Hemifacial microsomia: Case report and literature review

Hemifacial microsomia (HFM) is a sporadic congenital malformation of the craniofacial structures derived from the first and second branchial arches. The incidence of HFM has been reported to range from 1 in 3,0001 to 1 in 26,0002 live births, making HFM the second most common congenital malformation in the face after cleft lip and/or palate. An 11-year-old girl came at Galeazzi Institute (Milan) in January 2017. She presented left hemifacial microsomia with absence of the left ramus of mandible and the left temporomandibular joint (tmj), part of the zygomatic arch, hypoplasia of the lateral and inferior orbital bone and of the zygomatic bone. She also presented a medial canthal dystopia. She underwent to costochondral bone graft and calvaria bone graft for reconstruction of part of the mandible and the TMJ. An emi-Le Fort I, emi-Le Fort III, and sagittal segmental osteotomy of the right mandible were performed to improve the correct occlusion. Traditionally, the costochondral graft has been considered the gold standard for ramus-condyle reconstruction in the pediatric mandible when appropriate. Some studies cite growth unpredictability and ankylosis as concerns with rib. Further studies examining carefully the factors predicting graft growth, such as size of cartilage cap, surgical technique, and postoperative physiotherapy, are warranted

Borel summability: Application to the anharmonic oscillator

We prove that the energy levels of an arbitrary anharmonic oscillator ( x 2 m and in any finite number of dimensions) are determined uniquely by their Rayleigh-Schrodinger series via a (generalized) Borel summability method. To use this method for computations, one must make an analytic continuation which we accomplish by (a rigorously unjustified) use of Pade approximants in the case of p 2 + x 2 + β x 4 . The numerical results appear to be better than with the direct use of Pade approximants

Seismic analysis of the Roman Temple of Évora, Portugal

The Roman temple of Évora dates back to the 1st century AD and has undergone several changes throughout history, including various additions, which have been removed. Several archaeological studies have recently been carried out, but the structural safety of the temple is unknown. Of particular concern is the temple’s seismic resistance, as it is located in a region subjected to a moderate seismic hazard. The main purpose of this paper is to ascertain the temple’s behaviour under seismic excitation through limit analysis and discrete element analysis. Both analysis techniques will use the assumption that the structure is composed of rigid blocks connected with dry joints. Geometric information has been derived from a recent laser scanning surveying, while calibration undertaken using in-situ results from GPR and dynamic identification tests. The main results are presented and discussed in detail as well as the need for possible repair works within the framework of the ICARSAH guidelines

One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities

A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur

Current oscillations in a metallic ring threaded by a time-dependent magnetic flux

We study a mesoscopic metallic ring threaded by a magnetic flux which varies linearly in time PhiM(t)=Phi t with a formalism based in Baym-Kadanoff-Keldysh non-equilibrium Green functions. We propose a method to calculate the Green functions in real space and we consider an experimental setup to investigate the dynamics of the ring by recourse to a transport experiment. This consists in a single lead connecting the ring to a particle reservoir. We show that different dynamical regimes are attained depending on the ratio hbar Phi/Phi0 W, being Phi0=h c/e and W, the bandwidth of the ring. For moderate lengths of the ring, a stationary regime is achieved for hbar Phi/Phi0 >W. In the opposite case with hbar Phi/Phi0 < W, the effect of Bloch oscillations driven by the induced electric field manifests itself in the transport properties of the system. In particular, we show that in this time-dependent regime a tunneling current oscillating in time with a period tau=2piPhi0/Phi can be measured in the lead. We also analyze the resistive effect introduced by inelastic scattering due to the coupling to the external reservoir.Comment: 17 pages, 13 figure

Bender-Wu Formula and the Stark Effect in Hydrogen

We discuss a close connection between the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schrödinger coefficients of the two-dimensional rotationally symmetric anharmonic oscillator and the behavior of resonances of the hydrogen Stark problem in two regimes: small field (Oppenheimer's formula) and large field (where we obtain the new results arg E → −π/3, ∣E∣ ∼α[F(lnF)^(2/3) for F, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas

Two-parametric PT-symmetric quartic family

We describe a parametrization of the real spectral locus of the two-parametric family of PT-symmetric quartic oscillators. For this family, we find a parameter region where all eigenvalues are real, extending the results of Dorey, Dunning, Tateo and Shin.Comment: 23 pages, 15 figure