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.

   The technology of reducing dimensions and choosing variables are very important topics in statistical analysis to multivariate. When two or more of the predictor variables are linked in the complete or incomplete regression relationships, a problem of multicollinearity are occurred which consist of the breach of one basic assumptions of the ordinary least squares method with incorrect estimates results.

 There are several methods proposed to address this problem, including the partial least squares (PLS), used to reduce dimensional regression analysis. By using linear transformations that convert a set of variables associated with a high link to a set of new independent variables and unr

Abstract

This study aimed to identify the business risks using the approach of the client strategy analysis in order to improve the efficiency and effectiveness of the audit process. A study of business risks and their impact on the efficiency and effectiveness of the audit process has been performed to establish a cognitive framework of the main objective of this study, in which the descriptive analytical method has been adopted. A survey questionnaire has been developed and distributed to the targeted group of audit firms which have profession license from the Auditors Association in the Gaza Strip (63 offices). A hundred questionnaires have been distributed to the study sample of which, a total of 84 where answered and

ABSTRACT

Background : The aim of this work is to assess the role of breast sonography  and ductography in the evaluation of different causes of nipple discharge.

Methods :  The study will be carried out on twenty-five female patients referred to the Radiodiagnosis department at Alexandria Main University Hospital presenting with nipple discharge.

They were divided into two groups:

Group I include 10 patients (40%) with surgically significant nipple discharge who were the patients with unilateral, uniorificial surgically significant colour type nipple discharge .They were investigated by mammography, sonography, and ductography.

Group II include 15 patients

The neutron, proton, and matter densities of the ground state of the proton-rich ²³Al and ²⁷P exotic nuclei were analyzed using the binary cluster model (BCM). Two density parameterizations were used in BCM calculations namely; Gaussian (GS) and harmonic oscillator (HO) parameterizations. According to the calculated results, it found that the BCM gives a good description of the nuclear structure for above proton-rich exotic nuclei. The elastic form factors of the unstable ²³Al and ²⁷P exotic nuclei and those of their stable isotopes ²⁷Al and ³¹P are studied by the plane-wave Born approximation. The main difference between the elastic form factors of unstable nuclei and the

The proton-neutron interacting boson model (IBM-2) has been used to make a schematic study of the Ruthenium ( ) isotopes of mass region around with and . For each isotope of the values of the IBM-2 Hamiltonian parameters, which yield an acceptable results for excitation energies in comparison with those of experimental data, have been determined. Fixed values of the effective charges ( ) and of the proton and neutron g factors ( and ) have been chosen for all isotopes under study. The calculated electric quadrupole moments of state, transitions, the magnetic dipole moments transitions and mixing ratios are in reasonable agreement with the experimental data.

The nuclear structure included the matter, proton and neutron densities of the ground state, the nuclear root-mean-square (rms) radii and elastic form factors of one neutron ²³O and ²⁴F halo nuclei have been studied by the two body model of  within the harmonic oscillator (HO) and Woods-Saxon (WS) radial wave functions. The calculated results show that the two body model within the HO and WS radial wave functions succeed in reproducing neutron halo in these exotic nuclei. Moreover, the Glauber model at high energy has been used to calculated the rms radii and reaction cross section of these nuclei.