We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on category C. Not only this result allows to obtain categorical counterpart P of Császár-Pervin quasi-uniformity P, that we characterize as transitive compatible with an interior operator, but also permits describe those topogenous orders are induced by The P⁎ P−...

We study decoupling in quasi-Banach spaces. We show that decoupling is permissible in some quasi-Banach spaces (e.g., Lp and Lp/Hp when 0 < p < 1) but fails in other spaces such as the Schatten ideal Sp when 0 < p < 1. We also relate our ideas to a possible extension of the Grothendieck inequality.

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇) θ + κΛθ = 0 u = Λα−1R⊥θ. with κ > 0, α ∈ (0, 1] and θ0 ∈ L2(R2). We remark that the extra Λα−1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence an...

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The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function. However, most existing algorithms are too slow or even impractical for large-scale problems, due to the singular value decomposition (SVD) or eigenvalue decomposition (EVD) of the whole matrix in each iteration. In this paper, we rigorously prove that for any 0< p≤ 1, p1, p2 > 0 satisfying 1/p= 1/p...

In [3,4,5], we have developed a new tool called the quasi solution which approximate in some sense the compressible Navier-Stokes equation. In particular it allows to obtain global strong solution for the compressible Navier-Stokes equations with large initial data on the irrotational part of the velocity ( large in the sense that the smallness assumption is subcritical in terms of scaling, it ...

The differential uniformity of a mapping F : F2n → F2n is defined as the maximum number of solutions x for equations F (x+a)+F (x) = b when a ̸= 0 and b run over F2n . In this paper we study the question whether it is possible to determine the differential uniformity of a mapping by considering not all elements a ̸= 0, but only those from a special proper subset of F2n \ {0}. We show that the ans...