The discussion in this paper gives several theorems and lemmas on the Sums of Squares of consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.
The researcher used the experimental approach due to its suitability and the nature of the research problem. The research community was represented by the eighth-grade students in the Rozak Elementary Mixed School affiliated with the General Directorate of Education in Erbil / the center, for the academic year (2021-2022), the number is (96) students, and the research sample consisted of (63) male and female students, with (31) in the experimental group, and (32) in the control group, and (11) students were excluded by (5) students from the experimental group, and (6) students from the control group, as the excluded, are students who failed and were absent from the lessons, and accordingly, the research sample became composed of (52) mal
... Show MoreSeveral studies have indicated an unprecedented increase in the number of Arab youth who watch music videos. It is also a custom in Arab countries to broadcast songs at their happy parties such as weddings, engagements and birthdays. We see that guests and party owners interact by dancing and singing with the songs, while the viewership rates of Arab music videos have reached millions on YouTube. The researcher decided to study the image of women through the lyrics of these songs, due to their importance in shaping the image of women in the minds of young people and shaping the (self-image) of young women. Twenty songs were selected from the most watched songs on YouTube for the year 2024, and it was found that the negative qualities of t
... Show MorePraise be to God, who made the pegs of the earth and entrusted them with the task of keeping the earth from tilting, and prayers and peace be upon the one to whom the Qur’an was revealed, Muhammad, and upon his family and all his companions.
The topic of mountains is one of the important topics in human life, as God has associated great miracles with them that indicate the perfection of the power of God Almighty. God Almighty says: (And to the mountains, my palms have turned. This is worthy of every rational person to contemplate His signs, the Almighty, in this solid part and safety belt of the earth, in order to reveal the secrets of the mountains and uncover their treasures. The more the researcher studies the mountains and
... Show MoreFine art represents part of society's culture. The development of art was accompanied by the penetration of new worlds known as the fourth dimension. After art entered the boundaries of geometry and reduction; He began to break into the absurd, and the form and philosophy of art changed, moving from modernity to what came after it to contemporary. Transforming from a formal form into a symbolic form with philosophical implications linked to the light, audio and kinetic effects as they embody time, the concept became the master of the idea. The research aims to identify the concept of time and its types, then the philosophical concept of time and its reflection on contemporary art, through the analytical study of a selection of contempora
... Show MoreThe Pulse Coupled Oscillator (PCO) has attracted substantial attention and widely used in wireless sensor networks (WSNs), where it utilizes firefly synchronization to attract mating partners, similar to artificial occurrences that mimic natural phenomena. However, the PCO model might not be applicable for simultaneous transmission and data reception because of energy constraints. Thus, an energy-efficient pulse coupled oscillator (EEPCO) has been proposed, which employs the self-organizing method by combining biologically and non-biologically inspired network systems and has proven to reduce the transmission delay and energy consumption of sensor nodes. However, the EEPCO method has only been experimented in attack-free networks without
... Show MoreThe study focuses on Kamez model and the Claus Meyer model of instructional design, which are models that provide the learner with educational experiences to suit the logical information of the learner and the variety of instructional models. Research Objective: The present research aims to identify Limitations of the study. The current research is determined by ((fourth grade preparatory students, the book of the date of the fourth preparatory course)) Chapter II includes Arabic and foreign studies on the model of Kemp and Claus Mayer in the acquisition of concepts and direction towards the material. Chapter III Experimental Design: The researcher adopted an experimental design with two experimental groups and a control group. The resea
... Show MoreThe current research aims to identify the " impact of strategic warheads numbered ( NHT) in the collection average second grade students in the article of history). " To achieve this, I assumed the researcher that there is no different between the statistically significant the average score for the collection of experimental group who teaches the Arab Islamic history on and a strategic warheads numbered and the average score for the collection of the control group who were studying the same article according to the classic method ( traditional) . The study sample consisted of 64 students from the second grade average in the secondary warka bin nawfal in the general Directorate for education first karkh in Baghdad for the annual cources 2
... Show MoreThat achieve a level of excellence for the quality of university education cannot be achieved only by uniting the efforts of all employees at the university and active participation by students and by alumni and the labor market and society, however we can say that the administrative and academic university staff play an active role and the largest in achieving equivalent quality of higher education, It should unite the efforts of all employees in the educational institution in order to achieve quality education. It is the concept of quality of education, quality assurance and overall management of the quality of the basic pillars on which it is based university education. That highlight the need fo
... Show MoreThe first chapter the importance of research and need for education scientists see that the roots of the use of a specimen Wheatley in learning and teaching back to Grayson Wheatley, one of the largest supporters of a modern construction, which lay the groundwork for the specimen stage and the form in which it is. That was attributed to him, often called his name called while some educators based learning strategy on the issue. He sees the learner in this model make him a meaningful understanding of problems during his progress, thereby acting with his colleagues to find solutions to them in small groups. He
Borders Search: Search by students is determined by th
... Show MoreThis work includes two steps of synthesis, the first one is the synthesis of indole which was prepared according to literature of the reaction of phenyl hydrazine with acetaldehyde in glacial acetic acid afforded phenyl hydrazone of acetaldehyde , this product was fused with zinc chloride to give the indole.Reaction of cyclohexanone with phenyl hydrazine using the same procedure for the preparing giving 1,2,3,4-Tetrahydrocarbazole.Second step involved synthesis of a series of (17) of mannich bases derivatives of indole and 1,2,3,4-Tetrahydrocarbazle. Mannich reaction involves the condensation of aldehyde usually formaldehyde with different secondary amine and with compound containing an activated hydrogen.The reaction illustrated by the fo
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