Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

The In this experimental study, natural stone powder was utilized to improve a cohesive soil’s compaction and strength properties. According to the significant availability of limestone in the globe, it has been chosen for the purpose of the study, in addition to considering the existing rock industry massive waste. Stone powder was used in percentages of 4, 8, 12, 16% replaced from the soil weight in dry state. Some of cohesive soil’s consistency, shear, and compaction properties were depicted after improvement. The outcomes yielded in significant amendments in the experimented geotechnical properties after stone powder addition considering 60 days curing period. Cohesion and friction angle were notably increased by

Under-reamed piles defined by having one or more bulbs have the potential for sizeable major sides over conventional straight-sided piles, most of the studies on under-reamed piles have been conducted on the experimental side, while theoretical studies, such as the finite element method, have been mainly confined to conventional straight-sided piles. On the other hand, although several laboratory and experimental studies have been conducted to study the behavior of under-reamed piles, few numer­ical studies have been carried out to simulate the piles' performance. In addition, there is no research to compare and evaluate the behavior of these piles under dynamic loading. Therefore, this study aimed to numerically investigate bearing capaci

Fiber‐reinforced elastic laminated composites are extensively used in several domains owing to their high specific stiffness and strength and low specific density. Several studies were performed to ascertain the factors that affect the composite plates’ dynamic properties. This study aims to derive a mathematical model for the dynamic response of the processed composite material in the form of an annular circular shape made of polyester/E‐glass composite. The mathematical model was developed based on modified classical annular circular plate theory under dynamic loading, and all its formulas were solved using MATLAB 2023. The mathematical model was also verified with real experimental work involving the vibration test of the f

The evaluation of banks plays an important role in maintaining the interests of customers with the bank as well as providing continuous supervision and control by the Central Bank. The Central Bank of Iraq conducted an assessment of the Iraqi banks through the implementation of the CAMEL model during a certain period. This evaluation did not continue. The research provides continuity to the Central Bank's assessment and as a step to continue the evaluation process for all banks through the use of the CAMEL model. ROA and ROE by using the regression model for four Iraqi banks registered in the Iraqi market for securities during the period 2010-2016. The results showed that the capital and profitability indicators have a significan

An experiment was conducted in pots under field conditions during fall seasons of 2017 and 2018. This study aimed to improve a weak growth of seedlings under salt stress in sorghum. Three factors were studied. 1st factor was three cultivars (Inqath, Rabeh, and Buhoth70). 2nd factor was seed priming (primed and unprimed seed). Seed were primed by soaking for 12 hours in a solution containing 300 + 70 mg L−1 of gibberellic (GA3) and salicylic (SA) acids, respectively. 3rd factor was irrigation with saline water (6, 9 and 12 dS m−1) resulting from dissolving sodium chloride in distilled water in addition to control treatment (distilled water). Randomized complete block design was used with four replications. In both seasons: the results sh

 This study deals with segmenting the industrial market as an independent variable and targeting the industrial market as a dependent variable. Since the industrial sector represents one of the most important fundamental pillars to build the economies of countries and their development , the Iraqi industrial sector was chosen as a population for the study . Based on measuring the study variables , identifying them and testing the correlation and effect on each other , the study reached a group of findings:

1- Increasing the level of availability of study variables inside the companies “The study sample”.

2- There is a correlation between the independent v

This paper proposes and studies an ecotoxicant system with Lotka-Volterra functional response for predation including prey protective region. The equilibrium points and the stability of this model have been investigated analytically both locally and globally. Finally, numerical simulations and graphical representations have been utilized to support our analytical findings