Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

The main purpose of this paper is to study feebly open and feebly closed mappings and we proved several results about that by using some concepts of topological feebly open and feebly closed sets , semi open (- closed ) set , gs-(sg-) closed set and composition of mappings.

Empirical equation has been presented to predict the optimum hydrodynamic
pressure gradient with optimum mud flow rate (one equation) of five Iraqi oil wells
to obtain the optimum carrying capacity of the drilling fluid ( optimum transport
cuttings from the hole to the surface through the annulus).
This equation is a function of mud flow rate, mud density and penetration
rate without using any charts or graphs.
The correlation coefficient accuracy is more than 0.9999.

This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given.  As the first result, it has been proved that every  σ-algebra over a fuzzy set x*  is a  fuzzy σ-ring-over a fuzzy set x*  and construct their converse by example. Furthermore, the fuzzy ring  concept has been studied to generalize fuzzy algebra and its relation. Investigating  that the concept of fuzzy  σ-Ring is a stronger form of a fuzzy ring  that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied

The estimation of the regular regression model requires several assumptions to be satisfied such as "linearity". One problem occurs by partitioning the regression curve into two (or more) parts and then joining them by threshold point(s). This situation is regarded as a linearity violation of regression. Therefore, the multiphase regression model is received increasing attention as an alternative approach which describes the changing of the behavior of the phenomenon through threshold point estimation. Maximum likelihood estimator "MLE" has been used in both model and threshold point estimations. However, MLE is not resistant against violations such as outliers' existence or in case of the heavy-tailed error distribution. The main goal of t

     In this research investigation, a total of eighteen diverse tetra- and penta-lateral cyclic compounds were synthesized. These included 1,3,4-thiadiazole, thiazolidin-4-one (via an alternative method), 1,2,4-triazole, carbothioamide, thiazole-4-one, azetidin-2-one, and oxazole. The synthesis procedure entailed a sequence of reactions. The thiazolidine-4-one 1 was obtained by reaction p-aminobenzoic acid with thiosemicarbazide, followed by treatment with p-tolualdehyde to produce Schiff base 2. Reaction Schiff base 2 with mercaptoacetic acid in dry benzene was carried out to produce thiazolidine-4-one 3. In another synthesis pathway, the esterification of p-nitro benzoic acid with ethanol in the presence of sulfuric acid was

Introduction: This study aimed to assess the color change of human teeth with artificial enamel white spot lesions (WSLs) after sandblasting with bioactive glass, resin infiltration, and microabrasion and to test color stability after pH cycling. Methods: Fifty extracted human mandibular first molars were randomly assigned into five groups: Sound, WSLs (untreated), and WSLs sandblasted with bioactive glass (Sylc), WSLs treated by resin infiltration (ICON), and WSLs treated by microabrasion (Opalustre), respectively. All specimens underwent a pH cycling procedure. The color parameters for each specimen were assessed using an Easyshade dental spectrophotometer at different time stages then the color changes (ΔE) were calculated. Results: The

The study aimed to evaluate injuries and economic losses which caused by rose beetle Maladerainsanabilis (Brenske) on ornamental and fruit plants as introduced insect in Iraq during 2015 and determine infested host plants in addition to evaluate efficacy of pathogenic fungi Metarhiziumanisopiliae (1x10⁹ spore/ ml) and Beauvariabassiana (1x10⁸spore/ ml) in mortality of insect larvae in laboratory and field.The results showed that the insect was polyphagous infested many host plants (20 host plant)Which caused degradation and dead the plants through adult feeding on leaves and flower but large injury caused by larvae feeding on root plants which caused obligate dead to infested plant, the percentage mortality of rose plants 68.6%, pear

         Cardiovascular disorders  are  refer to the class of diseases that involve the heart or blood vessels (arteries and veins). While the term technically refers to any disease that affects the cardiovascular system. Cholesterol is classified as a sterol (a contraction of steroid and