Mediterranean Journal of Mathematics最新文献

We study the set ({text {MA}}(X,Y)) of operators between Banach spaces X and Y that attain their minimum norm, and the set ({text {QMA}}(X,Y)) of operators that quasi attain their minimum norm. We characterize the Radon–Nikodym property in terms of operators that attain their minimum norm and obtain some related results about the density of the sets ({text {MA}}(X,Y)) and ({text {QMA}}(X,Y)). We show that every infinite-dimensional Banach space X has an isomorphic space Y, such that not every operator from X to Y quasi attains its minimum norm. We introduce and study Bishop–Phelps–Bollobás type properties for the minimum norm, including the ones already considered in the literature, and we exhibit a wide variety of results and examples, as well as exploring the relations between them.

This article investigates generalized Ricci almost solitons, also known as GRA solitons, on contact metric manifolds, including the gradient case. At first, we establish that a complete K-contact or Sasakian manifold endowed with a closed GRA soliton satisfying (4c_1c_2 ne 1) is compact Einstein with scalar curvature (2n(2n+1)). As for the gradient case, it exhibits an isometry to the unit sphere ({mathbb {S}}^{2n+1}). Subsequently, we identify a few adequate conditions under which a non-trivial complete K-contact manifold with a GRA soliton is trivial ((eta )-Einstein). Following that, we establish certain results on H-contact and complete contact manifolds. We also demonstrate that a non-Sasakian ((k,mu ))-contact manifold with a closed GRA soliton is flat for dimension 3, and for higher dimensions, it is locally isometric to the trivial bundle ({mathbb {R}}^{n+1} times {mathbb {S}}^n(4)), provided (4c_1c_2 (1-2n)ne 1) and (c_2ne 0). Finally, we discuss a few applications of GRA solitons in general relativity. These include characterizing PF spacetimes with a concircular velocity vector field and determining a sufficient condition for a GRW spacetime to be a PF spacetime.

Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for the proposed method on arbitrary meshes. It is shown that the resulting error estimator can be used to steer an adaptive mesh algorithm that generates meshes resolving layers and singularities. Numerical results are presented that illustrate the theoretical findings.

Let ( {T_n}_{nge 0} ) be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation (T_n-2^x3^y=c), for (n,x,yin mathbb {Z}_{ge 0}). In particular, we show that there is no integer c with at least six representations of the form (T_n-2^x3^y).

The main goal of this paper is to show that helix surfaces and the Enneper surface are the only surfaces in the 3-dimensional Euclidean space (mathbb {R}^{3}) whose isogonal lines are generalized helices and pseudo-geodesic lines.

We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components of holomorphic maps between compact Kähler manifolds as well as homotopy automorphisms of Kähler manifolds.

In this paper, we compare two types of complex non-Kähler manifolds: LVM and lck manifolds. First, lck manifolds (for locally conformally Kähler manifolds) admit a metric which is locally conformal to a Kähler metric. On the other side, LVM manifolds (for López de Medrano, Verjovsky and Meersseman) are quotients of an open subset of ({mathbb {C}}^n) by an action of ({mathbb {C}}^*times {mathbb {C}}^m). LVM and lck manifolds have a fundamental common point: Hopf manifolds which are a specific case of LVM manifolds and which admit also lck metric. Therefore, the question of this paper is:

Are LVM manifolds lck ?

We provide some answers to this question. The results obtained are as follows. In the set of all LVM manifolds, there is a dense subset of LVM manifolds which are not lck. And if we consider lck manifolds with potential (whose metric derives from a potential), the diagonal Hopf manifolds are the only LVM manifolds which admit an lck metric with potential. However, we show that there exists an lck covering with potential (non-compact) of a certain subclass of LVM manifolds. Finally, we present some examples.

We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case, we also treat the classical weight function and weight sequence cases. Moreover, we construct a weight sequence which is oscillating around any weight sequence which satisfies some minimal conditions and, in particular, around the critical weight sequence ((p!)^{1/2}), related with the non-triviality of the classes. Finally, we also obtain comparison results both on classes defined by weight functions that can be defined by weight sequences and conversely.