We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−∆)γ/2, 0 < γ ≤ 1). We show in this paper that if θ ∈ C((0, T ); C1−γ), or θ ∈ Lr((0, T ); Cα) with α = 1−γ+ γ r is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in (0, T ]× R2. This result improves our previous result in [18].

We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on [0, 1]n . We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for n ≥ 3. As a consequence, we show that not every n-quasi-copula induces a signed measure on [0, 1]n . © 2010 Elsevier B.V. All rights reserved.

We introduce new necessary conditions, k-quasi-hamiltonicity (0 k n ? 1), for a digraph of order n to be hamiltonian. Every (k + 1)-quasi-hamiltonian digraph is also k-quasi-hamiltonian; we construct digraphs which are k-quasi-hamiltonian, but not (k + 1)-quasi-hamiltonian. We design an algorithm that checks k-quasi-hamiltonicity of a given digraph with n vertices and m arcs in time O(nm k). We...

In 1964, Erdős proved that for any α > 0, an l-uniform hypergraph G with n > n0(α, l) vertices and α ( n l ) edges contains a large complete l-equipartite subgraph. This implies that any sufficiently large G with density α > 0 contains a large subgraph with density at least l!/ll. In this note we study a similar problem for l-uniform hypergraphs Q with a weak quasi-random property (i.e. with ed...

The domain theoretic notion of lifting allows one to extend a partial order in a trivial way by a minimum. In the context of Quantitative Domain Theory (e.g. [BvBR98] and [FK93]) partial orders are represented as quasi-metric spaces. For such spaces, the notion of the extension by an extremal element turns out to be non trivial. To some extent motivated by these considerations, we characterize ...

Exsul Hutton (Diptera, Muscidae) is revised and the genus diagnosis is enlarged. The female of Exsul singularis Hutton is described for the first time. The male and female terminalia of all species are described and illustrated. Exsul alfredoi sp. n. is described and illustrated and compared with the other known species. A key to separate the species is given.

Two-dimensional (2-D) photo-count mapping on CMOS single photon avalanche diodes (SPADs) has been demonstrated. Together with the varied incident wavelengths, the depth-dependent electric field distribution in active region has been investigated on two SPADs with different structures. Clear but different non-uniformity of photo-response have been observed for the two studied devices. With the h...