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.

Background: Elastomeric chains are used to generate force in many orthodontic procedures, but this force decays over time, which could affect tooth movement. This study aimed to study the force degradation of elastomeric chains. Data and Sources: An electronic search on Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, LILACS, and PubMed was made, only articles written in English were included, up to January 2022.Study selection: Fifty original articles, systematic reviews, and RCTs were selected. Conclusion: Tooth movement, salivary enzymes, alcohol-containing mouthwash, whitening mouthwash, and alkaline and strong acidic (pH <5.4) solutions all have a significant impact on elastomeric chain force degradation. T

This is an empirical investigation of the tribal power in Iraq and its consequences on the socio-political system. A theoretical background concerning thestate kinship, tribe and tribal involvement in politics has been displayed with example of tribal power over people within the social context. Socio-anthropological method of data collection has been used, including a semi-structured interview with a sample of 120 correspondents. The outcome revealed that the feeble and corrupted state (government) play a vital role in encouraging the tribe to be dominant. The people of Iraq are clinging to the tribe regardless of whether they believe in it or not. Although they are aware that the tribe is a pre-state organisation and marred shape of ci

The notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.

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1. The need to ensure that the slippers are clean, visible and inwa

The Department of Chemical and Biological Engineering, Al-Khwarizmi College of Engineering at Baghdad University has lately renovated its own research laboratories to comply with international safety measures and conduct undergraduate and postgraduate research. In this regard, the department has harnessed some amenities within the college to establish these laboratories taking into accounts creating a convenient, safe, and developed working environment for both researchers and students. A precise procedure was followed to establish this laboratory which includes providing new bench tops which offer spacious working places for workers. These benches were supplied with power points, gas, water, and compressed air outlets. In addition,

An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.

Objective: To assess role of obesity in Covid-19 patients on antibodies production, diabetes development, and treatment of this disease. Methodology: This observational study included 200 Covid-19 patients in privet centers from January 1, 2021 to January 1, 2022. All patients had fasting blood sugars and anti-Covid-19 antibodies. Anthropometric parameters were measured in all participants. Results: The patients were divided into two groups according to body weight; normal body weight (50) and excess body weight (150). There was a significant difference between them regarding age. Diabetes mellitus developed in 20% of normal weight patients while 80% of excess weight patients had diabetes (p=0.0001). Antibodies production (IgM and

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that