Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces [PDF]
Consider the Cauchy problem (1) \(x' = f(t,x)\), \(x(0) = x_0\) in a Banach space \(E\). Let \(J = [0,T]\) and \(B_r = B (\theta, r)\) be the ball in the space \(E\). Assume that \(t \to f (t,x(t))\) is a Pettis integrable function for each strongly absolutely continuous function \(x : J \to E\).
Cichoń, Mieczysław +1 more
openaire +1 more source
A full classification of the isometries of the class of ball‐bodies
Abstract Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball‐bodies, endowed with the Hausdorff metric. ‘Ball‐bodies’ are convex bodies which are intersections of translates of the Euclidean unit ball.
Shiri Artstein‐Avidan +2 more
wiley +1 more source
TheanoLM - An Extensible Toolkit for Neural Network Language Modeling
We present a new tool for training neural network language models (NNLMs), scoring sentences, and generating text. The tool has been written using Python library Theano, which allows researcher to easily extend it and tune any aspect of the training ...
Enarvi, Seppo, Kurimo, Mikko
core +1 more source
Modeling musicological information as trigrams in a system for simultaneous chord and local key extraction [PDF]
In this paper, we discuss the introduction of a trigram musicological model in a simultaneous chord and local key extraction system. By enlarging the context of the musicological model, we hoped to achieve a higher accuracy that could justify the ...
Leman, Marc +2 more
core +1 more source
Normal covering numbers for Sn$S_n$ and An$A_n$ and additive combinatorics
Abstract The normal covering number γ(G)$\gamma (G)$ of a noncyclic group G$G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for γ(Sn)$\gamma (S_n)$ and γ(An)$\gamma (A_n)$ depending on the arithmetic structure of n$n$. In particular we determine the limsups over γ(Sn)/n$\gamma (S_n) / n$ and γ(An)
Sean Eberhard, Connor Mellon
wiley +1 more source
On the Kneser problem for two-dimensional differential systems with advanced arguments
For the differential system with advanced arguments , sufficient conditions are established for the existence and uniqueness of a solution of the Kneser problem and the asymptotic behaviour of this solution is studied.
Kiguradze I, Partsvania N
doaj
Approximate Graph Coloring by Semidefinite Programming [PDF]
We consider the problem of coloring k-colorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3-colorable graph on $n$ vertices with min O(Delta^{1/3} log^{1/2} Delta log n), O(n^{1/4} log^{1/2} n)
Karger, David +2 more
core +1 more source
Cubical coloring -- fractional covering by cuts and semidefinite programming
We introduce a new graph invariant that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings.
Šámal, Robert
core +2 more sources
Asymmetric graphs with quantum symmetry
Abstract We present an infinite sequence of finite graphs with trivial automorphism group and non‐trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are the first examples of any asymmetric classical space that has non‐trivial quantum symmetries.
Josse van Dobben de Bruyn +2 more
wiley +1 more source
Prosoluble subgroups of the profinite completion of the fundamental group of compact 3‐manifolds
Abstract We give a description of finitely generated prosoluble subgroups of the profinite completion of 3‐manifold groups and toral relatively hyperbolic virtually compact special groups.
Lucas C. Lopes, Pavel A. Zalesskii
wiley +1 more source

