An invertibility criterion in a C*-algebra acting on the Hardy space with applications to composition operators

In this paper we prove an invertibility criterion for certain operators which is given as a linear algebraic combination of Toeplitz operators and Fourier multipliers acting on the Hardy space of the unit disc. Very similar to the case of Toeplitz operators we prove that such operators are invertible if and only if they are Fredholm and their Fredholm index is zero. As an application we prove that for "quasi-parabolic" composition operators the spectra and the essential spectra are equal.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1002.4640, arXiv:1205.605

Does clinical findings correlate with magnetic resonance imaging (MRI) findings in patients with temporomandibular joint (TMJ) pain? A cross sectional study

Although magnetic resonance imaging (MRI) helps to clearly visualize the disorders in temporomandibular joint (TMJ), the relationship between cross-sectional and clinical findings has not been precisely established. The aim of this study was to evaluate the relationship between clinical symptoms and MRI findings in individuals with TMJ pain. This cross-sectional study, conducted on the clinical and MRI findings of the patients, who applied to U?ak University, Oral and Maxillofacial Surgery Clinic with TMJ pain between the years 2016-2019. The primary predictor variables were MRI findings; disc position (normal, disc displacement with reduction (DDWR), disc displacement without reduction (DDWOR)), disc structural distortion (normal, folded, lengthened, round, biconvex, thick), condyle degeneration type (normal, moderate, severe) and joint effusion (JE) (absent, present). The primary outcome variable was pain, recorded on a visual analog scale (VAS) (numbered between 0-10). The other variables were demographic variables (age/gender). The relationship between clinical and MRI findings were statistically evaluated. The data were analysed by Kruskal Wallis and Mann Whitney U test. Chi-square (x2) test was used for categorical variable comparisons. P values < .05 were considered to indicate statistical significance. Clinical and MRI records of 700 TMJ, from 350 patients with the mean age of the 31 (12-65) were evaluated in this study. Statistically significant differences were found between; disc position and pain, disc position and JE; JE and pain; disc structural distortion and pain; and disc structural distortion and disc position. JE was seen more common in DDWOR group. The most common disc distortion, seen in patients with JE, is the folded type. The present study can infer that pain is associated with disc position, JE, disc structural distortion, and DDWOR is associated with JE. Folded type disc is the most common disc type in TMJ with JE

Fredholm criteria in a C*-algebra acting on the Hardy space of the bi-disc with applications to composition operators

In this work we give a Fredholm criteria for the operators in the C*-algebra generated by certain Toeplitz operators and Fourier multipliers acting on the Hardy space of the bidisc. With help of the obtained results we also completely characterize the essential spectra of quasi-parabolic composition operators on the Hardy spaces of the bi-disc. (C) 2019 Elsevier Inc. All rights reserved

Surgically-assisted Rapid Maxillary Expansion under Local Anesthesia

PubMed ID: 31779766Developmental, traumatic and congenital factors, among many others, may lead to transverse maxillary deficiency (TMD). TMD can be corrected by orthodontic treatment, and may also require surgical intervention. The surgical technique is used in maxillary hypoplasia seen in cleft palate, crowding in maxillary teeth, which in cases where maxilla needs to be expanded more than 5 mm. Although it is a frequently used technique, there is no consensus on the operative technique and the apparatus used during the operation. Whether or not to separate, the pterygomaxillary junction is also one of the most common subjects of debate in this regard. In this case presentation, the transverse expansion of the maxilla was completed by means of surgically-assisted rapid maxillary expansion operation performed under local anesthesia without separating the pterygomaxillary junction and nasal septal osteotomy; and the patient, in whom orthodontic treatment had been completed, made a successful recovery without complications

İnferior Alveolar Sinir Lateralizasyonu Sırasında Oluşan Bir Komplikasyon ve Cerrahi Yaklaşım: Vaka Raporu

Alveolar kret tepesi ile inferior alveolar kanal arasında standart boyutlarda dental implant yerleşimi için yeterli kemik yüksekliği bulunmayan bir vakada uygulanan inferior alveolar sinir lateralizasyonu yöntemi sırasında ortaya çıkan bir komplikasyonu tanımlamak, cerrahi, fototerapi ve farmakolojik tedavi yaklaşımlarını güncel veriler ışığında tartışmaktır. Dental implant destekli sabit protetik restorasyon talebi ile başvuran 34 yaşında erkek hastanın implant operasyonu sırasında inferior alveolar sinir lateralizasyonu yapılırken sinir dokusunda transeksiyon meydana gelmiştir. Komplikasyona müdahale amacı ile inferior alveolar sinir transpozisyonu gerçekleştirilmiş ve yaralanma bölgesindeki serbest uçlar pasif olarak bir araya getirilip primer olarak suture edilmiştir. Postoperatif dönemde kortikosteroid ve düşük doz lazer tedavileri uygulanmıştır. Hasta aktif şikayeti bulunmadan takip sürecindedir. Literatürdeki veriler ışığında, dental implant tedavileri için uygulanan ileri cerrahi teknikler arasında inferior alveolar sinir yönelik transpozisyon teknikleri ve ilişkili komplikasyonlar ortaya çıkabilmektedir. Bu teknikler sırasında gerçekleşebilecek ve hastalarda kalıcı sekeller bırakabilecek komplikasyonlardan biri sinir transeksiyonudur. Transeksiyon komplikasyonunda uygulanabilecek primer müdahalelerden biri sinir uçlarının primer olarak yaklaştırılmasıdır. Postoperatif süreçte de iyileşmesinin desteklenmesi için kortikosteroid ve düşük seviye lazer tedavileri önerilmektedir. İnferior alveolar sinire yönelik müdahalelerde detaylı planlama, hassas cerrahi teknikler büyük önem taşısa da sinir yaralanmaları istenmeyen ancak karşılaşılabilecek komplikasyonlardandır. Ancak bu gibi komplikasyonlara müdahale amacı ile erken dönemde nöroenflamasyonu baskılayabilecek ajanlar ve iyileşmeyi destekleyecek tedavi seçenekleri göz önünde tutulmalıdı