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.
There is no doubt that development is a human necessity and an urgent technical imperative that science imposes on all aspects of societal life. Especially in the field of graphic design, as logos are among the most prominent graphic achievements of an interactive nature with the requirements of the technical and functional era to serve the recipient and the continuity of interaction with him through a visual message sent to him constantly to remind him of what he interacted with in advance, which is known as visual identity, and during the process of developing logos especially And by providing designs that suit the contemporary technical and functional development, we often see the logo lose its visual identity. Therefore, the research
... Show MoreWe try through this research to show the relationship between the crescent and the month in the Koran, and then their importance and their relationship to timing, and the timing of this relationship with people, and the significance of these timings, so we gathered verses that spoke about the family and the month, and we tried to study them in a detailed objective study, so this came The research of five subjects was the first topic introductory research and the time and month, while the remaining four detectives on the verses that talked about the timing of the month, and we have explained the relationship of this timing with people and the significance of these times.
The current research aims to verify the relationship and impact of internal control activities as an independent variable in its dimensions (efficiency, training, independence) in making administrative decisions as a responsive variable and its dimensions (identifying and diagnosing the problem, searching for alternatives, evaluating alternatives, choosing the appropriate alternative, implementing the decision, following up Decision and evaluation) in the Kirkuk Water Directorate, as well as to identify the levels of their practices, and then try to come up with a number of recommendations contribute to the strengthening of internal control activities and the process of making administrative decisions of the researched Directorat
... Show MoreThis 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 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 MoreIndexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t
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