Mediterranean Journal of Mathematics最新文献

In this paper, we discuss the form and related properties of meromorphic solutions of hyper-order strictly less than 1 to Fermat type difference equation, and extend the previous results.

We devote this paper to global estimate in weighted variable exponent Sobolev spaces for fully nonlinear parabolic equations under a relaxed convexity condition. It is assumed that the associated variable exponent is log-Hölder continuous, the weight belongs to certain Muckenhoupt class concerning the variable exponent, the leading part of nonlinearity satisfies a relaxed convexity in Hessian and is of VMO condition in space-time variables, and the boundary of underlying domain satisfies (C^{1,1})-smooth. Our key strategy is to utilize a unified approach based on the generalized versions of Fefferman–Stein theorem of the sharp functions and extrapolation to establish the estimates of (D^{2}u) and (D_{t} u) within the framework of weighted variable exponent Lebesgue spaces.

In this paper, first, we recall the notion of Clairaut Riemannian map (CRM) F using a geodesic curve on the base manifold and give the Ricci equation. We also show that if base manifold of CRM is space form then leaves of ((ker{F}_*)^perp ) become space forms and symmetric as well. Secondly, we define Clairaut semi-invariant Riemannian map (CSIRM) from a Riemannian manifold ((M, g_{M})) to a Kähler manifold ((N, g_{N}, P)) with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map (SIRM) to be geodesic. Further, we obtain necessary and sufficient conditions for a SIRM to be CSIRM. Moreover, we find necessary and sufficient condition for CSIRM to be harmonic and totally geodesic. In addition, we find necessary and sufficient condition for the distributions (bar{D_1}) and (bar{D_2}) of ((ker{F}_*)^bot ) (which are arisen from the definition of CSIRM) to define totally geodesic foliations. Finally, we obtain necessary and sufficient conditions for ((ker{F}_*)^bot ) and base manifold to be locally product manifold (bar{D_1} times bar{D_2}) and ({(range{F}_*)} times {(range{F}_*)^bot }), respectively.

In 1978, Campbell and Meyer proposed the notion of minimal rank weak Drazin inverses of complex matrices. In this paper, we define minimal weak Drazin inverses of elements in semigroups using Green’s preorder (leqslant _{{mathcal {R}}},) which generalize minimal rank weak Drazin inverses of complex matrices. For two elements a, y of a semigroup, it is proved that y is a minimal weak Drazin inverse of a if and only if (ya^{k+1}=a^{k}) for some nonnegative integer k and (ay^{2}=y.)

Let X be a ruled surface over a nonsingular curve C of genus (gge 0.) Let (M_H:=M_{X,H}(2;c_1,c_2)) be the moduli space of H-stable rank 2 vector bundles E on X with fixed Chern classes (c_i:=c_i(E)) for (i=1,2.) The main goal of this paper is to contribute to a better understanding of the geometry of the moduli space (M_H) in terms of its Brill–Noether locus (W_H^k(2;c_1,c_2),) whose points correspond to stable vector bundles in (M_H) having at least k independent sections. We deal with the non-emptiness of this Brill–Noether locus, getting in most of the cases sharp bounds for the values of k such that (W_H^k(2;c_1,c_2)) is non-empty.

In this manuscript, we introduce a new sub-supersolution result for a problem involving an integro-differential operator with local and nonlocal terms, which arise in several applications such as thermal process, plasma reaction, and populational growth. The result obtained allows to consider a wide class of equations. Several applications of the result are provided which complements recent studies in the field.

The big APN problem is one of the most important challenges in the theory of Boolean functions, i.e. finding a new APN permutation in even dimension. Among this class of functions, those with the lowest possible degree are cubic. Yet, none has been found so far. In this paper, we introduce new parameters for Boolean functions and for vectorial Boolean functions, mostly derived from the behavior of their second-order derivatives. These parameters are invariant under extended affine equivalence, and they are particularly relevant for small-degree functions. They allow studying bent, semi-bent and APN functions of degrees two and three. In particular, they allow tackling the big APN problem for cubic permutations. Notably, we focus on the case of dimension 8, providing some computational results.

The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized (mathbb {K})-oscillator algebras over an arbitrary field (mathbb {K}). Starting from basic structural properties and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras with quadratic dimension 2. This will enable us to recover the classification of real oscillator algebras, a.k.a Lorentzian algebras, given by Medina et al. (Ann Sci École Norm Sup 18:553–561, 1985).

Brück’s conjecture asserts that if a non-constant entire function f(z) with hyper-order (rho _{2}(f) not in mathbb {N}cup {infty }) shares one finite value a CM (counting multiplicities) with its derivative, then (f'-a=c(f-a)), for some non-zero constant c. This conjecture has been affirmed for entire functions with finite order and hyper-order less than one. In this paper, we show that Brück’s conjecture is true for entire functions that satisfy second order differential equations with meromorphic coefficients of finite order.

N. Gastinel and J.L. Joly defined the rectangular constant (mu ) in Banach spaces using the notion of orthogonality according to Birkhoff and its generalization (mu _p), with (pge 1). Recently, M. Baronti, E. Casini, and P.L. Papini defined a new constant, the isosceles constant H, in Banach spaces in a very similar way to the rectangular constant, but in this case using the isosceles orthogonality defined by James. In this paper, first of all, we generalize such constant, by defining a new constant (H_p) that generalizes the isosceles constant H as well (mu _p) generalizes (mu ). After that, we explain its properties, and we give a characterization of Hilbert spaces in terms of it. Moreover a partial characterization of uniformly non-square spaces is given. We conclude by a conjecture about the characterization of uniformly non-square spaces.