According to the wide appearance of Dedekind sums in different applications on different subjects, a new approach for the equivalence of the essential and sufficient condition for ( ) ( ) in and ( ) ( ) in where ( ) Σ(( ))(( )) and the equality of .two .Dedekind sums with their connections is given. The conditions for ( ) ( ) in which is equivalent to ( )– ( ) in were demonstrated with condition that of does not divide . Some applications for the important of Dedekind sums were given.

The Political loyalties of the individual considered as the most important democracies through direct psychological identification in a particular party. The political parties regarded as the important elements and the foundations of the democratic system. They have effective interaction between the voters and the government institutions. The aim of the current research is to identify the quality of Islamic, the Civilian parties, and the most preferred for students. also, the research attempt to identify the level of identification  party that the  university students have, and the difference of identification party  according to the gender (male, female), the difference of of social class (upper, middle, poor). The sample

This large book represents the research and is marked (Compilers of Hanbali jurisprudence of the Abbasid era). It includes, between its covers, a large group of scholars of the Islamic nation, with its great jurists and mujtahids, from the followers of the school of (Ahmed bin Hanbal) in the fundamentals and branches, and specific to the sciences of the Qur’an, its jurisprudence, and the narrators of the hadiths of the Noble Prophet The best of creation (Muhammad) peace and blessings be upon him, and it also includes a large number of reciters and ascetics, who are known for their abundance of authorship, especially with regard to the collection and numbers of classifications, and they are too large to be counted by number! But can we

A trademark is one of the most valuable elements in advertising. At the same time, it is a guarantee for both the producer and the consumer. It prevents the mixing of products with a certain mark with similar products bearing another mark; and creates confidence in the goods of the product.

With the increase in the types of goods and products and the emergence of similar goods, producers have turned to the use of the brand to identify their products and seek perfection in manufacture to maintain quality and continuous improvement which ensures good reputation and fame.

Hence, commercials for goods and services focused on the brand because they give in-depth connotations with the recipients of these ads. T

The main object of this paper is to study the representations of monomial groups and characters technique for representations of monomial groups. We refer to monomial groups by M-groups. Moreover we investigate the relation of monomial groups and solvable groups. Many applications have been given the symbol G e.g. group of order 297 is an M-group and solvable. For any group G, the factor group G/G? (G? is the derived subgroup of G) is an M-group in particular if G = Sn, SL(4,R).

With the quick grow of multimedia contents, from among this content, face recognition has got a lot of significant, specifically in latest little years. The face as object formed of various recognition characteristics for detect; so, it is still the most challenge research domain for researchers in area of image processing and computer vision. In this survey article, tried to solve the most demanding facial features like illuminations, aging, pose variation, partial occlusion and facial expression. Therefore, it indispensable factors in the system of facial recognition when performed on facial pictures. This paper study the most advanced facial detection techniques too, approaches: Hidden Markov Models, Principal Component Analysis (PCA)

The current research aims to identify the Vocational Self of the educational counselors as well as to identify the significant difference in the professional self according to the gender variable (male-female). The researcher adopted the scale of al-hasani (2015), which consisted of (34) items. It was applied to a sample of (300) school counselors (male-female) who were randomly selected from the six directorates in the Baghdad governorate for the academic year 2020/2021. The results showed that the research sample of educational counselors has a vocational self-concept. There are no statistically significant differences in the vocational self-concept between males and females among the educational counselors.

Experimental and theoretical investigations are presented on flocculation process in pulsator clarifier. Experimental system was designed to study the factors that affecting the performance of pulsator clarifier. These factors were water level in vacuum chamber which range from 60 to 150 cm , rising time of water in vacuum chamber which having times of 20,30 & 40 seconds , and sludge blanket height which having heights of 20,30 & 40 cm .The turbidity and pH of raw water used were 200 NTU and 8.13 respectively. According to the jar test, the alum dose required for this turbidity was 20 mg/l .The performance parameters of pulsator clarifier such as , turbidity ,total solid TS , shear rate , volume concentration of sludge blanket an

Aquatic Oligochaetes community in the Iraqi southern marshes, Al- Hawiezah, Al-Chibayish and Al-Hammar, have been studied for the period from July 2006 to June 2007. Two sites within each marsh, in addition to a reference site located at Shatt Al-Garma, have been chosen for sample collection using Ekman dredge. The results revealed that the highest average annual density was 16800 individual / m2 recorded in Al-Hawiezah marsh, while in Al-Chibayish and al-Hammar marsh the density did not exceed 5111 individual/m2. In contrast, the density of Oligochaetes recorded in Shatt Al-Garma was about 10500 individual / m2. The highest monthly density was recorded in April 2007.The highest local percentage occurrence was 96% recorded in Al-Hawiezah ma

The purpose of this paper is to give the condition under which every weakly closed
function is closed and to give the condition under which the concepts of weaklysemi
closed function and weakly pre-closed function are equivalent. Moreover,
characterizations and properties of weakly semi closed functions and weakly preclosed
function was given.