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

Statistical studies are reported in this article for an active galactic nuclei sample of different type of active galaxies Seyferts 1, Seyferts 2, and Quasars. These sources have been selected from a Catalogue for bright X-ray galaxies. The name of this index is ROSAT Bright Source Catalogue (RBSC) and the NRAO VLA Sky Survey (NVSS). In this research, multi-wavelength observational bands Radio at 1.4 GHz, Optical at 4400 A0, and X-ray at energy 0.1-2.4 KeV have been adopted in this study. The behavior of flux density ratios has been studied ,  with respect to the absolute magnitude . Furthermore, the Seyfert1 and Seyfert 2 objects are combined in one group and the QSOs are collectest in another group. Also, it has been found that t

The brief description to the theory of propagation of electromagnetic waves in plasma was done. The cutoff and resonance regions have been showed. The principles of plasma heating at electron cyclotron resonance (ECRH) method have been mentioned. The numerical simulation to three different station: Tosca station in United Kingdom, ISX-B station in USA and T-10 station in Russia had been done. The optical depth and the friction of energy absorbed A have been calculated. The simulation results indicate that both and A are increase with size of the tokamak and it is possible to obtain full absorption in large tokamak.

The Dirichlet process is an important fundamental object in nonparametric Bayesian modelling, applied to a wide range of problems in machine learning, statistics, and bioinformatics, among other fields. This flexible stochastic process models rich data structures with unknown or evolving number of clusters. It is a valuable tool for encoding the true complexity of real-world data in computer models. Our results show that the Dirichlet process improves, both in distribution density and in signal-to-noise ratio, with larger sample size; achieves slow decay rate to its base distribution; has improved convergence and stability; and thrives with a Gaussian base distribution, which is much better than the Gamma distribution. The performance depen

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky theorem of

The influence of Cr3+ doping on the ground state properties of SrTiO 3 perovskite was evaluated using GGA-PBE approximation. Computational modeling results infered an agreement with the previously published literature. The modification of electronic structure and optical properties due to Cr3+ introducing into SrTiO 3 were investigated. Structural parameters assumed that Cr3+ doping alters the electronic structures of SrTiO 3 by shifting the conduction band through lower energies for the Sr and Ti sites. Besides, results showed that the band gap was reduced by approximately 50% when presenting one Cr3+ atom into the SrTiO 3 system and particularly positioned at Sr sites. Interestingly, substituting Ti site by Cr3+ led to eliminating the ban

Many approaches have been developed over time to counter the bioavailability limitations of poorly soluble drugs. With advances in nanotechnology in recent decades, this issue has been approached through the formulation of drugs as nanocrystals. Nanocrystals consist of pure drug(s) and a minimum of surface active agent(s) required for stabilization. They are carrier-free submicron colloidal drug delivery systems with a mean particle size typically in the range of 200 - 500 nm. By reducing particle size to nanoscale, the surface area available for dissolution is increased, and thus bioavailability is enhanced. Drug nanocrystals constitute a versatile formulation approach to enhance the pharmacokinetic and pharmacodynamic properties of poorly