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...

Abstract Dry-snow slab avalanches release due to crack propagation in a weak snow layer under cohesive slab. Crack speeds can provide insights into the potential size of and inform fracture avalanche models. Despite their importance, slope-scale speed measurements from real are limited. Further, most existing utilize appearance fractures on surface. However, we have no evidence that surface cra...

Well test analysis of multi-layer reservoir comprises several parts. The first part concerns the estimation of parameters values and next considers finding an appropriate method to determine the unknown reservoir parameters. If the initial estimations are less accurate and weak, the final assessment may lead to incorrect results, which are totally different from the reality. Utilizing Automated...

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.