A Numerical scheme to Solve Boundary Value Problems Involving Singular Perturbation

نستخدم المصفوفات العملياتية لمشتقات وانج-بول متعددة الحدود في هذه الدراسة لحل المعادلات التفاضلية الشاذه المضطربة من الدرجة الثانية (WPSODEs) ذات الشروط الحدية. باستخدام مصفوفة كثيرات حدود وانج-بول، يمكن تحويل مشكلة الاضطراب الرئيسية الشاذ إلى أنظمة معادلات جبرية خطية. كما يمكن الحصول على معاملات الحل التقريبي المطلوبة عن طريق حل نظام المعادلات المذكور. وتم استخدام أسلوب الخطاء المتبقي أيضًا لتحسين الخطأ، كما تمت مقارنة النتائج بالطرق المنشورة في عدد من المقالات العلمية. استُخدِمت العديد من الأمثلة لتوضيح موثوقية وفائدة مصفوفات وانج بول العملياتية. طريقة وانج بول لديها القدرة على تحسين النتائج عن طريق تقليل درجة الخطأ بين الحلول التقريبية والدقيقة. أظهرت سلسلة وانج-بول فائدتها في حل أي نموذج واقعي كمعادلات تفاضلية من الدرجة الأولى أو الثانيةThe Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs)

Thoracoabdominal aortic aneurysms in Marfan patients

Aim: The aim if this study was to present our experience in the operative management of diseased thoracic aorta in patients with Marfan Syndrome (MFS). In the period 1993-2015 86 patients with MFS and diseased thoracic aorta were treated in our center. Methods: An open surgical treatment was performed in 63 cases and an endovascular exclusion was performed in 23 cases (including hybrid treatments). The larger part of those interventions were elective, and 21 cases were in urgent fashion. Result:. The perioperative mortality was 4.8%. At 30 postoperative day paraplegia was observed in 8.1 % of patients, renal and respiratory failure in 5.8% and 8.1%, respectively. After a mean follow-up of 13.2+3.6 years long-term survival rate was 79.1%. In the group of patients treated with open surgery we observed three cases of Carrell's patch aneurysm, which required open reintervention. In the endovascular cases we observed four cases of graft migration, two cases of aortic antegrade dissection and five cases of endoleak with significative sac growth. Conclusion: Perioperative mortality and morbidity after open and endovascular repair were acceptable in this series in patients with MFS. Because of the high risk of complications and reinterventions after TEVAR, however, we currently limited aortic stent grafting in selected patient in whom an aortic open repair is contraindicated or as bridge technique in urgent fashion

Clamped Carotid Dissection Can Reduce Postoperative Stroke After Carotid Endarterectomy

Background: The outcomes of carotid endarterectomy (CEA) are constantly reported in a multitude of studies; however, the specific causes of perioperative stroke have been scarcely investigated. The aim of the present study was to analyze and categorize the causes of perioperative strokes after CEA. Methods: All CEAs performed from 2006 to 2019 in a single center were collected. CEA was routinely performed under general anesthesia, with routine shunting and patching, using cerebral near-infrared spectroscopy monitoring. Carotid exposure technique was classified as either clamped-dissection (CD) or preclamping-dissection (PCD) if the carotid bifurcation was dissected after or prior to carotid clamping. Perioperative and 30-day strokes and their possible mechanisms were evaluated according to preoperative symptoms and surgical technique adopted. Results: Among 1760 CEAs performed, 30 (1.7%) perioperative strokes occurred. 14 (47%) were identified upon emergence from general anesthesia, and 16 (53%) were noted in the first 30 days following intervention. Stroke etiology was categorized as follows: technical (acute thrombosis or intimal flap or due to intraoperative complications), embolic (no recognized technical defect), hemorrhagic, or contralateral. Symptomatic patients had a significantly higher rate of any type of stroke than asymptomatic patients (3.8% vs 0.9%, P =.0001). CD was protective for postoperative stroke (0.9% vs 3.1%, P =.001) in both symptomatic and asymptomatic patients (2.5% vs 5.9%, P =.05; 0.4% vs 1.9%, P =.005), particularly for the cohort in which symptomatic patients (0.7% vs 3.2%, P =.04) suffered postoperative embolic stroke. Conclusion: Perioperative stroke in CEA may be multifactorial in etiology, including a result of technical errors. A CD technique may help reduce the incidence of perioperative stroke