Almost periodic linear differential equations with non-separated solutions

AbstractA celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes almost periodic solutions do not exist. Strongly non-separated solutions appear when the associated homogeneous system has homoclinic solutions. This point of view unifies two fascinating examples by Zhikov–Levitan and Johnson for the scalar case. Our construction uses the ideas of Zhikov–Levitan together with the theory of characters in topological groups

Favard Theory and fredholm alternative for disconjugate recurrent second order equations

Producción CientíficaWe discuss the existence of a Fredholm--type Alternative for a recurrent second order linear equation, which is disconjugate in a strong sense. The basic result is about bounded solutions of equations with bounded coefficients: it depends on kinematic similarities that allow to reduce the problem to a pair of very simple normal forms. Then the result is specialized to recurrent equations, by means of Favard theory.MINECO/FEDER MTM2015-6633

Recurrent equation with sign and Fredholm alternative

Producción CientíficaWe prove that a Fredholm--type Alternative holds for recurrent equations with sign, extending a previous result by Cieutat and Haraux in [3]. Moreover, we show that this can be seen a particular case of [1] and we provide a solution to an interesting question raised by Hale in [6]. Finally we characterize the existence of exponential dichotomies also in the nonrecurrent case.Junta de Castilla y Leon (VA118A12-1)MINECO/FEDER MTM2014-53406-

Favard theory for the adjoint equation and Fredholm alternative

Producción CientíficaFredholm Alternative is a classical tool of periodic linear equations, allowing to describe the existence of periodic solutions of an inhomogeneous equation in terms of the adjoint equation. A few partial extensions have been proposed in the literature for recurrent equations: our aim is to point out that they have a common root and discuss whether such a root gives rise to a general Fredholm-type Alternative. Sacker–Sell spectral theory and Favard theory are main ingredients in this discussion: a considerable effort is devoted to understand how Favard theory is affected by adjunction, at least for planar equations.MINECO/FEDER MTM2015-6633

Management of High-Pressure Injection Hand Injuries: A Multicentric, Retrospective, Observational Study

Hand injuries after high-pressure injection are a medical emergency. These events occur frequently in workers during industrial cleaning, painting, and lubrication, and may have devastating consequences, leading to eventual amputation and poor functional outcomes. The authors have investigated the evolution, management, and outcome. Medical records of occupational medicine units and hand surgery units were collected in order to spot the high-pressure gear accident cases. Records were analyzed by dividing the subjects into two groups: those treated within 6 h and after 6 h of the trauma. A follow-up was carried out at least 1 year after treatment; the post-treatment outcomes were assessed. Of the 71 (100%) subjects, 26 (37%) were treated ≤6 h and 45 (63%) >6 h. A total of 28% (n = 20) underwent amputation. In 61% of cases, accidents had occurred in the iron and steel sector. High viscosity materials with a delayed treatment beyond 6 h seemed to determine compartmental syndrome and following amputation. A significantly better outcome was reported among subjects treated ≤6 h compared to those treated >6 h, 20% (n = 7) versus 26% (n = 9), respectively. Early management of this type of injury is crucial. The results of this study may contribute to providing guidelines to occupational physicians in order to best manage this type of emergency

Study of a constrained finite element elbow prosthesis: the influence of the implant placement

BackgroundThe functional results of total elbow arthroplasty (TEA) are controversial and the medium- to long-term revision rates are relatively high. The aim of the present study was to analyze the stresses of TEA in its classic configuration, identify the areas of greatest stress in the prosthesis-bone-cement interface, and evaluate the most wearing working conditions.Materials and methodsBy means of a reverse engineering process and using a 3D laser scanner, CAD (computer-aided drafting) models of a constrained elbow prosthesis were acquired. These CAD models were developed and their elastic properties, resistance, and stresses were studied through finite element analysis (finite element method-FEM). The obtained 3D elbow-prosthesis model was then evaluated in cyclic flexion-extension movements (> 10 million cycles). We highlighted the configuration of the angle at which the highest stresses and the areas most at risk of implant mobilization develop. Finally, we performed a quantitative study of the stress state after varying the positioning of the stem of the ulnar component in the sagittal plane by +/- 3 degrees.ResultsThe greatest von Mises stress state in the bone component for the 90 degrees working configuration was 3.1635 MPa, which occurred in the most proximal portion of the humeral blade and in the proximal middle third of the shaft. At the ulnar level, peaks of 4.1763 MPa were recorded at the proximal coronoid/metaepiphysis level. The minimum elastic resistance and therefore the greatest stress states were recorded in the bone region at the apex of the ulnar stem (0.001967 MPa). The results of the analysis for the working configurations at 0 degrees and 145 degrees showed significant reductions in the stress states for both prosthetic components; similarly, varying the positioning of the ulnar component at 90 degrees (- 3 degrees in the sagittal plane, 0 degrees in the frontal plane) resulted in better working conditions with a greater resulting developed force and a lower stress peak in the ulnar cement.ConclusionThe areas of greatest stress occur in specific regions of the ulnar and humeral components at the bone-cement-prosthesis interface. The heaviest configuration in terms of stresses was when the elbow was flexed at 90 degrees. Variations in the positioning in the sagittal plane can mechanically affect the movement, possibly resulting in longer survival of the implant.Level of evidence:

Rilievi GPR multifrequenza in un sito test controllato in Campania, Italia

In questo report vengono presentati i risultati dell’attività geofisica svolta presso l’area test di Succivo (NA). Scopo del lavoro è verificare la risposta di antenne GPR (Ground Penetration Radar) a diversa frequenza (100 MHz – 270 MHz) in terreni di natura piroclastica dove sono stati interrati oggetti di varia natura (fusti metallici, muretti in tufo e tubi in PVC) e a diverse profondità (1m - 2m - 3m). Conoscendo la stratigrafia di massima del sottosuolo e la disposizione degli oggetti sepolti, sono stati ottenuti radargrammi 2D la cui analisi ed interpretazione hanno permesso di definire la risposta delle antenne GPR in termini di risoluzione e profondità. L’attività ha permesso di conseguire importanti informazioni sulla scelta della frequenza di utilizzo delle antenne GPR in terreni piroclastici e sulla risposta che tale tecnica fornisce nell’identificazione di oggetti sepolti .Tali informazioni risultano essenziali qualora venga usata la tecnica GPR per rilevare la presenza di oggetti sepolti (metallici e non) a varie profondità

Tomografia Geoelettrica 3D ad alta risoluzione nell’area di San Gregorio Magno (SA)

Nell’ambito delle attività di ricerca del progetto “TESIRA”, in cui partecipano il Dipartimento di Scienze della Terra dell’Ambiente e delle Risorse (DISTAR) dell’Università degli Studi di Napoli “Federico II”, l’Istituto di Scienze del Patrimonio Culturale del Consiglio Nazionale delle Ricerche CNR – ISPC e l'Istituto Nazionale di Geofisica e Vulcanologia sede di Roma (INGV), il gruppo di geofisica di Napoli dell’ISPC,ha condotto nell’area test del comune di San Gregorio Magno, SGM, (SA) un’indagine di tomografia geoelettrica 3D (ERT), per l’individuazione e la ricostruzione tridimensionale delle strutture presenti nel sottosuolo connesse con la faglia di SGM. In particolare in questo rapporto tecnico si riportano le procedure di acquisizione ed elaborazione di dati di tomografia geoelettrica 3D

Measurement of gravitational and thermal effects in a liquid-actuated torsion pendulum

We describe a proof-of-principle experiment aiming to investigate the inverse-square law of gravitation at the centimeter scale. The sensor is a two-stage torsion pendulum, while actuation is accomplished by a variable liquid mass. The time-varying gravitational force is related to the level of the circulating fluid in one or two containers at a short distance from the test mass, with all moving mechanical parts positioned at a large distance. We provide a description of the apparatus and present the first results. We identified a systematic effect of thermal origin, producing offsets of few fNm in torque and of about 10 pN in force. When this effect is neutralized, the measurements agree well with the predictions of simulations. We also discuss the upcoming instrument upgradations and the expected sensitivity improvement that will allow us to perform measurements with adequate accuracy to investigate the unexplored regions of the α−λ parameter space of a Yukawa-like deviation from the Newtonian potential