Annali dell''Universita di Ferrara最新文献

We give constructions of completions of the affine 3-space into total spaces of del Pezzo fibrations of every degree other than 7 over the projective line. We show in particular that every del Pezzo surface other than ({mathbb {P}}^{2}) blown-up in one or two points can appear as a closed fiber of a del Pezzo fibration (pi :Xrightarrow {mathbb {P}}^{1}) whose total space X is a ({mathbb {Q}})-factorial threefold with terminal singularities which contains ({mathbb {A}}^{3}) as the complement of the union of a closed fiber of (pi ) and a prime divisor (B_{h}) horizontal for (pi ). For such completions, we also give a complete description of integral curves that can appear as general fibers of the induced morphism (bar{pi }:B_{h}rightarrow {mathbb {P}}^{1}).

We consider the geometric map ( {mathfrak {C}}), called Cayleyan, associating to a plane cubic E the adjoint of its dual curve. We show that ( {mathfrak {C}}) and the classical Hessian map ( {mathfrak {H}}) generate a free semigroup. We begin the investigation of the geometry and dynamics of these maps, and of the geometrically special elliptic curves: these are the elliptic curves isomorphic to cubics in the Hesse pencil which are fixed by some endomorphism belonging to the semigroup ({{mathcal {W}}}(mathfrak {H}, mathfrak {C})) generated by ( mathfrak {H}, mathfrak {C}). We point out then how the dynamic behaviours of ( {mathfrak {H}}) and ( {mathfrak {C}}) differ drastically. Firstly, concerning the number of real periodic points: for ( {mathfrak {H}}) these are infinitely many, for ( {mathfrak {C}}) they are just 4. Secondly, the Julia set of ( {mathfrak {H}}) is the whole projective line, unlike what happens for all elements of ({{mathcal {W}}}(mathfrak {H}, mathfrak {C})) which are not iterates of ( {mathfrak {H}}).

We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of abelian differentials.

Introduced by Duffin and Schaefer as a part of their work on nonhamonic Fourier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field. In this work, we introduce a new concept that of integral operator frame for the set of all adjointable operators on a Hilbert (C^{*})-modules ({mathcal {H}}) and we give some new properties relating for some construction of integral operator frame, also we establish some new results. Some illustrative examples are provided to advocate the usability of our results.

Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups in the bounded derived category of a K3 surface. As an application, we prove the formality conjecture for polystable objects in the Kuznetsov components of Gushel–Mukai threefolds and quartic double solids.

The paper investigates current models of flows in porous media from the viewpoint of the mixture theory. The constitutive equations are investigated for compressible, viscous, heat-conducting fluids subject to relaxation phenomena. The thermodynamic analysis is performed via the Clausius-Duhem inequality based directly on the peculiar fields of the mixture. The detailed analysis so developed involves the peculiar heat fluxes and stresses per se while the balance equations for energy and entropy of the whole body would involve also diffusion effects. Following the objectivity principle, the constitutive equations for stresses and heat fluxes are taken to be governed by objective rate equations.

We classify 2-Fano horospherical varieties with Picard number 1. We also review all the known examples of 2-Fano manifolds and investigate the relation between the 2-Fano condition and different notions of stability.

In this paper, we study the Banach space (ell _{infty }) of the bounded real sequences, and a measure (N(a,Gamma )) over (left( textbf{R}^{infty },mathcal {B}^{infty }right) ) analogous to the finite-dimensional Gaussian law. The main result of our paper is a change of variables’ formula for the integration, with respect to (N(a,Gamma )), of the measurable real functions on (left( E_{infty },mathcal {B}^{infty }left( E_{infty }right) right) ), where (E_{infty }) is the separable Banach space of the convergent real sequences. This change of variables is given by some (left( m,sigma right) ) functions, defined over a subset of (E_{infty }), with values on (E_{infty }), with properties that generalize the analogous ones of the finite-dimensional diffeomorphisms.

This study is about a comprehensive convergence analysis of higher-order Newton-type iterative methods within the framework of Banach spaces. The primary objective is to ascertain locally unique solutions for systems of nonlinear equations. These Newton-type methods are notable for their reliance only on first-order derivative calculations. However, their conventional convergence analysis relies on Taylor expansions, which inherently assume the existence of higher-order derivatives, which are not present on the methods. This dependency limits their practicality. To overcome this limitation, we develop both local and semi-local convergence analysis by imposing hypotheses solely on first-order derivatives that are used by the methods. In the local analysis, our primary focus is to establish convergence domain boundaries while simultaneously estimating error approximations for successive iterates. In the semi-local analysis, we provide sufficient conditions based on arbitrarily chosen initial approximations within a given domain, ensuring the convergence of iterative sequence to a specific solution within that domain. Furthermore, we claim uniqueness of the solution by providing the requisite criteria within the specified domain.Therefore, with these actions, the applicability of these methods is extended in the cases not covered earlier, and under weak conditions. The same technique can be employed to extend the utilization of other methods relying on inverses of linear operators along the same lines. Finally, we validate our theoretical deductions by applying them to real-world problems and presenting the corresponding test results.

We show that many statements of the Minimal Model Program, including the cone theorem, the base point free theorem and the existence of Mori fibre spaces, fail for 1-foliated surface pairs ((X,mathcal {F})) with canonical singularities in characteristic (p>0).