Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method

Omuz-Boyun Postür Problemi Olan Yetişkin Hastalarda Klinik Pilates Egzersizlerinin Postüre Etkisinin Belirlenmesi

Bu çalışma omuz-boyun postür problemi olan yetişkin hastalarda klinik pilates egzersizlerinin postüre etkisinin belirlenmesi amacıyla planlandı. Çalışmaya baş anterior tilt, omuz protraksiyon postürü olan 51 kişi dahil edildi ve randomize olarak klinik pilates grubu (Grup 1, n=26) ve klasik postür egzersiz grubu (Grup 2, n=25) olarak 2 gruba ayrıldı. Hastaların özgeçmiş ve demografik bilgileri kaydedildi. Derin boyun fleksör kas kuvveti ve endurans ölçümünde Basınçlı Biyofeedback Ünitesi (BBÜ) kullanıldı. Baş, boyun ve omuz postür mesafe ölçümü olarak duvar-tragus, duvar-akromion, çene-sternal çentik, akromion-tragus mesafe ölçümleri, omuz bölgesi esneklik ölçümü için sırt kaşıma testi kullanıldı. Çalışmada 6 hafta boyunca servikal ve omuz kuşağı bölgesine özel 1. gruba klinik pilates egzersizleri, 2. gruba ise klasik postür egzersizleri uygulandı. Değerlendirmeler tedavi öncesi ve 6 hafta sonrasında yapıldı. Yapılan egzersiz uygulamaları sonucunda grup içi karşılaştırmalarda duvar- akromion, çene ucu- sternal çentik, duvar-tragus mesafe ölçümlerinde klinik pilates grubu yönünde anlamlı fark bulunmuştur (p< 0,05). Gruplar arası karşılaştırmalarda ise Derin Boyun Fleksör(DBF) kas enduransı, sırt kaşıma testi, duvar-tragus mesafe ölçümünde klinik pilates yönünden anlamlı fark bulunmuştur (p< 0,05). Çalışmamızın sonucunda omuz-boyun postür problemlerinin egzersiz tedavisinde klinik pilatesin klasik postür egzersizlerine göre DBF kas enduransı, omuz kuşağı esnekliği, postür değişimi yönünden daha etkili olduğu görüldü

On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented

Matematik Öğretmen Adaylarının Kanıtlama Becerilerini Geliştirmeye Yönelik Bir Öğretme Deneyi*

The purpose of this study is to determine pre-service mathematics teachers’ difficulties in constructing proofs and to investigate the changes in their proving skills after teaching activities that they experienced proving and interacted with group discussions. The study was conducted with six fourth grade secondary mathematics teachers. Pre-service teachers’ proving skills were investigated with respect to conditional statements and three proof methods; direct proof, proof by contradiction and proof by contraposition. In this qualitative study, teaching experiment method was used. As a result it can be concluded that students’ proving skills developed at different levels and they overcome some of their difficulties. Based on the results of the study suggestions are made for the instruction methods of undergraduate mathematics courses.Bu çalışmanın amacı, matematik öğretmen adaylarının kanıtlama sürecindeki güçlüklerini belirlemek, kanıtlama deneyimi yaşadıkları ve grup tartışmalarıyla sosyal etkileşimde bulundukları öğretim etkinlikleri sonrasında kanıtlama becerilerindeki değişimi incelemektir. Çalışma, ortaöğretim matematik öğretmenliği programının dördüncü sınıfına devam etmekte olan altı öğrenciyle gerçekleştirilmiştir. Öğretmen adaylarının kanıtlama becerileri, koşullu önermeler ve koşullu önermelerin kanıtlanmasında kullanılabilecek doğrudan kanıt, olmayana ergi ve karşıt ters ile kanıt yöntemleri kapsamında incelenmiştir. Verilerin toplanması ve analizinde nitel yaklaşım benimsenmiş ve öğretme deneyi yöntemi uygulanmıştır. Çalışmanın sonucunda, öğrencilerin kanıtlama süreçlerinde farklı düzeylerde de olsa ilerleme olduğu ve kanıtla ilgili bazı güçlüklerini giderebildikleri görülmüştür. Öğretmen adaylarının, çalışma süresince gösterdikleri gelişme göz önünde bulundurularak lisans düzeyindeki matematik derslerinin işlenişine yönelik önerilerde bulunulmuştur

A case of primary hypoparathyroidism presenting with acute kidney injury secondary to rhabdomyolysis

Hypoparathyroidism is the most common cause of symmetric calcification of the basal ganglia. Herein, a case of primary hypoparathyroidism with severe tetany, rhabdomyolysis, and acute kidney injury is presented. A 26-year-old male was admitted to the emergency clinic with leg pain and cramps, nausea, vomiting, and decreased amount of urine. He had been treated for epilepsy for the last 10 years. He was admitted to the emergency department for leg pain, cramping in the hands and legs, and agitation multiple times within the last six months. He was prescribed antidepressant and antipsychotic medications. He had a blood pressure of 150/90 mmHg, diffuse abdominal tenderness, and abdominal muscle rigidity on physical examination. Pathological laboratory findings were as follows: creatinine, 7.5 mg/dL, calcium, 3.7 mg/dL, alanine transaminase, 4349 U/L, aspartate transaminase, 5237 U/L, creatine phosphokinase, 262.000 U/L, and parathyroid hormone, 0 pg/mL.There were bilateral symmetrical calcifications in basal ganglia and the cerebellum on computerized tomography. He was diagnosed as primary hypoparathyroidism and acute kidney injury secondary to severe rhabdomyolysis. Brain calcifications, although rare, should be considered in dealing with patients with neurological symptoms, symmetrical cranial calcifications, and calcium metabolism abnormalities

The role of simple elbow dislocations in cubitus valgus development in children

We investigated the functional and radiological outcomes of conservatively treated simple traumatic elbow dislocations and subsequent incidence of cubitus valgus development in children. Eleven patients (one female, ten male; mean age 9.8 years, range seven to 12 years) who presented to our hospital with simple elbow dislocations and were conservatively treated between July 2008 and September 2010 were included in the study. All were posterolateral closed dislocations. None of the patients had accompanying elbow fractures. All patients had pre- and postoperative radiographic examinations. The carrying angle of the involved elbow was measured and compared to the contralateral non-injured elbow during follow-up. The incidence and severity of cubitus valgus development was assessed. The functional and clinical outcomes were evaluated using the Mayo Elbow Performance Scale. The mean monitoring period was 24.3 months (range 19-30 months). All patients had satisfactory good and excellent results (85-100 points; mean 96.8 points) according to the Mayo Elbow Performance Scale. The final average elbow flexion was 137A degrees (range, 130-145A degrees) and average extension was 8.6A degrees (range 0-20A degrees) with full supination and pronation in traumatic elbow. Four patients (36.4 %) had an average increase (cubitus valgus) of 14.5A degrees (10-20A degrees) in carrying angle compared to the other elbow. While isolated traumatic dislocation of the elbow is uncommon among children, it can be successfully treated by urgent closed reduction, proper fixation of the elbow and appropriate timely rehabilitation. However, it should be considered that some patients may develop cubitus valgus deformity in a later period. Therefore, each patient with a simple traumatic elbow dislocation should be followed, and the parents should be informed of the potential for any deformity development