Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

         This paper examines the use of one of the most common linguistic devices which is hyperbole. It shows how hyperbolic devices are used as an aspect of exaggeration or overstatement for an extra effect in which the speaker can use hyperbole to add something extra to a situation in order to exaggerate his idea or speech. It is, like other figures of speech, used to express a negative or positive attitude of a specific unit of language. Thus, this paper is set against a background of using hyperbole concerning two main fields (advertisements and propaganda). So, the use of hyperbole will be implied by analyzing them concerning their meaning) literal and non-literal).  Methodology of this

--The objective of the current research is to identify: 1) Preparing a scale level for e-learning applications, 2) What is the relationship between the applications of e-learning and the students of the Department of Chemistry at the Faculty of Education for Pure Sciences/ Ibn Al-Haytham – University of Baghdad. To achieve the research objectives, the researcher used the descriptive approach because of its suitability to the nature of the study objectives. The researcher built a scale for e-learning applications that consists of (40) items on the five-point Likrat scale (I agree, strongly agree, neutral, disagree, strongly disagree). He also adopted the scale of scientific values, and it consists of (40) items on a five-point scale as wel

In this research, the Williamson-Hall method and of size-strain plot method was employed to analyze X- ray lines for evaluating the crystallite size and lattice strain and of cadmium oxide nanoparticles. the crystallite size value is (15.2 nm) and (93.1 nm) and lattice strain (4.2 x10−4 ) and (21x10−4) respectively. Also, other methods have been employed to evaluate the crystallite size. The current methods are (Sherrer and modified Sherrer methods ) and their results are (14.8 nm) and (13.9nm) respectively. Each method of analysis has a different result because the alteration in the crystallite size and lattice strain calculated according to the Williamson-Hall and size-strain plot methods shows that the non-uniform strain in nan

This paper presents ABAQUS simulations of fully encased composite columns, aiming to examine the behavior of a composite column system under different load conditions, namely concentric, eccentric with 25 mm eccentricity, and flexural loading. The numerical results are validated with the experimental results obtained for columns subjected to static loads. A new loading condition with a 50 mm eccentricity is simulated to obtain additional data points for constructing the interaction diagram of load-moment curves, in an attempt to investigate the load-moment behavior for a reference column with a steel I-section and a column with a GFRP I-section. The result comparison shows that the experimental data align closely with the simulation

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  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es

Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.

In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.

The longitudinal balanced data profile was compiled into subgroup

Alopecia areata is considered as a major health problem, its importance is attributed to its
recent increased incidence in our population. Till now, there is no exact cause for alopecia areata
although researchers thought it's an autoimmune disease.
This clinical study was designed to evaluate the role of trace elements (zinc and copper) in patients
with alopecia areata. Twenty patients were diagnosed as having alopecia areata with an age range
(10-40 years) were involved in this study. Normal subjects of the same age group were also
evaluated as control. The level of serum Zn and Cu were measured by flame atomic absorption
spectrophotometry in both control and patient group. And the ratio of Zn/Cu was also estimated