Annali di Matematica Pura ed Applicata最新文献

Using Lie groups with left-invariant complex structure, we construct new examples of compact complex manifolds with flat affine structure in arbitrarly high dimensions. In the 2-dimensional case, we retrieve the Inoue surfaces (S^+).

The aim of this paper is to deal with the asymptotics of generalized Orlicz norms when the lower growth rate tends to infinity. We generalize results proven by Bertazzoni, Harjulehto and Hästö in Journ. of Math. Anal. and Appl. (2024) for integral type energies (in generalized Orlicz spaces), considering milder convexity assumptions. (Gamma )-convergence results and related representation theorems in terms of (L^infty ) functionals are proven. The convexity hypotheses are completely removed in the variable exponent setting, thus extending the results in Eleuteri-Prinari in Nonlinear Anal. Real. World Appl. (2021) and Prinari-Zappale in JOTA (2020).

The goal of this paper is to extend the quiver Grassmannian description of certain degenerations of Grassmann varieties to the symplectic case. We introduce a symplectic version of quiver Grassmannians studied in our previous papers and prove a number of results on these projective algebraic varieties. First, we construct a cellular decomposition of the symplectic quiver Grassmannians in question and develop combinatorics needed to compute Euler characteristics and Poincaré polynomials. Second, we show that the number of irreducible components of our varieties coincides with the Euler characteristic of the classical symplectic Grassmannians. Third, we describe the automorphism groups of the underlying symplectic quiver representations and show that the cells are the orbits of this group. Lastly, we provide an embedding into the affine flag varieties for the affine symplectic group.

This paper is devoted to the asymptotic behavior and some corrector-type results of an elastic deformation problem with highly oscillating coefficients posed in a domain periodically perforated with holes of four different sizes. On the boundary of the holes, a class of Signorini boundary condition is imposed; while a Dirichlet boundary condition is prescribed on the exterior boundary. For the critical-sized holes, the homogenization process via periodic unfolding method reveals two new terms at the limit, a reference cell average term and a strange term depending on the capacity of the holes and the negative part of the limit function. Meanwhile, the remaining cases provide either a Dirichlet limit problem or some nonnegative spreading effect at the limit.

Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context, scattered sequences extend the concept of scattered polynomials and can be viewed as geometric equivalents of exceptional MRD codes. Up to now, only scattered sequences of orders one and two have been developed. However, this paper presents an infinite series of exceptional scattered sequences of any order beyond two which correspond to scattered subspaces that cannot be obtained as direct sum of scattered subspaces in smaller dimensions. The paper also addresses equivalence concerns within this framework.

In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both monogenic functions and slice monogenic functions with values in a Clifford algebra. In this paper, we establish a version of the Fueter–Sce theorem in this new setting, which allows to construct monogenic functions in higher dimensions starting from generalized partial-slice monogenic functions. We also prove that an alternative construction can be obtained by using the dual Radon transform. It turns out that these two constructions are closely related to the generalized CK-extension.

We show that a minimal homogeneous submanifold (M^n), (nge 5), of a hyperbolic space up to codimension two is totally geodesic.

A recent method for acquiring new solutions of the Yang–Baxter equation involves deforming the classical solution associated with a skew brace. In this work, we demonstrate the applicability of this method to a dual weak brace (left( S,+,circ right) ) and prove that all elements generating deformed solutions belong precisely to the set (mathcal {D}_r(S)={z in S mid forall a,b in S , , (a+b) circ z = acirc z-z+b circ z}), which we term the distributor of S. We show it is a full inverse subsemigroup of (left( S, circ right) ) and prove it is an ideal for certain classes of braces. Additionally, we express the distributor of a brace S in terms of the associativity of the operation (cdot ), with (circ ) representing the circle or adjoint operation. In this context, ((mathcal {D}_r(S),+,cdot )) constitutes a Jacobson radical ring contained within S. Furthermore, we explore parameters leading to non-equivalent solutions, emphasizing that even deformed solutions by idempotents may not be equivalent. Lastly, considering S as a strong semilattice ([Y, B_alpha , phi _{alpha ,beta }]) of skew braces (B_alpha ), we establish that a deformed solution forms a semilattice of solutions on each skew brace (B_alpha ) if and only if the semilattice Y is bounded by an element 1 and the deforming element z lies in (B_1).

We introduce a type of local Hardy-Littlewood maximal function defined in terms of Choquet integrals associated with Bessel capacities. The weak and strong types estimates will be justified. As an application, we obtain a capacitary type of Lebesgue differentiation theorem.

In this paper, we prove some new inequality of Adams’ type for some new higher order Sobolev space whose norm is a combination of the norms of the ( frac{N}{2}-)Bilaplacian and the ( p-)Bilaplacian with ( p < frac{N}{2} ) in the whole euclidean space ( mathbb {R}^N, N ge 4. ) The inequality proved is completely new. Next, an improvement of this inequality, inspired by the concentration-compactness principle of P. Lions, is also provided. This improvement is not trivial and its proof needs some new sophisticated tools. Finally, using this inequality, we treat in the last part of this work, some biharmonic elliptic quasilinear equation involving ( (frac{N}{2},p)-)Bilaplacian operators and where the nonlinearities enjoy an exponential growth condition at infinity.