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.
In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.
In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.
In this paper we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of (denoted by ) Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.
Recently, the development and application of the hydrological models based on Geographical Information System (GIS) has increased around the world. One of the most important applications of GIS is mapping the Curve Number (CN) of a catchment. In this research, three softwares, such as an ArcView GIS 9.3 with ArcInfo, Arc Hydro Tool and Geospatial Hydrologic Modeling Extension (Hec-GeoHMS) model for ArcView GIS 9.3, were used to calculate CN of (19210 ha) Salt Creek watershed (SC) which is located in Osage County, Oklahoma, USA. Multi layers were combined and examined using the Environmental Systems Research Institute (ESRI) ArcMap 2009. These layers are soil layer (Soil Survey Geographic SSURGO), 30 m x 30 m resolution of Digital Elevati
... Show MoreBasrah province is situated at the extreme south of Iraq, it has an interesting reptile fauna (Squamata and Serpentes) and represents a land bridge between three different zoogeographical regions ( Oriental, Palaearctic and Ethiopian).
This situation gave Basrah province a topographic specific opportunity for raising its own faunal diversity including reptiles; in this study Basrah province was divided into four main zones: the cities and orchards, marshes and wetlands (sabkha), the true dessert, the seashore and Shat Al-Arab.
Forty nine reptile species were recorded including snakes, sea and fresh water turtles, and Lizards; brief notes and descriptions for the rare
... Show MoreThe successive international changes in the economic, political, cultural and other fields resulted in many phenomena that occupied different levels of interest, and have been followed up, studied and analysed by specialists and researchers especially under the development of the media in the global communication.
Even though these phenomena had reflections in the communication domain like development and changes in the mechanism of behaviours between the international communities, they created in the meantime a phenomenon that caused an imbalance in the production, spread and the use of the informations that were supposed to be for fewer than 5 countries whereas it actually it is for more than 180 countries.
Literature reviews of reports concerning the parasitic fauna of fishes of Al-Diwaniyah province, Iraq till the end of December 2018 showed that a total of 43 parasite species are so far known from 13 valid fish species investigated for parasitic infections. The parasitic fauna included one euglenozoan, two myzozoans, six ciliophorans, three myxozoans, three trematodes, nine monogeneans, four cestodes, six nematodes, three acanthocephalans and six crustaceans. The infection with the trematodes, one monogenean, two cestodes and one nematode occurred with larval stages, while the remaining infections were either with trophozoites or adult parasites. Among the inspected fishes, Carasobarbus luteus was infected wit
... Show MoreDiscretionary role of the provisions of the Federal Court of Cassation occupies a distinct role in the drafting of the legal base, thanks to vocational and higher professional level, which is practiced by this court in the adaptation of the civil law in light of the changing conditions of the community with the survival of inertia that characterizes the legal basis, so that the legislator important for precision and perfection in his work in drafting this rule, it cannot take in everything and put the necessary solutions to all the new issues that appear in the society. Therefore, the courts in this case is keen to reconcile the provisions of fixed base and the changing conditions of society , in order to reach the intent of
... Show MoreEducational of the mind is a weapon to a different knowledges which
benefit in ife and developed the mind in many field and practice him in a
regular form in a right thinking and practice sense on exactly recognizing and
conception things which is senses and regulating the memory and providing
with benefit information which fit to minded of person,the present research
aimed at answering the following two questions:
1-Does the concept of mind differ with age?
2-Does the recognition on function of mind developed with development of
age?
The research population consisted of the children in the primary schools
of Baghdad/center,and the students of the Education for woman
college/Baghdad university for the age