In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

 The logistic regression model of the most important regression models a non-linear which aim getting estimators have a high of efficiency, taking character more advanced in the process of statistical analysis for being a models appropriate form of Binary Data.                                                          

Among the problems that appear as a result of the use of some statistical methods I

Background: Nutrition can affect periodontal disease through contributing to microbial growth in the gingival crevice, affecting the immunological response to bacterial antigens and assisting the repair mechanism of the connective tissue at the local site after injury from plaque and calculus. The aim of this study was to assess the prevalence of Oral hygiene (plaque and calculus) and gingivitis in relation to age, gender and nutritional status. Materials and methods: The sample included (444) kindergarten children at age of (4 and 5 years old) males and females from urban areas in Al-Ramadi city. The assessment of nutritional status was performed using anthropometr

In this paper, we investigate some methods to solve one of the multi-criteria machine scheduling problems. The discussed problem is the total completion time and the total earliness jobs  To solve this problem, some heuristic methods are proposed which provided good results. The Branch and Bound (BAB) method is applied with new suggested upper and lower bounds to solve the discussed problem, which produced exact results for  in a reasonable time.

This paper proposes a new algorithm (F2SE) and algorithm (Alg(n – 1)) for solving the
two-machine flow shop problem with the objective of minimizing total earliness. This
complexity result leads us to use an enumeration solution approach for the algorithm (F2SE)
and (DM) is more effective than algorithm Alg( n – 1) to obtain approximate solution.

A study has been performed to compare the beddings in which ductile iron pipes are buried. In water transmission systems, bends are usually used in the pipes. According to the prescribed layout, at these bends, unbalanced thrust forces are generated that must be confronted to prevent the separation of the bend from the pipe. The bed condition is a critical and important factor in providing the opposite force to the thrust forces in the restraint joint system. Due to the interaction between the native soil and the bedding layers in which the pipe is buried and the different characteristics between them. Also, the interaction with the pipe material makes it difficult to calculate the real forces opposite to the thrust forces and the way they

Numerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case  on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate th

Artificial fish swarm algorithm (AFSA) is one of the critical swarm intelligent algorithms. In this
paper, the authors decide to enhance AFSA via diversity operators (AFSA-DO). The diversity operators will
be producing more diverse solutions for AFSA to obtain reasonable resolutions. AFSA-DO has been used to
solve flexible job shop scheduling problems (FJSSP). However, the FJSSP is a significant problem in the
domain of optimization and operation research. Several research papers dealt with methods of solving this
issue, including forms of intelligence of the swarms. In this paper, a set of FJSSP target samples are tested
employing the improved algorithm to confirm its effectiveness and evaluate its ex

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

Limitations of the conventional diagnostic techniques urged researchers to seek novel methods to predict, diagnose, and monitor periodontal disease. Use of the biomarkers available in oral fluids could be a revolutionary surrogate for the manual probing/diagnostic radiograph. Several salivary biomarkers have the potential to accurately discriminate periodontal health and disease. This study aimed to determine the diagnostic sensitivity and specificity of salivary interleukin (IL)‐17, receptor activator of nuclear factor‐κB ligand (RANKL), osteoprotegerin (OPG), RANKL/OPG for differentiating (1) periodontal health from disease and (2) stable a