In this article we will present some problems that have weak symmetries. In contrast to a proper symmetry, a weak symmetry acts only on a subset of the variables and preserves the feasibility state only with respect to a subset of the constraints. Therefore, breaking weak symmetries with standard techniques would lead to a loss of solutions. This article presents also a modelling technique whic...

In this paper, we classify all generalized quadrangles weakly embedded of degree 2 in projective space. More exactly, given a (possibly infinite) generalized quadrangle Γ = (P,L, I ) and a map π from P (respectively L) to the set of points (respectively lines) of a projective space PG(V ), V a vector space over some skew field (not necessarily finite-dimensional), such that: (i) π is injective ...

We discuss the axioms for vertex algebras and their modules, using formal calculus. Following certain standard treatments, we take the Jacobi identity as our main axiom and we recall weak commutativity and weak associativity. We derive a third, companion property that we call “weak skew-associativity.” This third property in some sense completes an S3-symmetry of the axioms, which is related to...

The purpose of this paper is to consider the Mond-Weir type dual model for a class of non-smooth multiobjective semi-infinite programming problem. In this work, we use generalization of convexity namely ( , ) G F θ − convexity and Kuhn-Tucker constraint qualification, to prove new duality results for such semi-infinite programming problem. Weak, strong and converse duality theorems are derived....

— We give a new proof for microlocal resolvent estimates for semi-classical Schrödinger operators, extending the known results to potentials with local singularity and to those depending on a parameter. These results are applied to the study of the stationary Schödinger equation with the approach of semi-classical measures. Under some weak regularity assumptions, we prove that the stationary Sc...

Given a finite point set P ⊂ R, we call a multiset A a one-sided weak ε-approximant for P (with respect to convex sets), if |P ∩ C|/|P | − |A ∩C|/|A| ≤ ε for every convex set C. We show that, in contrast with the usual (two-sided) weak ε-approximants, for every set P ⊂ R there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

A weak version of the cosmic censorship hypothesis is implemented as a set of boundary conditions on exact semi-classical solutions of two-dimensional dilaton gravity. These boundary conditions reflect low-energy matter from the strong coupling region and they also serve to stabilize the vacuum of the theory against decay into negative energy states. Information about low-energy incoming matter...

Named entity recognition (NER) plays an important role in the NLP literature. The traditional methods tend to employ large annotated corpus to achieve a high performance. Different with many semi-supervised learning models for NER task, in this paper, we employ the graph-based semi-supervised learning (GBSSL) method to utilize the freely available unlabeled data. The experiment shows that the u...

The dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as operator DAE of semi-explicit structure. These models include flexible multibody systems as well as applications with boundary control. In order to use adaptive methods in space, we analyse the properties of the Rothe method concerning stability and convergence for this kind of systems. For this, we c...