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...

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.

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [5, 8, 9]. The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) is the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a)− f(b)| ≤ k. We formulate the fractional weak...

Individual 1-3 mm biotite and muscovite clasts from Hanford sediment were contacted with 0.08 M CsNO3. They were examined using electron or X-ray microprobe methods, as intact specimens or sectioned perpendicular to their basal planes. Cs+ was observed to preferentially sorb to mica edges, steps on mica surfaces, or fractured regions. The localization of Cs conformed to hypothesized strong bind...

For small involutive and integral quantaloids Q it is shown that covariant presheaves on symmetric Q-categories are equivalent to certain subalgebras of a speci c monad on the category of symmetric Q-categories. This construction is related to a weakening of the subobject classi er axiom which does not require the classi cation of all subalgebras, but only guarantees that classi able subalgebra...

we start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{cambat}. as in cite{cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{n}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. the last chapter of this article asserts that, up to precise...

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 ± 7 kHz/√Hz with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as preci...

We first introduce 20 weak forms of continuity, which are closely related to 5 known weak forms of continuity. Then we classify them into 9 groups and give 12 decompositions of continuity. 1. Introduction. Continuity is one of the most important concepts in mathematics. In order to find deep properties of continuity, many weak forms of continuity were introduced in the literature. For instance,...

In this work we define generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures recently proposed in the literature. Moreover, we study some properties of the interior, the closure and other concepts in this new context. Mathematics Subject Classification: Primary 54A05, Secondary 54D10