iosr-Jm   Volume-20 ~ Issue-1 ~ Jan. – Feb. 2024

Abstract : In this paper, the concepts of fuzzy Baire irresolute functions and fuzzy pseudo irresolute functions between fuzzy topological spaces are introduced and studied. A condition for a fuzzy topological space to become fuzzy semi-normal spaces is obtained by means of fuzzy Baire- separated spaces . Conditions for the inverse images of fuzzy pseudo -open sets to become fuzzy simply*-open sets, fuzzy resolvable sets are also obtained by means of fuzzy pseudo- irresolute functions.

Keywords: Fuzzy first category set, fuzzy residual set , fuzzy pseudo-open set, fuzzy Baire set, fuzzy Baire- separated space, fuzzy seminormal space, somewhat fuzzy nearly open function , fuzzy resolvable function.

.........

Abstract : Background: Under Partial Differential Equations, an image is a function 2 f (x, y), X  . These equations are used in smoothening of images. The necessity to have an excellent image quality is increasingly required in the current world. Most of the obtained images are not as smooth as we would want hence they are blurred. Use of the nonlinear diffusion equation is essential in the current day smoothening of images. This model inputs smoothness in the denoising process. This research improved the quality of images through the use of nonlinear PDEs of parabolic nature i.e. the heat equation......

Keywords: Non-linear diffusion equation, Alternating Direction Implicit method,2-point Explicit Group Over- Relaxation

[1] Basran,N.A.,Saudi,J.H, And Suleiman,J.(2018) Implementation Of The Explicit Group Iterativemethod For Solving Image Blurring Problem Using Nonlinear Diffusion Equations.Iop Conf.Series .Journal Of Physics :Conf Series 1123(2018) 012027
[2] Chew,J.V.L., And Sulaiman, J.(2017) Application Of Four –Point Newton –Egsor Iteration For The Numerical Solution Of 2d Porous Medium Equations, Journal Of Physics :Conference Series 890.
[3] Osher,S.,And Rudin,L.(1990) Feature Oriented Image Enhancement Using Shock Filters.Siam J.Numerical Analysis, 27:919–940.
[4] Ozkan ,M.K., Sezan ,M.I., And Tekalp ,A.M. (1993) Adaptive Motion Compensated Filtering Of Noisy Image Sequences. Ieee Trans. Circuits And Systems For Video Technology, 3:277–290.
[5] Evans,D.J.(1986) Group Explicit Iterative Methods For Solving Large Linear Systems International Journal Of Computer Mathematics 17(1) 81-108

Abstract : Indonesia is rich in culture, including the Pasola Lamboya culture. Pasola Lamboya is a game of throwing a spear at each other while riding a horse. However, the mathematical concepts in Pasola culture have not been explored since Enomathematics entered Indonesia in 2013. The purpose of this research is to describe ethnomathematics in the Pasola cultural activities of the Lamboya community and its integration into learning mathematics. The research was conducted on Sumba Island, in Lamboya District, West Sumba, East Nusa Tenggara Province......

Keywords: Culture, Ethnomathematics, Exploration. Pasola Lamboya, Mathematical concepts

[1] W. S. Dominikus, "THE RELATIONSHIP OF ADONARA ETHNOMATHEMATICS AND SCHOOL MATHEMATICS [In Bahasa]," Media Nusa Creat., Pp. 1–100, 2021.
[2] F. N. Hidayati And R. C. I. Prahmana, "Ethnomathematics' Research In Indonesia During 2015-2020," Indones. J. Ethnomathematics, Vol. 1, No. 1, Pp. 29–42, 2022, [Online]. Available: Http://Doi.Org/10.48135/Ije.V1i1.29-42
[3] I. Risdiyanti And R. C. I. Prahmana, "Ethnomathematics: Exploration In Javanese Culture," J. Phys. Conf. Ser., Vol. 943, No. 1, 2018, Doi: 10.1088/1742-6596/943/1/012032.
[4] M. Rosa And D. Orey, "Ubiratan D'Ambrosio: Celebrating His Life And Legacy," J. Humanist. Math., Vol. 11, No. 2, 2021, Doi: 10.5642/Jhummath.202102.26.
[5] U. D'Ambrosio, "Ethnomathematics And Its Place In The History And Pedagogy Of Mathematics," Learn. Math., Vol. 5, No. February 1985, Pp. 44–48 (In "Classics"), 1985.

Abstract : Background: Millions of people throughout the world die every year from malaria, an illness spread by the bite of an infected female Anopheles mosquito. Busia, a county in Kenya, has been recorded to have the highest prevalent cases of 37% in Kenya. However, Busia has often been ignored in the mathematical modelling of malaria in Kenya. The SEIR model is widely used in mathematical simulations of malaria transmission. However, the paradigm is no longer relevant to malaria cases since asymptomatic Plasmodium parasites persist in the systems of persons who have recovered from malaria. In this study, the human subpopulation carrying the plasmodium parasites......

Keywords: Malaria transmission, Reproduction number, parameter optimisation and stability

[1]. Abimbade, S. F., Olaniyi, S., & Ajala, O. A. (2022). Recurrent Malaria Dynamics: Insight From Mathematical Modelling. The European Physical Journal Plus, 137(3), 292.
[2]. Abongo, B. (2019). Malaria Vector Surveillance In The Context Of Enhanced Vector Control In Western Kenya (Doctoral Dissertation, Liverpool School Of Tropical Medicine).
[3]. Aldila, D. (2022). Dynamical Analysis On A Malaria Model With Relapse Preventive Treatment And Saturated Fumigation. Computational And Mathematical Methods In Medicine, 2022.
[4]. Amoo, O. M., Fagbenle, R. O., & Oyewola, M. O. (2022). A Comparative Analysis Of Numerical Methods Applied To Nonsimilar Boundary Layer-Derived Infinite Series Equations. Ain Shams Engineering Journal, 13(5), 101713.
[5]. Baihaqi, M. A., & Adi-Kusumo, F. (2020, September). Modelling Malaria Transmission In A Population With Seirsp Method. In Aip Conference Proceedings 2264(1). Aip Publishing

Abstract : The present paper, we aim to establishing certain integral formulae involving the wright function. The obtained results are in the form of hypergeometric and wright function, which are made with the help of Hadamard product. We have derived some other interesting formulae as special cases of our main results......

Keywords: hypergeometric function, generalized wright hypergeometric function, Lavoie-Trottier, MacRobert and Edward integrals.

[1]. A. Erdelye, W. Magnus, F. Oberhettinger And F. G. Tricomi (1953). Higher Transcedental Functions, Vol. I, Mcgraw-Hill, New York, London
[2]. E. D. Rainville (1960). Special Functions, Chelsea Publication Co., New York
[3]. E. M. Wright (1940). The Asymptotic Expansion Of The Generalized Hypergeometric Function Ii, Proc. London Math. Soc., Vol. 46 (2), Pp.389-408
[4]. F. Oberhettinger (1974). Tables Of Mellin Transforms, Springer, New York
[5]. H. M. Srivastava (1972). A Contour Integral Involving Fox's H-Function, Indian J. Math. Vol. 14, Pp. 1-6

Abstract : In this paper, we undertake the transient analysis of a limited capacity queueing system with two environmental states in the presence of catastrophes. When a catastrophe occur at the service- facility as a Poisson process with rate , the number of customers is instantly reset to zero at certain random times. The change in the environment also affects the state of the queueing system. In other words, the state of the queueing system is a function of environmental change factors.The effects of environmental change and catastrophes are extensively dealt with a system are studied. The steady-state behavior of the queueing system is also derived. Some particular cases of the model with and without catastrophes are also obtained and discussed.

Keywords: Transient analysis, Catastrophes, Environment, Limited capacity, Steady-state solution

[1] Brockwell, P. J.,(1985) The Extinction Time Of A Birth, Death And Catastrophe Process And Of A Related Diffusion Model,
Advances In Applied Probability, 17, 42-52.
[2] Brockwell, P.J.,Gani, J. M., And Resnick, S. I., (1982) Birth Immigration And Catastrophe Processes, Advances In Applied
Probability Vol.14, 709-731.
[3] Chao, X., And Zheng, Y., (2003) Transient Analysis Of Immigration Birth-Death Processes With Total Catastrophes, Probability
Engg. Information Sci, Vol.17, 83-106.
[4] Chao, X., (1995) A Queueing Network Model With Catastrophes And Product Form Solution, Operations Research Letters, Vol.18,
75-79.
[5] Crescenzo, A. Di, Giorno, V., Nobile, A. G., And Ricciardi, L. M., (2003) On The M/M/1 Queue With Catastrophes And Its
Continuous Approximation, Queueing Systems, Vol.43, 329-347

Abstract :In this paper, several characterizations of fuzzy quasi- regular spaces, which are defined by means of fuzzy open sets and fuzzy regular closed sets, are established. It is obtained that each fuzzy set defined in a fuzzy quasi-regular space contains a fuzzy regular closed set and each fuzzy 𝑔𝛿-set contains a fuzzy closed set in a fuzzy quasi-regular space. The conditions under which fuzzy quasi- regular spaces become fuzzy weakly baire spaces and fuzzy baire spaces are obtained. It is obtained that fuzzy quasi- regular spaces are not fuzzy hyperconnected spaces.......

Keywords: fuzzy 𝑔𝛿-set, fuzzy 𝑓𝜎-set, fuzzy 𝜎-boundary set , fuzzy residual set, Fuzzy regular space, fuzzy baire space, fuzzy weakly baire space

[1]. S.Anjalmose And G.Thangaraj, Fuzzy Quasi-Regular Space, Communicated To Thai Journal Of Mathematics, Thailand.
[2]. K.K. Azad, On Fuzzy Semi Continuity, Fuzzy Almost Continuity And Fuzzy Weakly Contiunity, J. Math. Anal. Appl, 82 (1981), 14 – 32.
[3]. G.Balasubramanian , Maximal Fuzzy Topologies, Kybernetika, 31(5) (1995), 459 – 464.
[4]. C. L . Chang, Fuzzy Topological Spaces, J. Math. Anal. Appl. , 24, (1968), 182 − 190
[5]. B. Hutton And I. L. Reilly, Separation Axioms In Fuzzy Topological Spaces, Dept. Of Math., , University Of Auckland , Report No. 55, March 1974