Solving fractional Fredholm integro-differential equations by Laguerre polynomials

The main purpose of this study was to present an approximation method based on the Laguerre polynomials to obtain the solutions of the fractional linear Fredholm integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic equations by using the collocation points. In addition, the matrix relation for Caputo fractional derivative of Laguerre polynomials is also obtained. Besides, some examples are presented to illustrate the accuracy of the method and the results are discussed

Toplumun radyasyon farkındalığı ve radyasyonla ilgili bilgi düzeyi

Giriş: Son dönemlerde sıkça gündeme gelen radyasyon konusunda toplumun bilgi seviyesini ölçmek, radyasyon ile ilgili bilgi, tutum, davranış ve genel kültür seviyesini tespit etmek ve bu konuda eğitim taleplerinin olup olmadığını öğrenmek amaçlanmıştır.Gereç ve Yöntem: Toplumda radyasyon farkındalığı ve bilgi düzeylerini saptamaya yönelik 22 soruluk bir anketi hazırladık. Anket formu; yaş, cinsiyet, eğitim durumu, mesleği ve radyasyon sebepleri, radyasyondan korunma yöntemleri, radyasyon farkındalığı ile ilgili sorular içermekteydi. İstatistiki analizlerde Ki kare testi kullanılmıştır.

The frequency of Duchenne muscular dystrophy/Becker muscular dystrophy and Pompe disease in children with isolated transaminase elevation: results from the observational VICTORIA study

IntroductionElevated transaminases and/or creatine phosphokinase can indicate underlying muscle disease. Therefore, this study aims to determine the frequency of Duchenne muscular dystrophy/Becker muscular dystrophy (DMD/BMD) in male children and Pompe disease (PD) in male and female children with isolated hypertransaminasemia.MethodsThis multi-center, prospective study enrolled patients aged 3–216 months with serum alanine transaminase (ALT) and/or aspartate transaminase (AST) levels >2× the upper limit of normal (ULN) for ≥3 months. Patients with a known history of liver or muscle disease or physical examination findings suggestive of liver disease were excluded. Patients were screened for creatinine phosphokinase (CPK) levels, and molecular genetic tests for DMD/BMD in male patients and enzyme analysis for PD in male and female patients with elevated CPK levels were performed. Genetic analyses confirmed PD. Demographic, clinical, and laboratory characteristics of the patients were analyzed.ResultsOverall, 589 patients [66.8% male, mean age of 63.4 months (standard deviation: 60.5)] were included. In total, 251 patients (188 male and 63 female) had CPK levels above the ULN. Of the patients assessed, 47% (85/182) of male patients were diagnosed with DMD/BMD and 1% (3/228) of male and female patients were diagnosed with PD. The median ALT, AST, and CPK levels were statistically significantly higher, and the questioned neurological symptoms and previously unnoticed examination findings were more common in DMD/BMD patients than those without DMD/BMD or PD (p < 0.001).DiscussionQuestioning neurological symptoms, conducting a complete physical examination, and testing for CPK levels in patients with isolated hypertransaminasemia will prevent costly and time-consuming investigations for liver diseases and will lead to the diagnosis of occult neuromuscular diseases. Trial RegistrationClinicaltrials.gov NCT04120168

A method for fractional Volterra integro-differential equations by Laguerre polynomials

Abstract The main purpose of this study is to present an approximation method based on the Laguerre polynomials for fractional linear Volterra integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic equations by using the collocation points. In addition, the matrix relation for Caputo fractional derivatives of Laguerre polynomials is also obtained. Besides, some examples are presented to illustrate the accuracy of the method and the results are discussed

New exact solutions of space and time fractional modified Kawahara equation

One of the important nonlinear evolution equations in mathematical physics is the modified Kawahara equation. In this work, by utilizing an analytic method based on the Jacobi elliptic functions, a group of exact solutions of the fractional modified Kawahara equation had been found. The method can be applied to all of the time, space and space–time fractional equations. Four problems had also been given to demonstrate the application of the method and some solutions had been illustrated by the graphics. © 2020 Elsevier B.V

Prof. Dr Rıdvan Ege'nin hayatı ve Türk ortopedi tarihine katkıları

Ankara : İhsan Doğramacı Bilkent Üniversitesi İktisadi, İdari ve Sosyal Bilimler Fakültesi, Tarih Bölümü, 2016.This work is a student project of the The Department of History, Faculty of Economics, Administrative and Social Sciences, İhsan Doğramacı Bilkent University.by Pamuk, Fatih