Abstract. Fibrewise micro-topological spaces be a useful tool in various branches of mathematics. These mathematical objects are constructed by assigning a micro-topology to each fibre from a fibre bundle. The fibrewise micro-topological space is then formed by taking the direct limit of these individual micro-topological spaces. It can be adapted to analyze various mathematical structures, from algebraic geometry to differential equations. In this study, we delve into the generalizations of fibrewise micro-topological spaces and explore the applications of these abstract structures in different branches of mathematics. This study aims to define the fibrewise micro topological space through the generalizations that we use in this paper, which are fibrewise micro-regular, fibrewise micro-pre, fibrewise micro-semi, fibrewise micro-Ƅ, fibrewise micro-ꭀ, and fibrewise micro-semi-pre-topological space, and to study the correlation relations These generalizations and examples. As well as discussing and studying scientific terminology in continuity and micro open and micro closed sums when proving them with the generalizations contained in the fibrewise micro-topology, with the study of concepts between functions in terms of structure and transitional qualities between the field and the corresponding field via the influence of the fibrewise micro-topology and generalizations, and examining which of the proofs and theories are verified and which are not, with its refutation, with examples that achieve the scientific purpose.
This study specifically contributes to the urgent need for novel methods in Training of Trainers (ToT) programs which can be more effective and efficient through incorporation of AI tools. By exploring scenarios in which AI could be used to dramatically advance trainer preparation, knowledge-sharing, and skill-building across sectors, the research aims to understand the possibility. This study uses a mixed-methods approach, it surveys 500 trainers and conducts in-depth interviews with a further 50 ToT program directors across diverse industries to evaluate the impact of AI-enhanced ToT programs. The results showcase that the use of AI has a substantial positive effect on trainer performance and program outcomes. AI-enhanced ToT programs, fo
... Show MoreThe current research aims to analyze the mathematics book for the first intermediate grade according to the dimensions of mathematical power by answering the following question: What is the percentage of the availability of the dimensions of mathematical power included in the content of the mathematics textbook for first-grade students, average, in its first, and second parts for the academic year 2020-2021, approved by the Iraqi Ministry of Education / General Directorate of Curricula? The research community was determined by middle school mathematics books, and middle school students for middle ,and high school day schools affiliated to the Directorate of Education in Dhi Qar, and by the intentional test, the research sample was s
... Show MoreThe current research aims to identify: 1. The level of mathematical construct among the Department of Mathematics students in the colleges of education and basic education. 2. The level of effective mathematical operations in both sides of the brain at the Department of Mathematics students in the colleges of education and basic education. 3. The strength and direction of the correlation between the mathematical construct and effective mathematical operations on both sides of the brain at the Department of Mathematics students in the colleges of Education and Basic Education. To investigate the research objectives, the researcher formulated zero-main hypothesis for each aim and from the same hypothesis, three sub-zero hypotheses are deri
... Show MoreIn this work, microbubble dispersed air flotation technique was applied for cadmium ions removal from wastewater aqueous solution. Experiments parameters such as pH (3, 4, 5, and 6), initial Cd(II) ions concentration (40, 80, and 120 mg/l) contact time( 2, 5, 10 , 15, and 20min), and surfactant (10, 20and 40mg/l) were studied in order to optimize the best conditions .The experimental results indicate that microbubbles were quite effective in removing cadmium ions and the anionic surfactant SDS was found to be more efficient than cationic CTAB in flotation process. 92.3% maximum removal efficiency achieved through 15min at pH 5, SDS surfactant concentration 20mg/l, flow rate250 cm3/min and at 40mg/l Cd(II) ions initial co
... Show MoreBackground: The longevity of any prosthesis depends on the materials from which it was fabricated, that is why, defects in the material properties may reduce the service life of prosthesis and necessitate its replacement. The aim of this study was to evaluate the effect of adding different concentrations of Polyamide-6 (Nylon-6) on the tear and tensile strength of A-2186 RTV silicone elastomer. Materials and Methods: 80 samples were fabricated by the addition of 0%, 1%, 3% and 5% by weight PA-6 micro-particles powder to A-2186 platinum RTV silicone elastomer. The study samples were divided into four (4) groups, each group containing 20 samples. One control group was prepared without PA-6 micro particles and three experimental groups were pr
... Show MoreThe decorative supplements added are important factors in determining many decorative effects and how to implement them, whether in fabrics or fashion, and also work to determine the nature of perception for both the designer and the recipient and have a key role in shaping the human personality and determining his motives and emotional tendencies in the acquisition of fabrics and fashion and the vocabulary they carry A design that has certain connotations and symbols that gain its value from the effects it leaves on the physical formations of women. The problem of the research came with the following question (What are the decorative supplements and their role in the designs of fabrics and women’s fashion?) The research also dealt wit
... Show MoreThe study of the concepts of "democracy" and "human rights" and their impact on development, has taken a prominent place in the context of general political and cultural concerns, or in specialized studies even though researchers and scholars do not agree on defining the concepts: Democracy, Human Rights, Development or deriving a global definition hindering them, and that because of the importance of this topic, which proceeds from a number of considerations standing in the forefront, of which:
First: What the world witnesses today in the first decade of this century of consecration of the unipolar theory, trying to give its concepts and perceptions through the law ((excessive force)) to the power of international
... Show MoreAbstract: Background: Prediabetes and are increasing in prevalence all over the world, they each carry risks to the future development of diabetes mellitus and cardiovascular disease. These risks will be greatly exaggerated if they occur together in the same individual. The aim of the study was to find the prevalence and the association of prediabetes and metabolic syndrome, in addition to analyzing the correlation of the risk factors that lead to their development. Material and Methods: This was a cross-sectional, simple random study that included 300 Iraqi individuals, aged between 30-75 years, who accepted to take part in this study were recruited. Result: Prevalence of prediabetes and metabolic syndrome was (33.66%) and (42%) r
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