Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

This paper presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt  properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1)  is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method  (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to

     The objective of the study is to demonstrate the predictive ability is better between the logistic regression model and Linear Discriminant function using the original data first and then the Home vehicles to reduce the dimensions of the variables for data and socio-economic survey of the family to the province of Baghdad in 2012 and included a sample of 615 observation with 13 variable, 12 of them is an explanatory variable and the depended variable is number of workers and the unemployed.

     Was conducted to compare the two methods above and it became clear by comparing the  logistic regression model best of a Linear Discriminant  function written

In many scientific fields, Bayesian models are commonly used in recent research. This research presents a new Bayesian model for estimating parameters and forecasting using the Gibbs sampler algorithm. Posterior distributions are generated using the inverse gamma distribution and the multivariate normal distribution as prior distributions. The new method was used to investigate and summaries Bayesian statistics' posterior distribution. The theory and derivation of the posterior distribution are explained in detail in this paper. The proposed approach is applied to three simulation datasets of 100, 300, and 500 sample sizes. Also, the procedure was extended to the real dataset called the rock intensity dataset. The actual dataset is collecte

Let R be a commutative ring with identity, and let M be a unity R-module. M is called a bounded R-module provided that there exists an element x?M such that annR(M) = annR(x). As a generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element x?M such that . In this paper, some properties and characterizations of semi-bounded modules are given. Also, various basic results about semi-bounded modules are considered. Moreover, some relations between semi-bounded modules and other types of modules are considered.

These days, it is crucial to discern between different types of human behavior, and artificial intelligence techniques play a big part in that.  The characteristics of the feedforward artificial neural network (FANN) algorithm and the genetic algorithm have been combined to create an important working mechanism that aids in this field. The proposed system can be used for essential tasks in life, such as analysis, automation, control, recognition, and other tasks. Crossover and mutation are the two primary mechanisms used by the genetic algorithm in the proposed system to replace the back propagation process in ANN. While the feedforward artificial neural network technique is focused on input processing, this should be based on the proce

In an earlier paper, the basic analytical formula for particle-hole nuclear state densities was derived for non-Equidistant Spacing Model (non-ESM) approach. In this paper, an extension of the former equation was made to include pairing. Also a suggestion was made to derive the exact formula for the particle-hole state densities that depends exactly on Fermi energy and nuclear binding energies. The results indicated that the effects of pairing reduce the state density values, with similar dependence in the ESM system but with less strength. The results of the suggested exact formula indicated some modification from earlier non-ESM approximate treatment, on the cost of more calculation time

Direct measurements of drag force on two interacting particles  arranged in the longitudinal direction for particle Reynolds numbers varying from J O to 103 are conducted using a micro-force measurement system. The effect of the interparticle distance and Reynolds number on the drag forces  is examined. An empirical equation is obtained to describe the effect of the interparticle distance (l/d) on the dimensionless drag.

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