127