Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

This study takes its importance in the area of systemic and historical
studies because it stands on presenting such aspects from the systematic
respect and now Ibn AL-Jouzy dealt with the text of this subject and how he
was exact in telling them.
Therefore, this study sheds light on the important aspects of this
method in his book through reading and studying such texts whether they had
direct or indirect relationship with this subject.
This study is not an easy task since it is based on contriving the
intellectual aspects in the methods of lbn AL-Jouzy and how he deals with the
text of this subject in its hygienic, natural and geographical aspects in
constructing a historical method in most scripts, the gen

Criticism is inherently impolite and a face-threatening act generally leading to conflicts among interlocutors. It is equally challenging for both native and non-native speakers, and needs pre-planning before performing it. The current research examines the production of non-institutional criticism by Iraqi EFL university learners and American native speakers. More specifically, it explores to what extent Iraqi EFL learners and American native speakers vary in (i) performing criticism, (ii) mitigating criticism, and (iii) their pragmatic choices according to the contextual variables of power and distance. To collect data, a discourse-completion task was used to elicit written data from 20 Iraqi EFL learners and 20 American native speaker

Two decades after replacing the OAU, the AU’s record is best measured not by communiqués but by how fast it converts rules into results on the ground. In March 2022, the African Union’s Peace and Security Council (PSC) authorised the transition from AMISOM to ATMIS in Somalia — a reminder that, two decades after the African Union (AU) replaced the Organisation of African Unity (OAU), the Union’s rules are judged by execution, not intent. This article argues that the AU’s legal and institutional redesign shortened the warning‑to‑decision cycle and raised the credibility of enforcement, but performance still hinges on finance, logistics and political will. Where mandates are matched with money, enabling capabilities and enforc

in this paper, we study and investigate a simple donor-acceptor model for charge transfer formation using a quantum transition theory. The transfer parameters which enhanced the charge transfer and the rate of the charge transfer have been calculated. Then, we study the net charge transfer through interface of Cu/F8 contact devices and evaluate all transfer coefficients. The charge transfer rate of transfer processes is found to be dominated in the low orientation free energy and increased a little in decreased potential at interface comparison to the high potential at interface. The increased transition energy results in increasing the orientation of Cu to F8. The transfer in the system was more active when the system has large driving for

An investigation was conducted to suggest relations for estimating yield and properties of the improved light lubricating oil fraction produced from furfural extraction process by using specified regression.

Mass transfer in mixer-settler has been studied. Mass transfer coefficient of continuous phase, mass transfer coefficient of dispersed phase and the overall mass transfer coefficient extraction of light lubes oil distillate fraction by furfural are calculated in addition to all physical properties of individual components and the extraction mixtures.

The effect of extraction variables were studied such as extraction temperature which ranges from 70 to 110°C and solvent to oil ratio which ranges from 1:1 to 4:1 (wt/wt

The objective of this study was to develop neural network algorithm, (Multilayer Perceptron), based correlations for the prediction overall volumetric mass-transfer coefficient (k_La), in slurry bubble column for gas-liquid-solid systems. The Multilayer Perceptron is a novel technique based on the feature generation approach using back propagation neural network. Measurements of overall volumetric mass transfer coefficient were made with the air - Water, air - Glycerin and air - Alcohol systems as the liquid phase in bubble column of 0.15 m diameter. For operation with gas velocity in the range 0-20 cm/sec, the overall volumetric mass transfer coefficient was found to decrease w