Annali dell''Universita di Ferrara最新文献

For a Calabi–Yau variety X, Oguiso (Math Res Lett 25(1):181–198, 2018) gave a useful criterion for primitivity of a self-map of X in terms of the associated linear map on the Néron–Severi space of X. In this short note, we prove a variant of Oguiso’s criterion and use it to verify primitivity of a certain birational automorphism of a Calabi–Yau threefold, to which Oguiso’s original criterion does not apply.

We consider a class of bounded-range 1D network models on a cycle and prove that, unlike the corresponding infinite-volume models, which never contain infinite components, they actually exhibit a phase transition for connectivity. We further show that depending on the specific choice of the edge probabilities, the last obstruction to connectivity can either be the existence of isolated vertices or the split of the cycle into two spatially separated components.

This paper deals with the existence of solutions for a Robin boundary problem involving the p(z)-Laplacian-Like operator. Using Ricceri’s variational method, we prove the existence result of at least three nontrivial solutions of the considered problem in the framework of double weighted generalized Sobolev space.

We consider m-th order linear, uniformly elliptic equations (mathcal {L}u=f) with non-smooth coefficients in Banach–Sobolev spaces (W_{X_w}^m (Omega )) generated by weighted Banach Function Spaces (BFS) (X_w (Omega )) on a bounded domain (Omega subset {mathbb R}^{n}). Supposing boundedness of the Hardy–Littlewood Maximal operator and the Calderón–Zygmund singular integrals in (X_w (Omega )) we obtain solvability in the small in (W_{X_w}^m (Omega )) and establish interior Schauder type a priori estimates. These results will be used in order to obtain Fredholmness of the operator (mathcal {L}) in (X_w (Omega )).

The purpose of this article is to suggest a modified subgradient extragradient method that includes double inertial extrapolations and viscosity approach for finding the common solution of split equilibrium problem and fixed point problem. The strong convergence result of the suggested method is obtained under some standard assumptions on the control parameters. Our method does not require solving two strongly convex optimization problems in the feasible sets per iteration, and the step-sizes do not depend on bifunctional Lipschitz-type constants. Furthermore, unlike several methods in the literature, our method does not depend on the prior knowledge of the operator norm of the bounded linear operator. Instead, the step-sizes are self adaptively updated. We apply our method to solve split variational inequality problem. Lastly, we conduct some numerical test to compare our method with some well known methods in the literature.

This paper is devoted to discussing the existence of solutions for a class of Kirchhoff-type variational inequalities: (-mathcal {M}biggl (displaystyle int _{Omega }mathcal {A}(z,nabla u )mathrm {~d}zbiggl )~displaystyle int _{Omega }mathcal {G}(z,nabla u).(nabla vartheta -nabla u)mathrm {~d}z ge displaystyle int _{Omega }Phi (z,u)(vartheta -u)mathrm {~d}z ), for (upsilon ) belonging to the following convex set (mathcal {S}_{psi , theta }). By employing Young measure theory in conjunction with a theorem formulated by Kinderlehrer and Stampacchia, we attain the intended result.

The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel approach, demonstrating that the Cayley plane can be defined in an equally clean, straightforward and more economic way using two different division and composition algebras: the paraoctonions and the Okubo algebra. The result is quite surprising since paraoctonions and Okubo algebra possess a weaker algebraic structure than the octonions, since they are non-alternative and do not satisfy the Moufang identities. Intriguingly, the real Okubo algebra has (text {SU}left( 3right) ) as automorphism group, which is a classical Lie group, while octonions and paraoctonions have an exceptional Lie group of type (text {G}_{2}). This is remarkable, given that the projective plane defined over the real Okubo algebra is nevertheless isomorphic and isometric to the octonionic projective plane which is at the very heart of the geometric realisations of all types of exceptional Lie groups. Despite its historical ties with octonionic geometry, our research underscores the real Okubo algebra as the weakest algebraic structure allowing the definition of the compact 16-dimensional Moufang plane.

Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell’s equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initial-boundary value problem has solutions using the Schauder’s fixed point theorem.

We study the zero locus of the Futaki invariant on K-polystable Fano threefolds, seen as a map from the Kähler cone to the dual of the Lie algebra of the reduced automorphism group. We show that, apart from families 3.9, 3.13, 3.19, 3.20, 4.2, 4.4, 4.7 and 5.3 of the Iskovskikh–Mori–Mukai classification of Fano threefolds, the Futaki invariant of such manifolds vanishes identically on their Kähler cone. In all cases, when the Picard rank is greater or equal to two, we exhibit explicit 2-dimensional differentiable families of Kähler classes containing the anti-canonical class and on which the Futaki invariant is identically zero. As a corollary, we deduce the existence of non Kähler–Einstein cscK metrics on all such Fano threefolds.

Throughout the work, (Re ) is a prime ring which is non-commutative in structure with characteristic different from two, where the center of (Re ) is ({mathcal {Z}}(Re )). The rings (Q_r) and ({mathcal {C}}) are Utumi ring of quotients and extended centroid of (Re ) respectively. Consider ({mathcal {P}}) to be a Lie ideal of (Re ) which is non-central. Assume, the generalized derivation defined on (Re ) be ({mathcal {K}}) with associated derivation (mu ). If ({mathcal {K}}) satisfies certain typical power central functional identities along with an annihilator, then we have established the following: For instance, (0 ne e in Re ) with (e({mathcal {K}}(t)t)^m in {mathcal {C}}) for every (~t in {mathcal {P}} ) and (m>0) a fixed integer. Then one of the following conditions hold:

(i):

({mathcal {K}}(t)=qt), (q=a+b) with (a, b in Q_r), (b in {mathcal {C}}) and (e=beta ea), where (beta =-b^ {-1}), provided ({mathcal {K}}) is an inner generalized derivation;

(ii):

there exist (a, b in Q_r) and if (b in {mathcal {C}}) then (eq^m in {mathcal {C}}~text {where}~q=a+b), provided ({mathcal {K}}) is an inner generalized derivation and (Re ) satisfies (s_4);

(iii):

there exists (a in Q_r) with (ea=0), provided ({mathcal {K}}) is not an inner generalized derivation;

(iv):

there exists (a in Q_r) with (ea^m in {mathcal {C}}), provided ({mathcal {K}}) is not an inner generalized derivation and (Re ) satisfies (s_4).