iosr-Jm   Volume-20 ~ Issue-6 ~ Nov. – Dec. 2024

Abstract : This article presents a review of domination strategies in fuzzy graphs, with a focus on recent developments in the field. It summarizes outcomes from both foundational and recent developments in the literature. Numerous advancements have emerged in recent years, expanding its theoretical and practical applications. This review consolidates the most relevant and recent findings, providing an overview of current strategies and methodologies in domination theory for fuzzy graphs. The article also elaborate on the concept of fz-domination in fuzzy graphs. The fz-domination framework considers both vertex and edge membership values, ensuring a more realistic and effective measure of domination in fuzzy environments.

Key words: Fuzzy graphs; Dominating sets; domination number.

[1]. A. Kauffman, Introduction A La Theorie Des Sousemsembles Flous, Paris: Masson Et Cie Editeurs, 1973.
[2]. L. A. Zadeh, Fuzzy Sets, Information And Control, 8 (1965), 338-353.
[3]. A. Rosenfeld, Fuzzy Graphs. In Fuzzy Sets And Their Applications To Cognitive And Decision Processes, Academic Press, 1975. 77-95.
[4]. Akul Rana, A Survey On The Domination Of Fuzzy Graphs. Discrete Mathematics, Algorithms And Applications, 13(01), 2021.
[5]. J.N. Mordeson And Premchand S. Nair, Fuzzy Graphs And Fuzzy Hypergraphs, Physica- Verlag, 2000.

Abstract : Dark energy. It's that mysterious force shaping our universe, yet it's something we can't see or touch. If you've ever wondered how galaxies form or why the universe is expanding faster than ever, dark energy is the silent player in this cosmic drama. In this research, we take a closer look at how dark energy influences the growth of massive structures like galaxies and voids, and what it means for the ultimate fate of everything around us. Imagine gravity pulling things together—like how clusters of galaxies form—but then picture dark energy working against that pull, stretching space itself. Using models grounded in general relativity and real-world observations......

Keywords: Dark energy, general relativity, large-scale structure, cosmic evolution, equation of state, cosmological constant

[1] Planck Collaboration. (2020). "Planck 2018 Results: Cosmological Parameters." Astronomy & Astrophysics, 641, A6.
[2] Riess, A. G., Et Al. (1998). "Observational Evidence From Supernovae For An Accelerating Universe And A Cosmological Constant." Astronomical Journal, 116(3), 1009-1038.
[3] Caldwell, R. R. (2002). "Phantom Energy And Cosmic Doomsday." Physical Review Letters, 91(7), 071301.
[4] Tegmark, M., Et Al. (2004). "The 3d Power Spectrum Of Galaxies From The Sdss." Astrophysical Journal, 606, 702–740.
[5] Peebles, P. J. E., & Ratra, B. (2003). "The Cosmological Constant And Dark Energy." Reviews Of Modern Physics, 75(2), 559-606.

Abstract : Classic inventory models commonly assume that surplus demand is backordered. However, research analysing customer behaviour in practice demonstrate that in many retail situations, unsatisfied demand is lost or replaced with an alternative item/location. Inventory systems with this lost-sales characteristic appear to be more challenging to analyse and resolve. Furthermore, to save costs, lost-sales inventory systems require different replenishment procedures than backorder systems. In this work, we present a survey on inventory models with lost sales. Furthermore, directions for future investigation are suggested.

Key Word: Inventory model; Lost-sale.

[1]. C. Das, The (S − 1, S) Inventory Model Under Time Limit On Backorders, Operations Research, 25 (1977), Pp. 835-850
[2]. A. G. De Kok, Approximations For A Lost-Sales Production/Inventory Control Model With Service Level Constraints, Management Science, 31 (1985), Pp. 729-737
[3]. T.W. Gruen, D. Corsten, S. Bharadwaj, Retail Out-Of-Stocks: A Worldwide Examination Of Extent Causes And Consumer Responses, Grocery Manufacturers Of America (2002).
[4]. P.C. Verhoef, L.M. Sloot,Out-Of-Stock: Reactions, Antecedents, Management Solutions, And A Future Perspective,M. Krafft, M.K. Mantrala (Eds.), Retailing In The 21st Century: Current And Future Trends, Springer Publishers, Philadelphia, Pennsylvania, Usa (2006), Pp. 239-253
[5]. S. Nahmias, Perishable Inventory Theory: A Review Operations Research, 30 (1982), Pp. 680-708.

Abstract : Aim: The overall goal of this thesis work was to examine gender as a factor influencing math achievement, with a focus on secondary schools in the Shai-Osudoku District of the Greater Accra Region. In that the following were the study's objectives: To 1. Assess the gender-based disparities in mathematics performance of Senior High School students in the Shai-Osudoku district. 2. Ascertain the impact of societal factors on gender-based disparities in the mathematics performance of Senior High School students of Shai-Osudoku district?.......

Key Word: Students' performance, probability, gender equality and social inclusion (GESI).

[1] Ajai, J. T., & Imoko, B. I. (2014). Gender Differences In Mathematics Achievement And Retention Scores: A Case Of Problem-Based Learning Method. International Journal Of Research In Education And Science, 1(1), 45. Https://Doi.Org/10.21890/Ijres.76785
[2] Asare-Inkoom, A., Gyamerah, S., & Najimudeen, A. (2008). Effect Of Calculator Use In Mathematics Computation By Junior Secondary School Form Two Pupils: A Case Study In The Cape Coast Municipality In Ghana. Mathematics Connection, 6(1). Https://Doi.Org/10.4314/Mc.V6i1.21512
[3] Atman, C., Fleming, L., Kilgore, D., Miller, R., Sheppard, S., Smith, K., Stevens, R., Streveler, R., & Turns, J. (2008). Special Session - Linking Research Findings On Engineering Student Learning And Engineering Teaching: Implications For Engineering Education. 2008 38th Annual Frontiers In Education Conference. Https://Doi.Org/10.1109/Fie.2008.4720561
[4] Battey, D. (2013). "Good" Mathematics Teaching For Students Of Color And Those In Poverty: The Importance Of Relational Interactions Within Instruction. Educational Studies In Mathematics, 82(1), 125–144. Https://Doi.Org/10.1007/S10649-012-9412-Z
[5] Boakye-Gyasi, E., Henneh, I. T., Abotsi, W. K. M., Ameyaw, E. O., & Woode, E. (2017). Possible Mechanisms Involved In The Anti-Nociceptive Effects Of Hydro-Ethanolic Leaf Extract Of Ziziphus Abyssinica. Pharmaceutical Biology, 55(1), 1962–1971. Https://Doi.Org/10.1080/13880209.2017.1355927

Abstract : Elementary number theory is a key branch of mathematics focuses on integer properties and relationships. This review comprehensively covers the key concepts, theorems, and applications. It examines integer properties like divisibility, primality, and congruences, and introduces the division and Euclidean algorithms as essential tools. The paper explores prime numbers, their infinitude, and the prime number theorem. The fundamental theorem of arithmetic, stating that every positive integer has a unique prime factorization, is discussed with its proof and significance. Diophantine equations, polynomial equations involving integers, are investigated with solutions methods. Applications......

Keyword: Divisibility, Prime numbers, Euclidean algorithm, Congruences, Diophantine equations, Cryptography

[1]. Atiyah, M. (1983). The Prime Number Theorem. Proceedings Of The Royal Society Of London, 393(1804), 425-434.
[2]. Hardy, G. H., & Wright, E. M. (2008). An Introduction To The Theory Of Numbers. Oxford University Press.
[3]. Hilbert, D. (1909). On The Distribution Of Prime Numbers. Proceedings Of The London Mathematical Society, 8(2), 275-295.
[4]. Iwaniec, H., & Kowalski, E. (2004). Number Theory: A First Course. American Mathematical Society.
[5]. Niven, I., & Zuckerman, H. S. (2012). An Introduction To The Theory Of Numbers. Wiley.
[6]. Odlyzko, A. (1987). The Distribution Of Prime Numbers. Proceedings Of The National Academy Of Sciences, 84(22), 7828-7831.

Abstract : Many great success stories tell of great clinical work. They also tell about the patient's approach to treatment. Good care. By serving patients directly, they can better understand the details of the care they receive. Often these stories begin with a patient visiting a large hospital for treatment. Volume of process creates experience, which often translates into greater success. A doctor's willingness to take risks leads to confidence in the choice. Long-term care and patient care: Advertisers can benefit from the skills of professionals who persuade others to buy through recommendations. Doctors often become confidants or friends. Intercultural......

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