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)

Evaluation of Crocus sativus L. Quality Using FTIR Spectroscopy

Crocus sativus L. is one the important spices that gives food a distinctive color and taste as well as its medicinal value. Its quality can be estimated using different analysis methods. In This study we used FTIR spectroscopy to Evaluate Crocus sativus L. quality at MEDICO Lab 2023. FTIR Spectroscopy is a fast and reliable analytical method for quality saffron evaluation. The results of FTIR spectra indicated functional groups related to O-H, C=C, C=O, C-O, C(O)–O, C-H, C-H (cis-) and C-H (trans-). Also, our samples lacked the distinctive bands of the active substances of crocetin. Furthermore, the flowers in our samples contained different numbers of stigmas, evidence of the genetic mixing of the bulbs used

Improved Operational Matrices of DP-Ball Polynomials for Solving Singular Second Order Linear Dirichlet-type Boundary Value Problems

Solving Dirichlet-type boundary value problems (BVPs) using a novel numerical approach is presented in this study. The operational matrices of DP-Ball Polynomials are used to solve the linear second-order BVPs. The modification of the operational matrix eliminates the BVP\u27s singularity. Consequently, guaranteeing a solution is reached. In this article, three different examples were taken into consideration in order to demonstrate the applicability of the method. Based on the findings, it seems that the methodology may be used effectively to provide accurate solutions

Preparation and Characterization of SnO2 / AC as a Novel High Surface Area Nanocatalyst

A new solid nanoparticle sorbent (SnO2 / AC) could serve as high surface area and inexpensive nanocatalyst was prepared. Many properties were characterized by SEM and UV spectroscopy. High surface area, large micro pore volume and total pore volume were found to be 571 m2 g−1, 0.4785 cm3 g−1 and 0.7267 cm3 g−1 respectively even with very high loaded ratio (60 %) of tin dioxide to Activated Carbon (SnO2 / AC). Taguchi factorial design method was used to get the maximum MB dye adsorption on the surface of SnO2 / AC nanoparticle sorbent. Contact time (60 min), initial dye concentration (5 mM) and solution temperature (293 K) were found to be the best conditions for the more effective absorption process

Green Synthesis of Zinc Oxide Nanoparticles to Study its Effect on the Skin using IR Thermography

The aim of the research is the infrared imaging technique IR Imaging was used to detect temperature changes and their effects on the skin.In this study, ZnO nanoparticles (ZnO NPs) were prepared by Green's synthesis method. This method is considered the safest, easiest, and cheapest way to manufacture nanomaterials. The optical and structural properties of ZnO NPs have been studied by various techniques such as UV visible, X-ray diffraction, Field emission scanning electron microscopy, and Transmission electron microscopy. ZnO NPs had a UV- visible absorption peak at around 300 nm. ZnO's average crystallite diameter was calculated to be 15.41 nm using Scherrer's equation, which was derived from the width at half maximum of the peak more intense on the 101 planes at 36.28°. The Field emission scanning electron microscopy data showed that the synthesized ZnO NPs have a consistent shape and size throughout their range, these NPs are characterized by their diameter and were assembled into cylindrical clusters of varying diameters, with an average size of 106. Different magnifications of the ZnO NPs examined by Transmission electron microscopy showed that the majority of the particles were homogeneously scattered. Infrared thermal imaging technique (IRT) is used to clarify the change in temperature with the effect of the substance on the skin. The material was placed on the skin in two ways and put on the rabbit's front and back feet. When mixing the powder material of ZnO NPs with distilled water, and mixing the powder material of ZnO NPs with commercial Vaseline, we notice in both cases a temperature rise. The radiance was calculated for each image related to the change of temperature in the band (3-5) µm. The highest value in the range (3-5) µm for image R2 with radiation was (0.9209). The total spectral radioactive emission is proportional to the area under the curves and shifts towards shorter wavelengths with increasing temperature

The Effect of Biologically Synthesized Silver Nanoparticles on the Germination and Growth of Cucurbita pepo Seedlings

Silver nanoparties were synthesized from aqueous solution of silver nitrate, with different molar ratio of silver (0, 1, 2, and 3M), using leaf extraction of Neem as well as Saisban. The effect of silver nanoparticles of Neem and Saisban solution on seed germination, hypocotyls and semi root lengths of Cucurbita Pepo was investigated. The Cucurbita Pepo seeds were immersed for 20 minutes in silver nanoparticles solution of Neem and Saisban along with distilled water as control. The seeds allowed to grow in petri dishes. The results show no effect on growth percentage while a remarkable change in seeding speed and length were observed for all the different concentrations of silver nanoparticles. Silver nanoparticles that are treated with Saisban increase the seeding speed of Cucurbita Pepo, while the highest length of hypocotyls and semi root were noted for seeds treated with silver nanoparticles prepared using Neem

Pd Doped SnO2 Resistive Film As A Non-Enzymatic Glucose Sensor

A new sugar sensor based on metal oxide is presented here. The variation on the sensor resistance is studied against different glucose and fructose concentrations (1 - 360 mg/dl). The study is done for three different resistive films (i) pristine palladium oxide (PdOx); (ii) tin oxide (SnO2) and (iii) palladium doped tin oxide (Pd-SnO2). The chemical reactions of glucose and fructose with surface species were studied. Pd-SnO2 films show an excellent and reliable response to glucose and fructose solution in comparison with the bare films (PdOx and SnO2). Sensor performance was checked for the blood of normal (120 mg/d) and diabetic (420 mg/d) patients. The sensor showed remarkable responses of ~2 and 12 for normal and diabetic patients respectively. The non-enzymatic sensor showed good stability, repeatability and reproducibility. The structure and morphology of these films were characterized by an X-ray diffractometer, Transmission Electron Microscopy (TEM)