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

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

Enantiomer discrimination in absorption spectroscopy and in voltammetry: highlighting fascinating similarities and connections

Absorption spectroscopy and voltammetry, of known analogies and connections, share even more fascinating similarities and connections at a higher complexity level, when "upgrading" them with the ability to discriminate between enantiomers by chiral selector implementation. In both techniques either "molecular" selectors or "electromagnetic" ones (L- versus Rcircularly polarized light components for spectroscopy, ccversus b-spin electrons for voltammetry) can be considered; moreover, external magnetic field application can replace a truly chiral actor. A tentative schematization is provided. Analogies and connections also concern molecular features of the enantiodiscrimination actors. In both techniques outstanding performances are obtained with inherently chiral molecules, in which a conjugated backbone with tailored torsion is source of chirality as well as spectroscopic and electrochemical activity, in an attractive three-fold interconnection. Their outstanding effects can be justified by a combination of chemical and electromagnetic properties (excellent potential molecular spin filters), a fascinating challenge for future developments

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

Highly enantioselective “inherently chiral” electroactive materials based on a 2,2' -biindole atropisomeric scaffold

Chiral oligothiophene monomers with C2 symmetry, based on 3,30 -bithiophene atropisomeric cores with high racemization barriers, have recently been shown to provide excellent chiral starting materials with high electroactivity for the easy preparation of enantiopure electroactive films endowed with powerful chirality manifestations. We now introduce an inherently chiral monomer based on a 2,20 -biindole core, as the prototype of a new inherently chiral monomer family, whose properties could be modulable through functionalization of the pyrrolic N atoms. By fast, regular electrooligomerization the new monomer yields inherently chiral films with high, reversible electroactivity and, above all, impressive enantioselectivity towards very different chiral probes, some of pharmaceutical interest, as generalscope electrode surfaces. Such results, while opening the way to a new, attractive inherently chiral selector class, nicely confirm the general validity of the inherent chirality strategy for chiral electrochemistry. Furthermore, the enantioselectivity of the new selectors not only holds with electroactive chiral probes, but also with circularly polarized light components as well as electron spins, resulting in good chiroptical and spin filter performances, which suggests fascinating correlations between the three contexts

Helicity: a non-conventional stereogenic element for designing inherently chiral ionic liquids for electrochemical enantiodifferentiation

Configurationally stable 5-aza[6]helicene (1) was envisaged as a promising scaffold for non-conventional ionic liquids (IL)s. It was prepared, purified, and separated into enantiomers by preparative HPLC on a chiral stationary phase. Enantiomerically pure quaternary salts of 1 with appropriate counterions were prepared and fully characterized. N-octyl-5-aza[6]helicenium bis triflimidate (2) was tested in very small quantities as a selector in achiral IL media to perform preliminary electrochemical enantiodifferentiation experiments on the antipodes of two different chiral probes. The new organic salt exhibited outstanding enantioselection performance with respect to these probes, thus opening the way to applications in the enantioselective electroanalysis of relevant bioactive molecules

Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schr{ö}dinger-Poisson system and a reduced nonlinear model

Two different models are compared for the simulation of the transverse electronic transport through an heterostructure: a $1D$ self-consistent Schr{ö}dinger-Poisson model with a numerically heavy treatment of resonant states and a reduced model derived from an accurate asymptotic nonlinear analysis. After checking the agreement at the qualitative and quantitative level on quite well understood bifurcation diagrams, the reduced model is used to tune double well configurations for which nonlinearly interacting resonant states actually occur in the complete self-consistent model

Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit

We consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give the stationary solutions, up to an exponentially small term, and that symmetry-breaking bifurcation occurs at a given value for the strength of the nonlinear term. The kind of bifurcation picture only depends on the non-linearity power. We then discuss the stability/instability properties of each branch of the stationary solutions. Finally, we consider an explicit one-dimensional toy model where the double well potential is given by means of a couple of attractive Dirac's delta pointwise interactions.Comment: 46 pages, 4 figure

Thiahelicene-based inherently chiral films for enantioselective electroanalysis

Chiral electroanalysis could be regarded as the highest recognition degree in electrochemical sensing, implying the ability to discriminate between specular images of an electroactive molecule, particularly in terms of significant peak potential difference. A groundbreaking strategy was recently proposed, based on the use of \u201cinherently chiral\u201d molecular selectors, with chirality and key functional properties originating from the same structural element. Large differences in peak potentials have been observed for the enantiomers of different chiral molecules, also of applicative interest, using different selectors, all of them based on atropisomeric biheteroaromatic scaffolds of axial stereogenicity. However, helicene systems also provide inherently chiral building blocks with attractive features. In this paper the enantiodiscrimination performances of enantiopure inherently chiral films obtained by electrooxidation of a thiahelicene monomer with helicoidal stereogenicity are presented for the first time. The outstanding potentialities of this novel approach are evaluated towards chiral probes with different chemical nature and bulkiness, in comparison with a representative case of the so far exploited class of inherently chiral selectors with axial stereogenicity. It is also verified that the high enantiodiscrimination ability holds as well for electron spins, as for atropisomeric selectors