Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

The last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an enhancement for supporting the others waiting search activities in this field.

This paper presents a modified training method for Recurrent Neural Networks. This method depends on the Non linear Auto Regressive (NARX) model with Modified Wavelet Function as activation function (MSLOG) in the hidden layer. The modified model is known as Modified Recurrent Neural (MRN). It is used for identification Forward dynamics of four Degrees of Freedom (4-DOF) Selective Compliance Assembly Robot Arm (SCARA) manipulator robot. This model is also used in the design of Direct Inverse Control (DIC). This method is compared with Recurrent Neural Networks that used Sigmoid activation function (RS) in the hidden layer and Recurrent Neural Networks with Wavelet activation function (RW). Simulation results shows that the MRN model is bett

The hydraulic conditions of a flow previously proved to be changed when placing large-scale geometric roughness elements on the bed of an open channel. These elements impose more resistance to the flow.  The geometry of the roughness elements, the numbers used, and the configuration are parameters that can affect the hydraulic flow characteristics. The target is to use inclined block elements to control the salt wedge propagation pointed in most estuaries to prevent its negative effects. The Computational Fluid Dynamics CFD Software was used to simulate the two-phase flow in an estuary model. In this model, the used block elements are 2 cm by 3 cm cross-sections with an inclined face in the flow direction, with a length

Objective. This study aimed to evaluate and compare the force degradation of two types of elastomeric chains following different periods of immersion in zinc-containing mouthwashes. Materials and Methods. Four hundred and forty pieces of Elasto-Force and Super Elasto-Force elastomeric chains were divided into two control and eight experimental groups. The pieces were stretched to 25 mm on pins mounted on an acrylic block and stored in distilled water at 37°C. The experimental groups were immersed in four different types of mouthwash for one minute twice a day throughout the test period. Ten continuous thermocycles per day between cold and hot water baths (5–55°C) were carried out. Forces were measured at six-time intervals (in

Background: Fractures of patella constitute 1% of all fractures. Various techniques have been described for internal fixation of patella fractures. Superiority of one technique over the other has long been debated. Objective: We reviewed a series of seventy patients with transverse or comminuted fractures of patella treated with cerclage and tension band wiring technique to assess if it had any advantages over k. wires and tension band wiring technique. Type of the study: Retrospective study. Methods; Seventy patients with displaced patella fracture, with a mean age of 47 years (range 13-75) were divided into two groups :group A 36 patients were treated with cerclage and tension bands technique ,and group B 34 patients were fixed by 2 K.

Background:Fractures of patella constitute 1% of all fractures. Various techniques have been described for internal fixation of patella fractures. Superiority of one technique over the other has long been debated. Objective:We reviewed a series of seventy patients with transverse or comminuted fractures of patella treated with cerclage and tension band wiring technique to assess if it had any advantages over k. wires and tension band wiring technique. Type of the study:Retrospective study.Methods; Seventy patients with displaced patella fracture, with a mean age of 47 years (range 13-75) were divided into two groups :group A 36 patients were treated with cerclageand tensi

     In the present work, a kinetic study was performed to the extraction of phosphate from Iraqi Akashat phosphate ore using organic acid. Leaching was studied using lactic acid for the separation of calcareous materials (mainly calcite). Reaction conditions were 2% by weight acid concentration and 5ml/gm of acid volume to ore weight ratio. Reaction time was taken in the range 2 to 30 minutes (step 2 minutes) to determine the reaction rate constant k based on the change in calcite concentration. To determine value of activation energy when reaction temperature is varied from 25 to 65 , another investigation was accomplished. Through the kinetic data, it was found that selective leaching was controlled by

In this paper the chain length of a space of fuzzy orderings is defined, and various properties of this invariant are proved. The structure theorem for spaces of finite chain length is proved. Spaces of Fuzzy Orderings Throughout X = (X,A) denoted a space of fuzzy orderings. That is, A is a fuzzy subgroup of abelian group G of exponent 2. (see [1] (i.e. x 2 = 1,  x  G), and X is a (non empty) fuzzy subset of the character group  (A) = Hom(A,{1,–1}) satisfying: 1. X is a fuzzy closed subset of  (A). 2.  an element e  A such that (e) = – 1    X. 3. X :={a  A\ (a) = 1    X} = 1. 4. If f and g are forms over A and if x  D(