Annali di Matematica Pura ed Applicata最新文献

A magma S is said to be antiassociative if ((ab)c ne a(bc)) holds for any elements a, b, c of S. Antiassociative magmas lie at the opposite pole from associative ones, known as semigroups. In this paper, we study antiassociative magmas focusing on their properties and examples that can be seen from Cayley tables. We provide a test for the antiassociativity of a finite magma and give some general methods for constructing antiassociative magmas. We also characterize, describe, and count all antiassociative magma structures on a 3-element set, all their isomorphism classes, and all classes of equivalent magmas of this type.

The paper deals with the stochastic two-dimensional Navier–Stokes equations for homogeneous and incompressible fluids, set in a bounded domain with Dirichlet boundary conditions. We consider additive noise in the form (G,textrm{d}W), where W is a cylindrical Wiener process and G a bounded linear operator with range dense in the domain of (A^gamma ), A being the Stokes operator. While it is known that existence of invariant measure holds for (gamma >1/4), previous results show its uniqueness only for (gamma > 3/8). We fill this gap and prove uniqueness and strong mixing property in the range (gamma in (1/4, 3/8]) by adapting the so-called Sobolevskiĭ-Kato-Fujita approach to the stochastic N–S equations. This method provides new a priori estimates, which entail both better regularity in space for the solution and strong Feller and irreducibility properties for the associated Markov semigroup.

We study the behavior of the fractional convexity when the fractional parameter goes to 1. For any notion of convexity, the convex envelope of a datum prescribed on the boundary of a domain is defined as the largest possible convex function inside the domain that is below the datum on the boundary. Here we prove that the fractional convex envelope inside a strictly convex domain of a continuous and bounded exterior datum converges when (snearrow 1) to the classical convex envelope of the restriction to the boundary of the exterior datum.

We study some properties of (SU_n) endowed with the Frobenius metric (phi ), which is, up to a positive constant multiple, the unique bi-invariant Riemannian metric on (SU_n). In particular we express the distance between (P, Q in SU_n) in terms of eigenvalues of (P^*Q); we compute the diameter of ((SU_n, phi )) and we determine its diametral pairs; we prove that the set of all minimizing geodesic segments with endpoints P, Q can be parametrized by means of a compact connected submanifold of (mathfrak {su}_n), diffeomorphic to a suitable complex Grassmannian depending on P and Q.

We prove a result of existence and a maximum principle for strong solutions, for (t>0), to a parabolic p-Laplacian system with convective term.

This paper builds upon the work of D. Krejčiřík and V. Lotoreichik, focusing on optimizing the lowest point of the spectrum of the Laplacian in the exterior of a compact set under attractive Robin boundary conditions. We characterize the discrete spectrum of the Laplace operator under Robin boundary conditions using a harmonic Steklov eigenvalue problem in exterior domains. Assuming the lowest point of the spectrum is a discrete eigenvalue, we show that the exterior of a ball is a local maximizer among nearly spherical domains with prescribed measure in any dimension. However, generally, it is not the global maximizer of the first Robin eigenvalue under either prescribed measure or prescribed perimeter.

An abstract characterization of weakly monotone (C^*)-algebras, namely the concrete (C^*)-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotients of) suitable Exel–Laca algebras. The weakly monotone (C^*)-algebra indexed by ({mathbb N}) is shown to be a type-I (C^*)-algebra and its representation theory is entirely determined, whereas the weakly monotone (C^*)-algebra indexed by ({mathbb Z}) is shown not to be of type I.

Let (omega ) be a radial weight on the unit disc of the complex plane (mathbb {D}) and denote by (widehat{omega }(r)=int _r^1 omega (s),ds) the tail integrals. A radial weight (omega ) belongs to the class (widehat{mathcal {D}}) if satisfies the upper doubling condition

If (nu ) or (omega ) belongs to (widehat{mathcal {D}}), we describe the boundedness of the Bergman projection (P_omega ) induced by (omega ) on the growth space (L^infty _{widehat{nu }} ={ f: Vert fVert _{infty ,v}=text {ess sup}_{zin mathbb {D}} |f(z)|widehat{nu }(z)<infty }) in terms of neat conditions on the moments and/or the tail integrals of (omega ) and (nu ). Moreover, we solve the analogous problem for (P_omega ) from (L^infty _{widehat{nu }}) to the Bloch type space (mathcal {B}^infty _{widehat{nu }} = {f, text {analytic in} mathbb {D}: Vert fVert _{mathcal {B}^infty _{widehat{nu }}} ) (= sup _{zin mathbb {D}}(1-|z|)widehat{nu }(z)|f'(z)|<infty }.) Similar questions for exponentially decreasing radial weights will also be studied.

In this article, we study the asymptotic behavior of anisotropic nonlocal nonstandard growth seminorms and modulars as the fractional parameter goes to 1 without requiring the (Delta _2)-condition on the generalized Young function or its complementary function. This provides a so-called Bourgain-Brezis-Mironescu type formula for a very general family of functionals. In the particular case of fractional Sobolev spaces with variable exponent, we point out that our proof asks for a weaker regularity of the exponent than the considered in previous articles.