On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

On a Babu\u161ka Paradox for Polyharmonic Operators: Spectral Stability and Boundary Homogenization for Intermediate Problems

We analyse the spectral convergence of high order elliptic differential operators subject to singular domain perturbations and homogeneous boundary conditions of intermediate type. We identify sharp assumptions on the domain perturbations improving, in the case of polyharmonic operators of higher order, conditions known to be sharp in the case of fourth order operators. The optimality is proved by analysing in detail a boundary homogenization problem, which provides a smooth version of a polyharmonic Babuska paradox

Notas sobre la concepción de Maxwell acerca de la fisica experimental

El Laboratorio Cavendish fue inaugurado en 1874 y James Clerk Maxwell fue su primer director. En ese momento Maxwell ocupaba el cargo de Profesor de Física Experimental en la cátedra Cavendish de la Universidad de Cambridge. La creación de este laboratorio tuvo la intención de fortalecer la física experimental en el Reino Unido. Se asocia su creación con la "necesidad de entrenamiento práctico de científicos e ingenieros" tras el éxito de la Gran Exhibición Industrial de 1851, que dejó claramente expuestos los requerimientos de una sociedad industrial. Hasta ese momento, la física en Inglaterra significaba física teórica y se la pensaba en el ámbito de las matemáticas. Hubo mucha especulación sobre la elección del Profesor de Física Experimental. Tanto William Thomson (de Glasgow) como John Rayleigh (de Essex) fueron candidatos con grandes posibilidades, pero ambos rechazaron la oferta Cuando se anunció la designación de Maxwell, hubo cierto asombro (y malestar) en la comunidad científica londinense. El nuevo profesor Maxwell era, por aquel entonces, relativamente desconocido. Su nombramiento como profesor fue anunciado el 8 de marzo de 1871, y más allá de las críticas iniciales, su clase inaugural fue seguida por una gran cantidad de estudiantes e investigadores de Cambridge. Sus libros más influyentes, Teoría Cinética ( 1871) y el Tratado de Electricidad y Magnetismo ( 1873), -no habían sido todavía publicados. En esta clase, Maxwell dejó claramente expuesta la impronta que él darla unos años después al Laboratorio Cavendish, cuando fuera su Director. Una de sus primeras acciones al asumir como Director del laboratorio, fue la construcción de un conjunto de equipos de física experimental, muchos de los cuales eran producto de sus propios desarrollos y concepciones. Entre ellos se destaca un modelo mecánico que tenía por objetivo representar la interacción de dos circuitos eléctricos. El estudio de este modelo es el propósito primordial del presente trabajo. Para una mejor comprensión de los objetivos perseguidos por Maxwell con este tipo de desarrollos, haremos, por un lado una breve descripción de las ideas que Maxwell tenía sobre la física experimental y por el otro, un análisis del modelo desde la concepción mecanicista que él tenía del electromagnetismo

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1

Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

Autoluminescent Metal-Organic Frameworks (MOFs): Self-Photoemission of a Highly Stable Thorium MOF

A novel thorium(IV) metal-organic framework (MOF), Th(2,6-naphtalenedicarboxylate)2, has been synthesized via solvothermal reaction of thorium nitrate and 2,6-naphtalendicarboxilyc acid. This compound shows a new structural arrangement with an interesting topology and an excellent thermal resistance, as the framework is stable in air up to 450 \ub0C. Most notably, this MOF, combining the radioactivity of its metal center and the scintillation property of the ligand, has been proven capable of spontaneous photon emission

Large Cell Neuroendocrine Carcinoma of the Lung: Current Understanding and Challenges

Large cell neuroendocrine carcinoma of the lung (LCNEC) is a rare and highly aggres-sive type of lung cancer, with a complex biology that shares similarities with both small-cell lung cancer (SCLC) and non-small-cell lung cancer (NSCLC). The prognosis of LCNEC is poor, with a median overall survival of 8–12 months. The diagnosis of LCNEC requires the identification of neuroendocrine morphology and the expression of at least one of the neuroendocrine markers (chromogranin A, synaptophysin or CD56). In the last few years, the introduction of next-generation sequencing allowed the identification of molecular subtypes of LCNEC, with prognostic and potential therapeutic implications: one subtype is similar to SCLC (SCLC-like), while the other is similar to NSCLC (NSCLC-like). Because of LCNEC rarity, most evidence comes from small retrospective studies and treatment strategies that are extrapolated from those adopted in patients with SCLC and NSCLC. Nevertheless, limited but promising data about targeted therapies and immune checkpoint inhibitors in patients with LCNEC are emerging. LCNEC clinical management is still controversial and standardized treatment strategies are currently lacking. The aim of this manuscript is to review clinical and molecular data about LCNEC to better understand the optimal management and the potential prognostic and therapeutic implications of molecular subtypes

Harbour Sea-floor Clearance: “HD” High Definition Magnetic Survey Performance

Seafloor clearance methods based on acoustic, direct-inspection, and single-sensor magnetic approaches suffer from limitations in controlling the target-sensor distance, and may prove ineffective when the small size or the dangerous nature of targets requires high accuracy in localization. Moreover, random magnetic variations over time bring about spatial decorrelation phenomena, and hinder the application of double-sensor methods in noisy harbour environments. The new High Definition (HD) magnetic survey protocol tackles the measurement-distance problem in two ways: first, by varying the sensor depth dynamically, and secondly by backprojecting the measured field according to seafloor data and vertical incremental factors associated with the bandwidth characteristics of targets. The method to make up for timeinduced loss in spatial localization ability exploits the local behaviour of a coherence function, which correlates local observations to a set of spatially-stabilized reference stations. The consequent normalization of measured magnetic signals allows one to assign the monitored areas with a specific level of confidence in the detection results, ranging from 100% (certainty) to 0% (random events). The principles of HD detection have been fully applied in the seafloor clearance of the firing test site located south of Cape Teulada (Sardinia, Italy), where very weak signal sources such as cartridge cases, mines, and small objects down to 1 Kg mass values (lobster pots) have been successfully localized, even when covered by extensive colonies of Posidonia