Ricerc@Sapienza

We prove that there exist exactly three non-equivalent symplectic semifield spreads of PG ( 5 , q2), for q2> 2 .38odd, whose associated semifield has center containing Fq. Equivalently, we classify, up to isotopy, commutative semifields of order q6, for q2> 2 .38odd, with middle nucleus containing q2Fq2and center containing q Fq.

For any smooth bounded domain (Formula presented.), we consider positive solutions to (Formula presented.)which satisfy the uniform energy bound (Formula presented.)for (Formula presented.). We prove convergence to (Formula presented.) as (Formula presented.) of the (Formula presented.)-norm of any solution. We further deduce quantization of the energy to multiples of (Formula presented.), thus completing the analysis performed in De Marchis et al. (J Fixed Point Theory Appl 19:889–916, 2017).

The 2-adic ring C∗-algebra Q2naturally contains a copy of the Cuntz algebra O2and, a fortiori, also of its diagonal subalgebra D2 with Cantor spectrum. This paper is aimed at studying the group AutD2(Q2) of the automorphisms of Q2fixing D2pointwise. It turns out that any such automorphism leaves O2globally invariant. Furthermore, the subgroup AutD2(Q2) is shown to be maximal abelian in Aut(Q2). Saying exactly what the group is amounts to understanding when an automorphism of O2that fixes D2pointwise extends to Q2.

We undertake a systematic study of the so-called 2-adic ring C‡-algebra Q2. This is the
universal C‡-algebra generated by a unitary U and an isometry S2 such that S2U = U2S2
and S2S‡
2+US2S‡
2U‡ = 1. Notably, it contains a copy of the Cuntz algebra O2 = C‡(S1;S2)
through the injective homomorphism mapping S1 to US2. Among the main results, the
relative commutant C‡(S2)œ 9 Q2 is shown to be trivial. This in turn leads to a rigidity
property enjoyed by the inclusion O2 ` Q2, namely the endomorphisms of Q2 that restrict

We build solutions with boundary-layers for a Neumann problem at higher
critical exponents.

Given (M, g), a smooth compact Riemannian n-manifold, we prove that for a generic Riemannian
metric g the critical points of the norm of the Weyl's tensor are non-degenerate.

Given an action ? of a discrete group G on a unital C?-algebra A, we
introduce a natural concept of ?-negative definiteness for functions from G to A,
and examine some of the first consequences of such a notion. In particular, we prove
analogs of theorems due to Delorme–Guichardet and Schoenberg in the classical case
where A is trivial. We also give a characterization of the Haagerup property for the
action ? when G is countable.

Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians.
For type A flag varieties, we obtain characterizations of flatness, irreducibility and
normality of these degenerations via rank tuples. Some of them are shown to be isomorphic
to Schubert varieties and can be realized as highest weight orbits of partially degenerate
Lie algebras, generalizing the corresponding results on degenerate flag varieties. To study
normality, cell decompositions of quiver Grassmannians are constructed in a wider context

This paper concerns the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter ? that defines the periodic structure of the interface and on n, which is the index of the prefractal iteration. First, we study the limit as ? vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition.

In this article we consider the Keller-Segel model for chemotaxis on networks, both in the doubly parabolic case and in the parabolic-elliptic one. Introducing appropriate transition conditions at vertices, we prove the existence of a time global and spatially continuous solution for each of the two systems. The main tool we use in the proof of the existence result are optimal decay estimates for the fundamental solution of the heat equation on a weighted network.