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 pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

The present work investigates the effect of; superficial air velocities of: 1, 3, and 6 cm/s for two types of perforated distributor on hydrodynamic characteristic in a gas-liquid dispersion column of; air-water, and airaqueous-n-propanol solution. Bubble distribution, gas holdup, and power consumption are parameters take in consideration. Experimental work was carried out in perspex column of 8.5 cm inside diameter and 1.5 m height. Two types of bubble generator (perforated plate) were fixed at the bottom of the column; plate A (99 holes of 0.5 mm diameter and free area of 0.34%), plate B (20 holes of 1.5 mm diameter and free area of 0.62%). Photographic technique was used to measure the bubble parameters. The experimental results were

This work is concerned with the design and performance evaluation of a shell and double concentric tubes heat exchanger using Solid Works and ANSY (Computational Fluid Dynamics).

Computational fluid dynamics technique which is a computer-based analysis is used to simulate the heat exchanger involving fluid flow, heat transfer. CFD resolve the entire heat exchanger in discrete elements to find: (1) the temperature gradients, (2) pressure distribution, and (3) velocity vectors.  The RNG k-ε model of turbulence is used to determining the accurate results from CFD.

The heat exchanger design for this work consisted of a shell and eight double concentric tubes. The number of inlets are three and that of o

In the United States, the pharmaceutical industry is actively devising strategies to improve the diversity of clinical trial participants. These efforts stem from a plethora of evidence indicating that various ethnic groups respond differently to a given treatment. Thus, increasing the diversity of trial participants would not only provide more robust and representative trial data but also lead to safer and more effective therapies. Further diversifying trial participants appear straightforward, but it is a complex process requiring feedback from multiple stakeholders such as pharmaceutical sponsors, regulators, community leaders, and research sites. Therefore, the objective of this paper is to describe three viable strategies that can p

Multi-spectral satellite images of the Landsat satellite by the tow sensitive Thematic Mapper (TM) and Thematic Mapper Enhancement (ETM+), which covered the study area located south east of Iraq. In this research; used the sixth thermal spectral band (Thermal Band) for study the water cover in the Al-Razzaza Lake located within the province of Karbala. We intended to study the cover a case of the study area, used satellite images showing the status of region during the period from 1990 to 2001 and 2007. From this study we conclude that cover the water of the study area change in sequence case to decrease during these years.

This study presents the multi criteria single-machine model. The machine scheduling problem (MSP) for ntasks on a single machine involves minimizing a function of three criteria: total completion time (C_j),maximum earliest (E_max), and tardiness (〖ΣT〗_j), This is an NP-hard issue. Within this work's theoretical section, we present the mathematical formulation of The presented topic thenhighlights the usefulness of the dominance rule (DR), which may be used to develop effective solutions. Whilein the practical part, one of the important exact methods; The proposed MSP tricriteria are solved by applyingthe Branch and Bound (BAB) method, which finds a set of efficient solutions for 1//F(ΣC_j ,ΣT_j ,E_max) upto n=100 jobs. The BAB appro

In the cuurent article, the photophysical properties of 3,6-bis(5-bromothiophen-2-yl)-2,5-bis(2-ethylhexyl)-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione were investigated. The visible absorption bands at 527, 558 and 362 nm in propylene carbonate and the compound was found to be fluorescent in solution and in the plastic film with emission wavelengths between 550- 750 nm. The Stokes Shift of P.C., acetonitrile, diethyl ether, Tetrahydrofuran THF, cyclohexane, dibutyl ether, and dichloromethane DCM  are 734, 836, 668, 601, 601, 719, and 804 cm^-1 in respectively. The Stokes Shift Δ was less in THF and cyclohexane, than the solvents, which indicates that the energy loss is less between the excitation and fluorescence states. The

Background: The association between facial types and dental arches forms has considerable implications in orthodontic diagnosis and treatment planning. The aim was to establish the maxillary and mandibular dental arches width and length in skeletal and dental class II division 1 and class III malocclusion groups, find out the most frequent dental arch form and facial type and the association between them and to check the gender differences. Materials and Methods: Frontal and lateral facial photographs and maxillary and mandibular occlussal photographs for 90 iraqi subjects with age 18-25 years old (45 males and 45 females) divided equally into three groups, the 1st group with class II division 1malocclusion (overjet more than 3mm but less t