iosr-Jm   Volume-21 ~ Issue-3 ~ May – Jun. 2025

Abstract : In the last two to three decades, significant research has focused on special functions related to statistical distributions. This includes the Generalized Hurwitz-Lerch Zeta Beta type-2 distributions and Gamma distribution, generalized hypergeometric distributions, Parabolic cylinder distribution, generalized Hurwitz Zeta Beta prime distributions, Mathieu distribution, Plank distribution, Mittag-Leffler distribution, Hurwitz Lerch Zeta distribution. Furthermore........

Keywords: Special functions, Statistical distributions, Generalized Hurwitz-Lerch Zeta, Gamma Distribution, Hypergeometric Distributions, Parabolic Cylinder Distribution, Moment Generating Function, Survival Function, Hazard Rate Function, Method of Moments..

[1]. Mathai, A. M. (1966). Some Characterizations of the One-Parameter Family of Probability Distributions. Canadian Mathematical Bulletin, 9(1), 95-102.
[2]. Mathai, A. M., & Saxena, R. K. (1968). Distributions having the gamma properties. Metrika, 13(1), 10-16.[3].
Mathai, AM* & Saxena, R. (1969). Applications of special functions in the characterization of probability distributions. South African Statistical Journal, 3(1), 27-34.
[4]. Mathai, A. M., & Moschopoulos, P. G. (1991). On a multivariate gamma. Journal of Multivariate Analysis, 39(1), 135-153.
[5]. A.M. Mathai, A Handbook of Generalize Special Functions for Statistical and Physical Sciences, Oxford University Press, Oxford, (1993).

Abstract : Multi-Criteria Decision Making (MCDM) techniques have attracted significant attention from researchers and professionals across diverse industries due to their ability to effectively evaluate, assess, and rank alternatives. However, choosing the most suitable MCDM method for a specific problem can be challenging, especially when several methods appear equally applicable. Among these methods, the Technique for Order of Performance by Similarity to Ideal Solution (TOPSIS).....

Keywords: TOPSIS, Revised TOPSIS, Euclidean distance, Weighted Euclidean distance, Simulation comparison

[1]. Agrawal, V., V. Kohli, S. Gupta, Computer aided robot selection: the ‘multiple attribute decisionmaking’approach, Int. J. Prod. Res. 29(8) (1991) 1629–1644.
[2]. Akgül, E., Bahtiyari, M. I., KizilkayaAydoğan, E., and Benli, H. (2022). Use of TOPSIS method for designing different textile products in coloration via natural source “madder”. Journal of Natural Fibers, 19(14), 8993-9008.
[3]. Arabameri, A., Rezaei, K., Cerda, A., Lombardo, L., and Rodrigo-Comino, J. (2019). GIS-based groundwater potential mapping in Shahroud plain, Iran. A comparison among statistical (bivariate and multivariate), data mining and MCDM approaches. Science of the total environment, 658, 160-177.
[4]. Athawale, V. M., and Chakraborty, S. (2010, January). A TOPSIS method-based approach to machine tool selection. In Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh (Vol. 2, pp. 83-94).
[5]. Aydogan, E. K. Performance measurement model for Turkish aviation firms using the rough-AHP and TOPSIS methods under fuzzy environment, Expert Syst. Appl. 38 (4) (2011) 3992–3998.

Abstract : In this research work, a five-dimensional LRS Bianchi type-V string cosmological model with the
electromagnetic field in the framework of Lyra’s manifold is investigated. A determinate solution of the field
equations is obtained with the help of the special law of variation for the Hubble parameter. Some physical and
kinematical properties of the model are discussed.......

Key Words: LRS Bianchi type-V; Lyra’s manifold; String Cloud with Electromagnetic Field

[1]. Sen, D.K.: Z. Phys. 149, 311 (1957)
[2]. Mohanty G., Sahoo R.R., Mahanta K.L.:Astrophys Space Sci 312: 321–324(2007)
[3]. Mohanty, G., Sahoo, R.R.:Astrophys Space Sci. 315: 319–322(2008)
[4]. Mohanty, G., Mahanta, K.L.:Astrophys Space Sci. 312: 301–304(2007)
[5]. Daimary, J.,Baruah R.R.: Front. Astron. Space Sci. 9:878653, doi: 10.3389/fspas.2022.878653(2022)..

Abstract : This paper introduces a novel Recursive Partitioning Framework that builds upon additive number theory, with specific application to Lemoine's Conjecture, which asserts that every odd integer greater than 5 can be expressed as the sum of a prime and a semiprime. Inspired by recent developments in algorithmic formulations of Goldbach-type conjectures, we adapt the framework proposed by Sankei et al. (2023), originally used to partition even integers via expressions.......

Key Words: Additive number theory, Lemoine's Conjecture, Semiprime decomposition, Recursive partitioning, Prime arithmetic structures

[1]. Hardy, G. H., & Wright, E. M. (1979). An introduction to the theory of numbers. Oxford university press.
[2]. Riesel, H. (2013). Prime numbers and computer methods for factorization (Vol. 57). Springer Science & Business Media.
[3]. Oliveira e Silva, T., Herzog, S., & Pardi, S. (2014). Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅ 10¹⁸. Mathematics of Computation, 83(288), 2033-2060.
[4]. Daniel, S., Njagi, L., & Mutembei, J. (2023). A numerical verification of the strong Goldbach conjecture up to 9× 10^ 18. GPH-International Journal of Mathematics, 6(11), 28-37.
[5]. Shanks, D. (1964). On maximal gaps between successive primes. Mathematics of Computation, 18(88), 646-651.

Abstract : Mathematics is a one major area of science that is of great important that interrelate all other science. One of the important goals of mathematics is to transform a student into an individual with high decision power and creative solving problems and the power of reasoning. Information Communication technology tools and software are of great support for solving mathematical problem. Several application software are available for solving mathematical problem in different academic level. This research work gave a general survey of various mathematical software, ideas of their applications and their effects.

Key Words: Mathematics, Information Communication Technology (ICT), computational software, Problem solving

[1]. Adey, P., Csapo, B., Demtrious, A., Hautamaki, J. & Shayer, M. (2007). Can we be Intelligent about Intelligence? Why Education Needs the Concept of Plastic General Ability. Education
[2]. Aidoo, B., Vesterinen, V., Macdonald, A. & Gisladottir, B. (2022). Perceptions of Ghanaian Student Teachers on the Benefita and Challenges of Flipped Classroom: A Case Study. Contemporary Educational Technology, 14(4):ep377. https://doi:10.30935/cedtech/12163
[3]. Alim, E.S., Uman, K. & Rohim, S. (2015). Integration of Reciprocal Teaching-ICT Model to Improve Students Mathematics Critical Thinking Ability. Proceedings of the 23rd International Conference on Computers in Education. ICCE, 483-487.
[4]. Al-Hilli H. Wafaa (2018). Using Software’s and Technology in Solving Mathematics Problem to Motivate and Accelerate the Learning Process. EURASIA Journal of Mathematics, Science and Technology Education, 2019, 15(3). https://doi.org/10.29333/ejmste/102421.
[5]. Bataineh, H., Zoubi, A. & Khataybeh, A. (2019). Utilizing MATHEMATICA Software to Improve Students’ Problem Solving Skills of Derivative and application. International Journal of Education and Research. 7(11), 57-70