In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

Background: Laser urinary stone lithotripsy is an established endourological modality. Ho:YAG(2100nm) laser have broadened  the indications for ureteroscopic stone managements  to include larger stone sizes throughout the whole urinary tract.

Purpose: To evaluate the effectiveness and safety of Holmium: YAG(2100nm) laser lithotripsy with a semirigid uretero scope for urinary stone calculi in a prospective cohort of 17 patients.

Patients and Methods: Holmium: YAG(2100nm) laser lithotripsy was performed with a semirigid ureteroscope in 17 patients from September 2016 to December  2016. Calculi were located in the lower ureter in 9 patients (52.9%), the midure

An ingrowing toenail is a common problem affecting mainly adolescents and young adults, with a male predominance of 3:1. The disorder generally occurs in big toes. It is painful and often chronic and it affects work and social activities. Most patients initially complain of pain and later discharge, infection and difficulty in walking occur. The Objectives: The purpose of the study was to evaluate the efficacy and safety of (10600nm) CO2 laser in the treatment of ingrowing toe nail. Patients, Materials & Methods: This study was done in laser medicine research clinics from July 2013 to the end of December 2013; 10 patients including 7(70%) males and 3 (30%) females with age ranging from 18 years to 70 years with mean age of 44 years o

In this paper, split-plate airlift electrochemical reactor as an apparatus with new configuration for wastewater treatment was provided. Two aluminum plates were fixed inside the reactor and present two functions; first it works as split plates for internal loop generation of the airlift system (the zone between the two plates acts as riser while the other two zones act as downcomer) and second it works as two electrodes for electrocoagulation process. Simulated wastewater contaminated with zinc ions was used to test the performance of this apparatus for zinc removal by studying the effect of different experimental variables such as initial concentration of zinc (50-800 ppm), electrical current density (2.67-21.4 mA/cm²), init

The objective of this study is to investigate the application of advanced oxidation processes (AOPs) in the treatment of wastewater contaminated with furfural. The AOPs investigated is the homogeneous photo-Fenton (UV/H₂O₂/Fe⁺²) process. The experiments were conducted by using cylindrical stainless steel batch photo-reactor. The influence of different variables: initial concentration of H₂O₂ (300-1300mg/L), Fe⁺²(20-70mg/L), pH(2-7) and initial concentration of furfural (50-300 mg/L) and their relationship with the mineralization efficiency were studied.

 Complete mineralization for the system UV/H₂O₂/Fe⁺² was achieved at: initi

Low-intensity laser irradiation has been explored as an alternative, non-invasive method to encourage chronic wounds to heal. This study aimed to evaluate the effects of low level laser therapy (biostimulation) using semiconductor diode laser with wavelength (785 nm) on the enhancement of chronic wound healing. Fifty patients with chronic wounds were selected to be treated with Low Level Laser Therapy. Their ages ranged between 1 to 76 years. The wound sites were distributed in the lower limb, upper limb, trunk , perineum and head (70%,14%,12%,2%,2%, respectively). Application of laser therapy by noncontact method few millimeters from the skin for 15 minutes per one session twice weekly for two months ; ie,16 sessions for each patient. R