This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of ri

Using the Neural network as a type of associative memory will be introduced in this paper through the problem of mobile position estimation where mobile estimate its location depending on the signal strength reach to it from several around base stations where the neural network can be implemented inside the mobile. Traditional methods of time of arrival (TOA) and received signal strength (RSS) are used and compared with two analytical methods, optimal positioning method and average positioning method. The data that are used for training are ideal since they can be obtained based on geometry of CDMA cell topology. The test of the two methods TOA and RSS take many cases through a nonlinear path that MS can move through tha

Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.

Resumen

    Sotileza , localismo santandrino de sutileza , es la parte más fina del aparejo de pescar donde va el anzuelo. Es la obra maestro de José María de Pereda.Su ambiente , el Santander viejo, anterior al año 50,evocado emocionadamente - emociόn romántica contenida en los trazos sobrios y firmes de un naturalism psicolόgico y paisajista,el Santander que el autor confiesa poseer en el fondo de su corazόn,«y tenerlo esculpido en la memoria de tal suerte que ,a ojos cerrados,me atrevería a trazarle con todo su perímetro y sus calles, y el color de sus piedras, y el número, y los nombres, y hasta las caras de sus habitantes».Dentro de la grandeza primaria de las criaturas de Pere

Using the Neural network as a type of associative memory will be introduced in this paper through the problem of mobile position estimation where mobile estimate its location depending on the signal strength reach to it from several around base stations where the neural network can be implemented inside the mobile. Traditional methods of time of arrival (TOA) and received signal strength (RSS) are used and compared with two analytical methods, optimal positioning method and average positioning method. The data that are used for training are ideal since they can be obtained based on geometry of CDMA cell topology. The test of the two methods TOA and RSS take many cases through a nonlinear path that MS can move through that region. The result

studied, and its important properties and relationship with both closed and open Nano sets were investigated. The new Nano sets were linked to the concept of Nano ideal, the development of nano ideal mildly closed set and it has been studied its properties. In addition to the applied aspect of the research, a sample was taken from patients infected with viral hepatitis, and by examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous disease.

Substantial research has been performed on Building Information Modeling (BIM) in various topics, for instance, the use and benefit of BIM in design, construction, sustainable environment building, and Facility assets over the past several years. Although there are various studies on these topics, Building Information Modeling (BIM) awareness through facilities management is still relatively poor. The researcher's interest is increased in BIM study is based heavily upon the perception that it can facilitate the exchange and reuse of information during various project phases. This property and others can be used in the Iraqi Construction industry to motivate the government to eliminate the change resistance to use innovat