This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

Background: Consideration of mandibular third molar is important from orthodontic perspective due to several factors such as, lower anterior arch crowding, relapse in lower anterior region, interference with uprighting of mandibular first and second molars during anchorage preparation and molar distalization. The aims of this study were to assess of gender differences in the mandibular third molar position and compare and evaluate whether there is any differences in the results provided by CT scan and lateral reconstructed radiograph. Materials and Methods: The sample of present study consisted of 39 patients (18 males and 21 females) with age range 11-15 years. CT images for patients who were attending at Al Suwayra General Hospital/the C

A successful synthesis of mesoporous Santa Barbara amorphous (SBA-15) with nanoparticle size was attempted using prepared sodium silicate from Iraqi high silica sand. EO20PO70EO20 copolymer was used as a template at highly acidic conditions (pH < 2). The effect of crystallization temperature of (100, 110, 120, and 130 0C), and crystallization time of (24, 48, 72, and 120 h) on surface properties was studied. The experiments were characterized using XRD, FTIR, AFM, BET, and FESEM. The XRD and FTIR tests represent amorphous SBA-15 without any impurities. Decreasing average particle size distribution increased the surface area, and decreased the porosity (pore volume, and pore size) in all experiments. The texture properties were su

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

The Boltzmann equation has been solved using (EEDF) package for a pure sulfur hexafluoride (SF6) gas and its mixtures with buffer Helium (He) gas to study the electron energy distribution function EEDF and then the corresponding transport coefficients for various ratios of SF6 and the mixtures. The calculations are graphically represented and discussed for the sake of comparison between the various mixtures. It is found that the various SF6 – He content mixtures have a considerable effect on EEDF and the transport coefficients of the mixtures

A vector in a separable infinite dimensional Hilbert space is called disk-cyclic for bounded operator if the orbit α : 0, α∈;|∝| 1is dense in. The useful tool used to discover codisk-cyclic operation is called the disk-cyclic Criterion. In this paper we will show that some equivalent conditions of the

Mosquitoes like Culex quinquefasciatus are the primary vector that transmits many causes of diseases such as filariasis, Japanese encephalitis, and West Nile virus, in many countries around the world. The development in the scientific fields, such as nanotechnology, leads to use this technique in control programs of insects including mosquitoes through the use of green synthesis of nanoemulsions based on plant products such as castor oil.  Castor oil nanoemulsion was formulated in various ratios comprising of castor oil, ethanol, tween 80, and deionized water by ultrasonication. Thermodynamic assay improved that the formula of (10 ml) of castor oil, ethanol (5ml), tween 80 (14 ml) and deionized water (71ml)   was mor