Annali dell''Universita di Ferrara最新文献

Our aim is to prove the following result. Let the 2-torsion-free rings be ( mathfrak {U} ) and ( mathfrak {V} ), such that both are semiprime or fulfill the conditions of Fact A, and let ( mathfrak {R} ) be a 2-torsion-free faithful ((mathfrak {U}, mathfrak {V})) bimodule possessing the property in case ( r in mathfrak {R} ) and ( mathfrak {U}r = {0} ) (resp. ( rmathfrak {V} = {0} )), then ( r = 0 ). If ( mathfrak {J} ) is a Jordan biderivation that commutes on the triangular ring ( mathfrak {P} = {Tri}(mathfrak {U}, mathfrak {R}, mathfrak {V}) ), then ( mathfrak {J} ) is zero. Moreover, we establish that every Jordan biderivation that commutes on a triangular ring under a specific setting is precisely a zero map.

By developing Buzano type inequalities in semi-Hilbertian spaces, we obtain several (A_{0})-numerical radius inequalities for (2times 2) block matrices, where (A_{0}mathbf {=}left( begin{array}{cc} A & 0 0 & A end{array} right) ) is a (2times 2) diagonal block matrix, whose each diagonal entry is a positive bounded linear operator A on a complex Hilbert space. These inequalities improve and generalize some previously related inequalities. We also deduce several improved A-numerical radius inequalities for semi-Hilbertian space operators.

This paper studies biharmonic hypersurfaces with constant-norm second fundamental form in non-flat pseudo-Riemannian space forms (N_q^6(c)). Under the assumptions that the shape operator is diagonalizable and has at most four distinct principal curvatures, we prove that such a hypersurface must have constant mean curvature and constant scalar curvature.

In this paper, we investigate the geometric structure of Sasakian manifolds that admit smooth solutions to a generalized vacuum static equation (GVSE) involving the contact 1-form. We derive key identities characterizing such solutions and establish several rigidity results. In particular, we show that if the potential function is constant, the manifold becomes (eta )-Einstein. Moreover, for compact connected Sasakian manifolds with constant structure function, the scalar curvature must also be constant. We prove that on an (eta )-Einstein Sasakian manifold, either the scalar curvature vanishes or the potential function remains invariant under the Reeb vector field. Furthermore, we demonstrate that the structure functions defining the (eta )-Einstein condition are necessarily constant throughout the manifold. These results impose strong geometric constraints and highlight the interplay between curvature, potential functions, and contact structures. Finally, an explicit example is constructed on a 5-dimensional Sasakian manifold to illustrate and validate the theoretical framework developed in this work.

In this article we obtain a number of integral formulas for foliated sub-Riemannian manifolds; the main geometric object is a Riemannian manifold endowed with a distribution (mathcal {D}) and a foliation (mathcal {G}) such that the tangent bundle of (mathcal {G}) is a subbundle of (mathcal {D}). Our integral formulas generalize some results for foliated Riemannian manifolds; they are expressed by the shape operators of (mathcal {G}) with respect to normals in (mathcal {D}) and by the curvature tensor of the induced connection on (mathcal {D}). The formulas also contain arbitrary functions (f_j), (0le j<dim mathcal {G}), of scalar invariants of (mathcal {G}), and by a special choice of (f_j) they reduce to integral formulas obtained by means of a new transformation called the (eta )-Poincaré transformation of the shape operators. We apply our integral formulas to foliated sub-Riemannian manifolds with restrictions on the curvature and on the extrinsic geometry of (mathcal {G}), and to codimension-one foliations.

We establish continuity and uniqueness results for the (BV(Omega )) minimisers of multidimensional scalar variational problems formulated on a bounded open set (Omega ). The integrand is assumed to be convex (but not necessarily strictly convex), with linear growth from below (but not necessarily from above), while the domain (Omega ) and the boundary condition must satisfy suitable geometric and regularity conditions, such as convexity or Lipschitz continuity.

Let R be a commutative ring with nonzero unit, and (delta ) an expansion function of its ideals. In this paper, we introduce sdf-absorbing (delta )-primary ideals. A proper ideal I of R is termed square-difference factor absorbing (delta )-primary (sdf-absorbing (delta )-primary) if, for all (0 ne a, b in R) with (a^2 - b^2 in I), it follows that (a + b in I) or (a - b in delta (I)). Several properties and results are presented and supported by illustrative examples showing, in particular, the nontrivial nature of the introduced class. Moreover, we examine the transfer of sdf-absorbing (delta )-primary ideals under ring homomorphisms, and their behavior across various fundamental ring-theoretic constructions, including localization rings, polynomial rings, product rings, trivial ring extensions and amalgamated rings.

This research investigates the two-sided quaternionic Dunkl transform of functions that satisfy specific Lipschitz conditions. In particular, we focus on Lipschitz functions belonging to the function space (L^{2}left( mathbb {R}^{2}, mathbb {H}right) ) and study how these smoothness constraints influence the behavior of their quaternionic Dunkl transforms. Motivated by Theorems 84 and 85 of Titchmarsh, which characterize the transforms of Lipschitz functions on the real line, we extend these classical results to the quaternionic Dunkl framework, providing a natural generalization in the context of quaternion-valued functions and Dunkl-type analysis.

In this paper, we prove that every algebraic structure is the fundamental algebraic structure of a VT-(H_v)-structure. Moreover, we investigate some properties related to the automorphism group of VT-(H_v)-structures.

In this paper, we calculate the centroid of the zeroes of semi-classical orthogonal polynomials of class one, which are derived from cubic decompositions (CD) satisfying the relation (W_{3n}(x) = P_n(x^{3} + q x + r)).