In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

Background: Severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) is still a severe threaft for human health currently, and the researches about it is a focus topic worldwide.

Aim of the study: In this study, we will collect some laboratory results of the patients with coronavirus disease (COVID-19) to assess the function of liver, heart, kidney and even pancreas. 

Subjects and Methods: Laboratory results of the patients with COVID-19 are collected. The biochemical indices are classified and used to assess the according function of liver, heart, kidney; meantime, and blood glucose is also observed and taken as an index to roughly evaluate pancreas.

Results: There were some in

Beta-irradiation effects on the microstructure of LDPE samples have been investigated
using Positron Annihilation Lifetime Technique (PALT). These effects on the orthopositronium
(o-Ps) Lifetime t3, the free positron annihilation lifetime 2 t , the free-volume
hole size (Vh) and the free volume fraction (fh) were measured as functions of Beta
irradiation - dose up to a total dose of 30.28 kGy.
The results show that the values of t3, Vh and fh increase gradually with increasing Beta
dose up to a total dose of 1.289 kGy, and reach a maximum increment of 17.4%, 32.8% and
5.86%, respectively, while t2 reachs maximum increment of 211.9% at a total dose of 1.59
kGy. Above these doses, the values show nonlinear changes u

Objectives: To evaluate the effect of vitamin D3 local injections on apical root resorption, alveolar bone integrity, and chair-side time following three and six months of canine retraction. Subjects and Methods: Seventeen adult patients (18-35 years old) of class I and II malocclusions were recruited, who required bilateral maxillary 1st premolars extraction before starting maxillary canines retraction. The experimental side received 25 pg dose of vitamin D3 injected locally into the distal periodontal sulcus of the canine (before force application) every three weeks, while the control side received retraction force only. Periapical radiographic evaluation was conducted after 3 and 6 months of the start of canines' retraction. Results: At

Objectives: To evaluate the effect of vitamin D3 local injections on apical root resorption, alveolar bone integrity, and chair-side time following three and six months of canine retraction. Subjects and Methods: Seventeen adult patients (18-35 years old) of class I and II malocclusions were recruited, who required bilateral maxillary 1st premolars extraction before starting maxillary canines retraction. The experimental side received 25 pg dose of vitamin D3 injected locally into the distal periodontal sulcus of the canine (before force application) every three weeks, while the control side received retraction force only. Periapical radiographic evaluation was conducted after 3 and 6 months of the start of canines' retraction. Results: At

ABSTRACT

The research focuses on the key issue concerning the use of the best ways to test the financial stability in the banking sector, considering that financial stability cannot be achieved unless  the financial sector in general and the banking sector  in particular are able to perform its key role in addressing the economic and social development requirements, under the laws and regulations that control  banking sector , as the only way that increases its ability to deal with any risks or negative effects experienced by banks and other financial institutions. The research goal is  to evaluate the stability of the banking system in Iraq, through the use of a set of econometrics an

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

A set of hydro treating experiments are carried out on vacuum gas oil in a trickle bed reactor to study the hydrodesulfurization and hydrodenitrogenation based on two model compounds, carbazole (non-basic nitrogen compound) and acridine (basic nitrogen compound), which are added at 0–200 ppm to the tested oil, and dibenzotiophene is used as a sulfur model compound at 3,000 ppm over commercial CoMo/ Al2O3 and prepared PtMo/Al2O3. The impregnation method is used to prepare (0.5% Pt) PtMo/Al2O3. The basic sites are found to be very small, and the two catalysts exhibit good metal support interaction. In the absence of nitrogen compounds over the tested catalysts in the trickle bed reactor at temperatures of 523 to 573 K, liquid hourly space v