In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two types of regular spaces have been presented, namely the topological space Rp and the topological space S-Rp. The properties of these two spaces and their relationship with each other, as well as the effect of functions on them, have been studied. In addition several theorems have been proved regarding the sufficient and necessary conditions to make the topological spaces Rp-regular or S-Rp-regular. The above concepts have been linked with a new type of Hausdorff space and the concepts under study are reinforced with examples.
Spatial Intelligence is a mental ability to understand and solve real-world problems. These visual-spatial representations are fundamental in learning various "STEM" topics, like digital drawing, art presentations, creating graphical representations, 2D designs. Opportunity to interact with real and/or virtual objects. It is a good opportunity in applying new techniques such as the augmenter, which is able to clarify mathematical tables, concepts and generalizations greatly to the visualization, understanding and mastery of concepts mathematically. The purpose of the research is to investigate impact of using AR technology in developing spatial intelligence for secondary school students, Baghdad. The quasi-experimental design was us
... Show MoreThis study aims to reveal the role of one of the artificial intelligence (AI) techniques, “ChatGPT,” in improving the educational process by following it as a teaching method for the subject of automatic analysis for students of the Chemistry Department and the subject of computer security for students of the Computer Science Department, from the fourth stage at the College of Education for Pure Science (Ibn Al-Haitham), and its impact on their computational thinking to have a good educational environment. The experimental approach was used, and the research samples were chosen intentionally by the research community. Research tools were prepared, which included a scale for CT that included 12 items and the achievement test in b
... Show MoreRecently, wireless communication environments with high speeds and low complexity have become increasingly essential. Free-space optics (FSO) has emerged as a promising solution for providing direct connections between devices in such high-spectrum wireless setups. However, FSO communications are susceptible to weather-induced signal fluctuations, leading to fading and signal weakness at the receiver. To mitigate the effects of these challenges, several mathematical models have been proposed to describe the transition from weak to strong atmospheric turbulence, including Rayleigh, lognormal, Málaga, Nakagami-m, K-distribution, Weibull, Negative-Exponential, Inverse-Gaussian, G-G, and Fisher-Snedecor F distributions. This paper extensive
... Show MoreThe gypseous soil may be one of the problems that face the engineers especially when it used as a foundation for hydraulic structures, roads, and other structures. Gypseous soil is strong soil and has good properties when it is dry, but the problem arises when building hydraulic installations or heavy buildings on this soil after wetting the water to the soil by raising the water table level from any source or from rainfall which leads to dissolve the gypsum content.
Cement-stabilized soil has been successfully used as a facing or lining for earth channel, highway embankments and drainage ditches to reduce the risk of erosion and collapsibility of soil. This study is deliberate the treatment of gypseous soil by u
... Show MoreThis study employs wavelet transforms to address the issue of boundary effects. Additionally, it utilizes probit transform techniques, which are based on probit functions, to estimate the copula density function. This estimation is dependent on the empirical distribution function of the variables. The density is estimated within a transformed domain. Recent research indicates that the early implementations of this strategy may have been more efficient. Nevertheless, in this work, we implemented two novel methodologies utilizing probit transform and wavelet transform. We then proceeded to evaluate and contrast these methodologies using three specific criteria: root mean square error (RMSE), Akaike information criterion (AIC), and log
... Show MoreIn this work, a deep computational study has been conducted to assign several qualities for the graph . Furthermore, determine the amount of the dihedral subgroups in the Held simple group He through utilizing the attributes of gamma.
In this paper, a dynamic investigation is done for strip, rectangular and square machine foundation at the top surface of two-layer dry sand with various states (i.e., loose on medium sand and dense on medium sand). The dynamic investigation is performed numerically using finite element programming, PLAXIS 3D. The soil is expected as a versatile totally plastic material that complies with the Mohr-Coulomb yield criterion. A harmonic load is applied at the base with an amplitude of 6 kPa at a frequency of (2 and 6) Hz, and seismic is applied with acceleration – time input of earthquake hit Halabjah city north of Iraq. A parametric study is done to evaluate the influence of changing L/B ratio (Length=12,6,3 m and width=3 m), type of sand
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