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 mix promotion important to any organization in general, has been selected promotional mix tools in this research to identify the role in maximizing the Organization of sales growth business, which included the research problem several fundamental questions about the role of each promotional tool of advertising, public relations and personal selling and sales promotion direct marketing within the promotional mix in the promotion of business sales organization. The research aims to provide theoretical and field organizations surveyed about the role played by the mix promo in sales growth, and  importance of research on the identification of more than promotional tools impact on sales gr

The aim of this study is to develop a novel framework for managing risks in smart supply chains by enhancing business continuity and resilience against potential disruptions. This research addresses the growing uncertainty in supply chain environments, driven by both natural phenomena-such as pandemics and earthquakes—and human-induced events, including wars, political upheavals, and societal transformations. Recognizing that traditional risk management approaches are insufficient in such dynamic contexts, the study proposes an adaptive framework that integrates proactive and remedial measures for effective risk mitigation. A fuzzy risk matrix is employed to assess and analyze uncertainties, facilitating the identification of disr

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

The art of batik is one of the ancient arts that has a long history in East Asian countries, especially in Indonesia, where it was considered a traditional craft with which many Indonesian tribes lived. This art began to move to other continents and develops and progresses due to the artist’s connection to the surrounding technological and intellectual development, as art became more outgoing and liberated, it helped the artist to create and innovate in his designs. In this research, he focuses on modern performance methods through which print paintings can be produced through design elements, especially calligraphy, to create aesthetic and creative effects in the productive work. The current research aims to identify the various perfo

In this research is estimated the function of reliability dynamic of multi state systems  and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of

The present study is concerned with the role of income tax in implementing economic goals in Iraq and treating the problems and pitfalls in the Iraq economy.

The study also aims at investigating the role of income tax in attracting promising favorite effects into economy.

The study was performed on data covering the period (2003 - 2012) with respect to the variables of (income tax, oil profits) as independent variables and (private consuming expenditure, private investmental expenditure, and standard figure of prices) as dependent variables. To analyze these data, a number of statistical descriptive and analytical techniques were used such as (percentage, standard variance, mediums, F test, T test and SPSS). It has been c

The purpose of this paper is use the Dynamic Programming to solve a deterministic periodic review model for inventory problem and then to find the optimal policies that the company must uses in the purchase or production  (in the practical application example the Al Aksa company purchase the generators from out side country).

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.