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 Esterification kinetics of acetic acid with ethanol in the presence of sulfuric acid as a homogenous catalyst was studied with isothermal batch experiments at 50-60°C and at a different molar ratio of ethanol to acetic acid [EtOH/Ac]. Investigation of kinetics of the reaction indicated that the low of [EtOH/Ac] molar ratio is favored for esterification reaction, this is due to the reaction is catalyzed by acid. The maximum conversion, approximately 80% was obtained at 60°C for molar ratio of 10 EtOH/Ac. It was found that increasing temperature of the reaction, increases the rate constant and conversion at a certain mole ratio, that is due to the esterification is exothermic. Activity coefficients were calculated using UNIFAC progra
... Show MoreIn this paper we define and study new generalizations of continuous functions namely, -weakly (resp., w-closure, w-strongly) continuous and the main properties are studies: (a) If f : X®Y is w-weakly (resp., w-closure, w-strongly) continuous, then for any AÌX and any BÌY the restrictions fïA : A®Y and fB : f -1(B)®B are w-weakly (resp., w-closure, w-strongly) continuous. (b) Comparison between deferent forms of generalizations of continuous functions. (c) Relationship between compositions of deferent forms of generalizations of continuous functions. Moreover, we expanded the above generalizations and namely almost w-weakly (resp., w-closure, w-strongly) continuous functions and we state and prove several results concerning it.
The protection of the rights of minorities is primarily an internal issue that depends on the nature of the political system of the state, and it is one of the internal means to reassure minorities and ensure their enjoyment of those rights. It can be a safety valve against the problems that these minorities may raise. that live in our society, but rather work on developing a legal system that can serve as a role model to protect our minorities, which contributed to drawing a picture that reflected the diversity of our society
Thep resent study was conducted for monitoring of the evaporative cooling tower in methanol production plant using digital computer' visuql Basic computer program was used for the monitoring of the performance of the cooling tower. The structure program consists of sub programs and forms to show all the related variabltes such as temperature, flow rate, pressure ...etc, that affect the cooling tower operation and give alarms and important function informition regarding these variables.
Facial trauma in children and adolescents is reported to range from 1% to 30%. Because of many anatomical, physiological, and psychological characteristics of the pediatric population, maxillofacial injuries in children should be treated with special consideration that is attributable to certain features inherent in facial growth patterns of children. This study evaluated maxillofacial injuries in 726 children in terms of incidence, patterns of injury, causes, and treatment modalities and compared these parameters among 3 pediatric age groups. Intergroup differences were analyzed using Z test for 2 populations' proportion. The results showed that the incidence of pediatric maxillofacial injuries and fractures is higher than that reported el
... Show Moreهذا البحث يتحدى الافتراض القائل أن العراق بعد عام 2003 يجب دراسته بمعزل عن ديناميات التي سبقت عام 2003، اذ تبرهن هذه الدراسة على ان الشعبوية هي احدى الديناميات التي تمظهرت بصورة شعبوية استبدادية في النظام الديكتاتوري، نظرًا لأنه كان زعيم حزب علماني وعربي على نطاق واسع، لكنه استخدم الدين والقومية بشكل استراتيجي وانتقائي في ظروف معينة، مما خلق سياق الشعبوية الحديثة. الموجة الثانية هي الشعبوية العرقية والطائف
... Show MoreIn the name of God the Merciful
After .....
This is discussed in the hadeeth of Shaaban's speech, in which there is much talk in modern terms about the ruling
It has to be corrected, improved, weakened or denied, and it has a title (modern)
Shaaban's sermon is a modern study). It is an attempt to judge me after I come
In the text and then came out of the books and works that mentioned the sermon in its verses and then a statement of the ruling
And then I studied the rules and ruled them according to the rules
Followed by the scientists wound and amendment, and then the conclusion and deposited the most important results that came out
He accepts this purely for his generous consideration of this humble research, an
The aims of this thesis are to study the topological space; we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore, we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied. On the other hand, we studied weakly/ strongly forms of ω-perfect mappings, namely -ω-perfect mappings, weakly -ω-perfect mappings and strongly-ω-perfect mappings; also, we investigate their fundamental properties. We devoted to study the relationship between weakly -ω-perfect mappings and strongly -ω-perfect mappings. As well as, some new generalizations of some definitions wh
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