Eigenvalue Asymptotics for the Schr\"odinger Operator with a Matrix Potential in a Single Resonance Domain

We consider a Schr\"odinger Operator with a matrix potential defined in $L_2^m(F)$ by the differential expression\begin{equation*} L(\phi(x))=(-\Delta+V(x))\phi(x) \end{equation*}and the Neumann boundary condition, where $F$ is the $d$ dimensional rectangle and $V$ is a martix potential, $m\geqslant 2, d\geqslant 2$. We obtain the asymptotic formulas of arbitrary order for the single resonance eigenvalues of the Schr\"odinger operator in $L_2^m(F)$.Comment: Presented by Setenay Akduman in the International Conference "Analysis, Topoogy and Applications (ATA 2014)", Vrnja\v{c}ka Banja, Serbia, May 26-29, 2014, Keywords: Schr\"odinger operator, Neumann condition, perturbation, matrix potentia

The comparative study of nursing pads by electrospun cellulose acetate, polyethylene oxide and thermoplastic polyurethane nanofibers

This study summarizes the general information about nursing pads and novel electrospun nanofiber mats as potential component for nursing pads. It also compares electrospun thermoplastic polyurethane (TPU), cellulose acetate (CA) and polyethylene oxide (PEO) nanofibers with a polypropylene conventional disposable nursing pad (NP) in terms of hydrophilicity, breathability, air permeability and swelling properties. Nanofiber mats prepared by the electrospinning method have unique properties such as smooth surface, high specific surface area and high porosity with fine pores which will lead to improved wicking properties. These properties make nanofibers potential component for disposable nursing pads. Mean diameters of produced nanofibers were 284.39, 609.70 and 219.30 nm for CA, TPU and PEO, respectively. Water contact angle measurement revealed that these nanofibers show good wettability properties better than commercial nonwoven nursing mat and air permeability results revealed that these nanofibrous mats have considerably adequate permeability. Besides, water vapor permeability results showed these nanofibers still show good breathability despite their compact structure. © Published under licence by IOP Publishing Ltd

A conformal mapping algorithm for the Bernoulli free boundary value problem

International audienceWe propose a new numerical method for the solution of Bernoulli's free boundary valueproblem for harmonic functions in a doubly connected domain $D$ in $\real^2$ where an unknown free boundary $\Gamma_0$ is determined by prescribed Cauchy data on $\Gamma_0$ in addition to a Dirichlet condition on the known boundary $\Gamma_1$.Our main idea is to involve the conformal mapping methodas proposed and analyzed by Akduman, Haddar and Kress~\cite{AkKr,HaKr05}for the solution of a related inverse boundary value problem. For this we interpret the free boundary $\Gamma_0$as the unknown boundary in the inverse problem to construct $\Gamma_0$ from the Dirichlet condition on $\Gamma_0$ and Cauchy data on the known boundary $\Gamma_1$. Our method for the Bernoulli problem iterates on the missing normal derivative on $\Gamma_1$by alternating between the application of the conformal mapping method for the inverse problemand solving a mixed Dirichlet--Neumann boundary value problem in $D$. We present the mathematicalfoundations of our algorithm and prove a convergence result. Some numerical examples will serve as proof of concept of our approach

Laser treatment in diabetic retinopathy

Diabetic retinopathy is a leading cause of visual impairment and blindness in developed countries due to macular edema and proliferative diabetic retinopathy (PDR). For both complications laser treatment may offer proven therapy: the Diabetic Retinopathy Study demonstrated that panretinal scatter photocoagulation reduces the risk of severe visual loss by >= 50% in eyes with high-risk characteristics. Pan-retinal scatter coagulation may also be beneficial in other PDR and severe nonproliferative diabetic retinopathy (NPDR) under certain conditions. For clinically significant macular edema the Early Treatment of Diabetic Retinopathy Study could show that immediate focal laser photocoagulation reduces the risk of moderate visual loss by at least 50%. When and how to perform laser treatment is described in detail, offering a proven treatment for many problems associated with diabetic retinopathy based on a high evidence level. Copyright (c) 2007 S. Karger AG, Basel

Purification of yeast alcohol dehyrogenase by immobilized metal affinity chromatography

Bu tezde, poli(2-hidroksietil metakrilat-glisidilmetakrilat) [poli(HEMA-GMA)] kriyojelleri, HEMA ve fonksiyonel komonomer GMA'nın çapraz bağlayıcı olarak N,N'-metilen bisakrilamid (MBAAm) kullanılarak radikalik kriyokopolimerizasyon ile hazırlanmıştır. İminodiasedik asit (IDA) fonksiyonel grupları, poli(HEMA-GMA) kriyojellerindeki epoksi gruplarının halka yapılarının açılmasıyla kriyojellere bağlanmış ve daha sonra Zn2+ iyonları ile şelatlaştırılmıştır. Kriyojeller FTIR, SEM, EDX ve şişme çalışmaları ile karakterize edilmiştir. Bu kriyojeller 30-50 'm büyüklüğünde birbirine bağlı gözeneklere sahiptir. Zn2+ ile şelatlaştırılmış poli(HEMA-GMA)-IDA kriyojellerinin denge şişme derecesi yaklaşık % 600'dür. Zn2+ ile şelatlaştırılmı şpoli(HEMA-GMA)-IDA kriyojelleri sulu çözeltiden alkol dehidrogenaz adsorpsiyonu için kullanılmış ve adsorpsiyon sürekli sistemde gerçekleştirilmiştir. Adsorpsiyona pH, alkol dehidrogenaz derişimi, sıcaklık, iyonik şiddet ve akış hızının etkisi araştırılmıştır. Maksimum alkol dehidrogenaz miktarı, 1,0 mg/mL alkol dehidrogenaz derişiminde ve 0,5 mL/dak akış hızındaki pH 5,0 asetat tamponunda 9,94 mg/g polimer olarak bulunmuştur. Adsorplanan alkol dehidrogenazın desorpsiyonupH 8,0 fosfat tamponunda 1,0 M NaCl içerisinde gerçekleştirilmiş ve % 93,5 olarak bulunmuştur. Ayrıca bu kriyojeller tek bir adımda mayadan alkol dehidrogenaz saflaştırılmasında kullanılmıştır. Desorbe edilen alkol dehidrogenazın saflığı gümüş ile boyanmış SDS-PAGE ile gösterilmiştir. Bu saflaştırma işlemi ham maya homojenatından alkol dehidrogenaz enziminin saflaştırılması için başarılı bir şekilde kullanılabilir.In this thesis, poly(2-hydroxyethyl methacrylate-glycidyl methacrylate) [poly(HEMA-GMA)] cryogels were prepared by radical cryocopolymerization of HEMA with GMA as a fonctional comonomer and N,N'-methylene-bisacrylamide(MBAAm) as a crosslinker. Iminodiacetic acid (IDA) fonctional groups were attached via ring opening of the epoxy group on the poly(HEMA-GMA) cryogels and then Zn2+ ions were chealeted with this structures. Characterization of cryogels was performed by FTIR, SEM, EDX and swelling studies. These cryogels have interconnected pores of 30-50 µm size. The equilibrium swelling degree of Zn2+ chealeted poly(HEMA-GMA)-IDA cryogels was approximately 600%. Zn2+ chealeted poly(HEMA-GMA)-IDA cryogels were used in the adsorption of alcohol dehydrogenase from aqueous solutions and adsorption was performed in continuous system. The effects of pH, alcohol dehydrogenase concentration, temperature, ionic strengt hand flow rate on adsorption were investigated. The maximum amount of alcohol dehydrogenase adsorption wasd etermined to be 9,94 mg/g cryogel at 1,0 mg/mL alcohol dehyrogenase concentration and acetate buffer at pH 5,0 with flow rate of 0,5 mL/min. Desorption of adsorbed alcohol dehyrogenase was carried out by 1,0 M NaCI at pH 8,0 phosphate buffer and desorption rate was found to be 93,5 %. Additionally, these cryogels was used for purification of alcohol dehydrogenase from yeast with a single-step. The purity of desorbed alcohol dehydrogenase was shown by silver-stained SDS-PAGE. This purification process can successfully be used for the purification of alcohol dehydrogenase from unclarified yeast homogenates

The Glasgow Benefit Inventory: a systematic review of the use and value of an otorhinolaryngological generic patient-recorded outcome measure

The Glasgow Benefit Inventory (GBI) is a validated, generic patient-recorded outcome measure widely used in otolaryngology to report change in quality of life post-intervention.To date, no systematic review has made (i) a quality assessment of reporting of Glasgow Benefit Inventory outcomes; (ii) a comparison between Glasgow Benefit Inventory outcomes for different interventions and objectives; (iii) an evaluation of subscales in describing the area of benefit; (iv) commented on its value in clinical practice and research.Systematic review.'Glasgow Benefit Inventory' and 'GBI' were used as keywords to search for published, unpublished and ongoing trials in PubMed, EMBASE, CINAHL and Google in addition to an ISI citation search for the original validating Glasgow Benefit Inventory paper between 1996 and January 2015.Papers were assessed for study type and quality graded by a predesigned scale, by two authors independently. Papers with sufficient quality Glasgow Benefit Inventory data were identified for statistical comparisons. Papers with 50% and gave sufficient Glasgow Benefit Inventory total and subscales for meta-analysis. For five of the 11 operation categories (vestibular schwannoma, tonsillectomy, cochlear implant, middle ear implant and stapes surgery) that were most likely to have a single clear clinical objective, score data had low-to-moderate heterogeneity. The value in the Glasgow Benefit Inventory having both positive and negative scores was shown by an overall negative score for the management of vestibular schwannoma. The other six operations gave considerable heterogeneity with rhinoplasty and septoplasty giving the greatest percentages (98% and 99%) most likely because of the considerable variations in patient selection. The data from these operations should not be used for comparative purposes. Five papers also reported the number of patients that had no or negative benefit, a potentially a more clinically useful outcome to report. Glasgow Benefit Inventory subscores for tonsillectomy were significantly different from ear surgery suggesting different areas of benefitThe Glasgow Benefit Inventory has been shown to differentiate the benefit between surgical and medical otolaryngology interventions as well as 'reassurance'. Reporting benefit as percentages with negative, no and positive benefit would enable better comparisons between different interventions with varying objectives and pathology. This could also allow easier evaluation of factors that predict benefit. Meta-analysis data are now available for comparison purposes for vestibular schwannoma, tonsillectomy, cochlear implant, middle ear implant and stapes surgery. Fuller report of the Glasgow Benefit Inventory outcomes for non-surgical otolaryngology interventions is encouraged

On open book analogs of quantum graphs

Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground for hard higher dimensional problems. It was clear from some applications that thin surface structures (looking as stratified varieties) also arise, for instance in photonic crystals theory and dynamical systems. However, both justification and studying of these models is much harder and very little progress has been made by now. The goal of this note is to set down some basic notions and results for such structures. The name ``open book'' has been used for such geometric structures in topology and comes from an image of several smooth $n$-dimensional ``pages'' bound to an $(n-1)$- dimensional ``binding.'