Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

In this paper, some commonly used hierarchical cluster techniques have been compared. A comparison was made between the agglomerative hierarchical clustering technique and the k-means technique, which includes the k-mean technique, the variant K-means technique, and the bisecting K-means, although the hierarchical cluster technique is considered to be one of the best clustering methods. It has a limited usage due to the time complexity. The results, which are calculated based on the analysis of the characteristics of the cluster algorithms and the nature of the data, showed that the bisecting K-means technique is the best compared to the rest of the other methods used.

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimati

The article aims to consider the concept of language metaphor in Russian and Arabic languages and the problem of metaphor functioning in language, since it is one of the most important figurative components of the structural organization of the text and an important means of reflecting the national culture of each people. and often in revealing the image of a metaphor one can feel the full flexibility of the language and its beauty.

There is currently a pressing need to create an electro-analytical approach capable of detecting and monitoring genosensors in a highly sensitive, specific, and selective way. In this work, Functionalized Multiwall Carbon Nanotubes, Graphene, Polypyrrole, and gold nanoparticles nanocomposite (f-MWCNTs-GR-PPy-AuNP) were effectively deposited on the surface of the ITO electrode using a drop-casting process to modify it. The structural, morphological, and optical analysis of the modified ITO electrodes was carried out at room temperature using X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM) images, atomic force microscopy (AFM) and Fourier transform infrared (FTIR) spectra. Cyclic voltammetry (CV) and electrochemi

Lower neck pain is one of the problems facing all ages, especially the elderly, as it revolves around the causes of this pain from many diverse factors. The aim of the research is to use special intense exercise accompanied by intermittent electrical stimulation to get rid of lower neck pain among professors of the College of Science - University of Baghdad for ages. (40-60) years and to identify the extent of the effect. The research assumed the presence of statistically significant differences. The research sample represented professors at the University of Baghdad - College of Science who suffer from continuous pain for the period between (10/15/2023) and (1/15/) 2024) and their number is (5), The researchers used the experimenta

Sansevieriatrifasciata was studied as a potential biosorbent for chromium, copper and nickel removal in batch process from electroplating and tannery effluents. Different parameters influencing the biosorption process such as pH, contact time, and amount of biosorbent were optimized while using the 80 mm sized particles of the biosorbent. As high as 91.3 % Ni and 92.7 % Cu were removed at pH of 6 and 4.5 respectively, while optimum Cr removal of 91.34 % from electroplating and 94.6 % from tannery effluents was found at pH 6.0 and 4.0 respectively. Pseudo second order model was found to best fit the kinetic data for all the metals as evidenced by their greater R2 values. FTIR characterization of biosorbent revealed the presence of carboxyl a

In this work, the effect of vortex shedding on the solar collector performance of the parabolic trough solar collector (PTSC) was estimated experimentally. The effect of structure oscillations due to wind vortex shedding on solar collector performance degradation was estimated. The performance of PTSC is evaluated by using the useful heat gain and the thermal instantaneous efficiency. Experimental work to simulate the vortex shedding excitation was done. The useful heat gain and the thermal efficiency of the parabolic trough collector were calculated from experimental measurements with and without vortex loading. The prototype of the collector was fabricated for this purpose. The effect of vortex shedding at different operation condition