Background: The cells of periodontium contain many intracellular enzymes like (alkaline phosphatase ALP) that are released outside into the saliva and gingival crevicular fluid (GCF) after destruction of periodontal tissue. The aim of study was to determine the activity of this enzyme in saliva and its relation to the salivary flow rate, PH and clinical periodontal parameters in patients with chronic periodontitis. Subject, Materials and methods: Sample population consist of 75 individuals ;divided into four groups , the first group (15):control subject, the second group (20):mild chronic periodontitis, the third group(20) moderate chronic periodontitis and the fourth group (20) sever chronic periodontitis, Measurements of plaque index (PL

The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

The radial wave functions of the generalise dWoods–Saxon (GWS) potential within the two-body model of (Core + n) have been used to study the ground-state density distributions of protons, neutrons and matter and the associated root mean square (rms) radii of neutron-rich 14B, 22N, 23O and 24F halo nuclei. The calculated results show that the radial wave functions of the generalised Woods–Saxon potential within the two-body model succeed in reproducing neutron halo in these exotic nuclei. Elastic electron scattering form factors for these nuclei are studied by combining the charge density distributions with the plane-wave Born approximation (PWBA).

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.