Laplacians with point interactions -- expected and unexpected spectral properties

We study the one-dimensional Laplace operator with point interactions on the real line identified with two copies of the half-line $[0,\infty)$. All possible boundary conditions that define generators of $C_0$-semigroups on $L^2\big([0,\infty)\big)\oplus L^2\big([0,\infty)\big)$ are characterized. Here, the Cayley transform of the boundary conditions plays an important role and using an explicit representation of the Green's functions, it allows us to study invariance properties of semigroups

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.Comment: 8 page

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe

Tratamiento antifúngico tópico en pacientes con candidosis crónica bucal. Estudio comparativo.

El objetivo del presente trabajo fue evaluar el efecto del fenticonazol en el tratamiento tópico de las candidosis crónicas bucales y compararlo con el del ketoconazol y la nistatina. Se incluyeron ochenta pacientes con candidosis crónica eritematosa, de los cuales cincuenta y uno finalizaron la prueba. Fueron divididos en cuatro grupos a los cuales se les administró: fenticonazol al 3%, fenticonazol al 2%, nistatina 100000 UI y ketoconazol al 2%, en orabase respectivamente. Se los controló a los 7, 15, 30 y 45 días. Los datos obtenidos se analizaron estadísticamente con el ANAVA y los test de Kruskall Wallis y Wilcoxon. Se encontró una disminución de las lesiones altamente significativa en todos los grupos de pacientes (p≤ 0,0001). Se analizó el grado de remisión según la localización de las lesiones; se encontró que en todos los pacientes las localizadas en mucosa yugal y comisura alcanzaron la remisión total, mientras que las lesiones de lengua y paladar mostraron una disminución significativa de la intensidad de las mismas (p≤ 0,00001) con todos los tratamientos. El fenticonazol demostró ser tan efectivo como la nistatina y el ketoconazol en el tratamiento tópico de las candidosis orales.publishedVersio

COVID-19-Related Social Isolation Predispose to Problematic Internet and Online Video Gaming Use in Italy

COVID-19 pandemic and its related containment measures have been associated with increased levels of stress, anxiety and depression in the general population. While the use of digital media has been greatly promoted by national governments and international authorities to maintain social contacts and healthy lifestyle behaviors, its increased access may also bear the risk of inappropriate or excessive use of internet-related resources. The present study, part of the COVID Mental hEalth Trial (COMET) study, aims at investigating the possible relationship between social isolation, the use of digital resources and the development of their problematic use. A cross sectional survey was carried out to explore the prevalence of internet addiction, excessive use of social media, problematic video gaming and binge watching, during Italian phase II (May-June 2020) and III (June-September 2020) of the pandemic in 1385 individuals (62.5% female, mean age 32.5 ± 12.9) mainly living in Central Italy (52.4%). Data were stratified according to phase II/III and three groups of Italian regions (northern, central and southern). Compared to the larger COMET study, most participants exhibited significant higher levels of severe-to-extremely-severe depressive symptoms (46.3% vs. 12.4%; p < 0.01) and extremely severe anxiety symptoms (77.8% vs. 7.5%; p < 0.01). We also observed a rise in problematic internet use and excessive gaming over time. Mediation analyses revealed that COVID-19-related general psychopathology, stress, anxiety, depression and social isolation play a significant role in the emergence of problematic internet use, social media addiction and problematic video gaming. Professional gamers and younger subjects emerged as sub-populations particularly at risk of developing digital addictions. If confirmed in larger and more homogenous samples, our findings may help in shedding light on possible preventive and treatment strategies for digital addictions

iMARS Phase 2

The file attached is the Published/publisher’s pdf version of the articl

Parabolic equations with dynamic boundary conditions and drift terms

The aim of this paper is to study the wellposedness and $L^2$-regularity, firstly for a linear heat equation with dynamic boundary conditions by using the approach of sesquilinear forms, and secondly for its backward adjoint equation using the Galerkin approximation and the extension semigroup to a negative Sobolev space.Comment: Sorry. It was a mistake. This paper was already submitted by my coauthor Lahcen Maniar 2 years ago. I have only to update arXiv:1909.0237

Higher-Order Operators on Networks: Hyperbolic and Parabolic Theory

We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations driven by this class of operators. We observe that they extend to the higher-order case and discuss well-posedness and conservation of energy of beam equations, along with regularizing properties of polyharmonic heat kernels. A noteworthy finding is the discovery of a new class of well-posed evolution equations with Wentzell-type boundary conditions