This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

In this paper, we present a study of examples of writings that are known in the science of Semitic research compared to the texts (Jewish-Arab, Samaritan-Arabic) written in Hebrew script and texts from the Bible. We try to explain the role of these literary works in Islamic history and civilization, as one of the most important documents are the writings (Gniza), which contributed to provide a full presentation on life in the Islamic community in all aspects of life, especially religious activity and showed the sincere relationship in dealing with the other under tolerance The University of Cambridge has prepared Islamic documents and kept them in separate boxes and presented them to researchers to convey the Islamic heritage written by

The Semitic Languages have    her its  Articulatory   That  what  we  attend  to  discuss  In  this  Research  to  Represent the  Relation  Between  them  and  the Light  Of  Semitics   a Comparative Studies  where  ever  It's  Exists   The Semitic languages by comparing the words whish most Semitic languages share with each other. We call such Words the Semitic denominator. We have adopted a comparative framework in our Research, which is based on comparing an Arabic word with its Semitic counterpart in Order to identify the forms that control grammatical  change in both language

The study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy

Addressed the problem of the research is marked (experimentation in caves fee) concept and its role in experimentation deviate Display Num formal charges caves. The search came in four sections: general framework for research and identified the research problem and the need for him. With an indication of the importance of his presence. Then specify the search for the goals of (revealed the nature and role of experimentation in determining the nature of Manifesting fee documented on the walls of caves), followed by the establishment of the three search limits (objectivity, the temporal and spatial) were then determine the terms related to the title. Then provide the theoretical framework and indicators that resulted from academic theorizi

The evolution of cryptography has been crucial to preservation subtle information in the digital age. From early cipher algorithms implemented in earliest societies to recent cryptography methods, cryptography has developed alongside developments in computing field. The growing in cyber threats and the increase of comprehensive digital communications have highlighted the significance of selecting effective and robust cryptographic techniques. This article reviews various cryptography algorithms, containing symmetric key and asymmetric key cryptography, via evaluating them according to security asset, complexity, and execution speed. The main outcomes demonstrate the growing trust on elliptic curve cryptography outstanding its capabi

Reflection cracking in asphalt concrete (AC) overlays is a common form of pavement deterioration that occurs when underlying cracks and joints in the pavement structure propagate through an overlay due to thermal and traffic-induced movement, ultimately degrading the pavement’s lifespan and performance. This study aims to determine how alterations in overlay thickness and temperature conditions, the incorporation of chopped fibers, and the use of geotextiles influence the overlay’s capacity to postpone the occurrence of reflection cracking. To achieve the above objective, a total of 36 prism specimens were prepared and tested using an overlay testing machine (OTM). The variables considered in this study were the thickness of the

Reflection cracking in asphalt concrete (AC) overlays is a common form of pavement deterioration that occurs when underlying cracks and joints in the pavement structure propagate through an overlay due to thermal and traffic-induced movement, ultimately degrading the pavement’s lifespan and performance. This study aims to determine how alterations in overlay thickness and temperature conditions, the incorporation of chopped fibers, and the use of geotextiles influence the overlay’s capacity to postpone the occurrence of reflection cracking. To achieve the above objective, a total of 36 prism specimens were prepared and tested using an overlay testing machine (OTM). The variables considered in this study were the thickness of the

In this work, a comparative analysis for the behavior and pattern of the variations of the IF2 and T Ionospheric indices was conducted for the minimum and maximum years of solar cycles 23 and 24. Also, the correlative relationship between the two ionospheric indices was examined for the seasonal periods spanning from August 1996 to November 2008 for solar cycle 23 and from December 2008 to November 2019 for solar cycle 24. Statistical calculations were performed to compare predicted values with observed values for the selected indices during the tested timeframes. The study's findings revealed that the behavior of the examined indices exhibited almost similar variations throughout the studied timeframe. The seasonal variations were