iosr-Jm   Volume-20 ~ Issue-3 ~ May – Jun. 2024

Abstract : A new class of fuzzy topological spaces, namely fuzzy Baire -dominated spaces, is introduced and studied in this paper. It is established that fuzzy Baire dominated and fuzzy extraresolvable spaces are fuzzy hyperconnected spaces, and fuzzy extremally disconnected spaces. The conditions under which fuzzy Baire -dominated and fuzzy submaximal spaces become fuzzy first category spaces are also obtained. It is established that fuzzy Baire - dominated and fuzzy hyperconnected......

Keywords : Fuzzy nowhere dense set, fuzzy first category set, fuzzy residual set, fuzzy Baire set, fuzzy first category space, fuzzy submaximal space, fuzzy semiregular space, fuzzy extremally disconnected space.

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Abstract : The main aim of the present study is to analyze the risk parameters involved in HIV transmission. The probability of becoming infected with HIV is formulated in terms of the total number of sexual contacts, the probability that a sexual act is infectious and the prevalence. We show that for many realistic situations the probability of becoming infected by multiple partners is equal to the probability of becoming infected by one partner in a monogamous relationship.........

Keywords:- HIV/AIDS transmission, Mathematical Modelling, Probabilistic analysis, Risk parameter, Numerical analysis etc

[1] Anderson, R.M. And May, R.M. (1987): Transmission Dynamics Of Hiv Infection; Nature; Vol. 326, Pp. 136–142.
[2] Anderson, R.M. And May, R.M. (1988): Epidemiological Parameters Of Hiv Transmission; Nature; Vol. 333; Pp. 514–519
[3] Baral, S., Et Al. (2012): Burden Of Hiv Among Female Sex Workers In Low-Income And Middle-Income Countries: A Systematic Review And Meta-Analysis; Lancet Infectious Diseases; Vol. 12, Pp. 538-549.
[4] Bhave, G., Lindan, C.P., Hudes, E.S., Desai, S., Wagle, U., Tripathi, S.P. And Mandel, J.S. (1995): "Impact Of An Intervention On Hiv, Sexually Transmitted Diseases, And Condom Use Among Sex Workers In Bombay, India", Aids; Vol. 9; No. L1; Pp. S21-S30.
[5] Blower, S.M. And Dowlatabadi, H. (1994): "Sensitivity And Uncertainty Analysis Of Complex Models Of Disease Transmission: An Hiv Model, As An Example", Int. Stat. Rev., Vol. 62, Pp. 229–243

Abstract : In this paper, an age-structured model was used to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was struc-tured into 20 clusters each of 5 year interval, and assigned different birth and death rate parameters. Crank-Nicolson numerical scheme was used to simulate the model and the 2019 initial population of 38,589,011 was found to increase by 50% to 57,956,100........

Keywords:- Age-Structured; Constrictive; Dependency ratio; Expansive; Population; Simulation.

[1]. Hugo, G., Future Demographic Change And Its Interactions With Migration And Climate Change. Global Environmental Change, 2011. 21: P. S21-S33.
[2]. Brauer, F., C. Castillo-Chavez, And C. Castillo-Chavez, Mathematical Models In Population Biology And Epidemiology. Vol. 2. 2012: Springer.
[3]. Ehrlich, P.R., A.H. Ehrlich, And G.C. Daily, Food Security, Population And Environment. Population And Development Review, 1993: P. 1-32.
[4]. Uniyal, S., Et Al., Human Overpopulation: Impact On Environment, In Megacities And Rapid Urbanization: Breakthroughs In Research And Practice. 2020, Igi Global. P. 20-30.
[5]. Smith, D.W., Et Al., Population Dynamics And Demography. Yellowstone Wolves: Science And Discovery In The World's First National Park, 2020: P. 77-92

Abstract : A real or complex valued function defined on the set of all positive integers is called an arithmetic function. An arithmetic function f is said to be multiplicative function in one argument if f is not identically zero and f(mn) = f(m) f(n) whenever (m,n) = 1. The objective of this paper is to prove few useful identities using strongly multiplicative functions and using K – Prime integers.

Keywords:- Arithmetic function, Complex valued function, Multiplicative function, K – prime integers

[1]. Apostel, T.M. An Introduction to Analytical Number Theory, Springer International Student edition, Narosa Publishing House.
[2]. Brown, T. C. and L. C. Hsu, J. Wang, and P. J.-S. Shiue, "On a certain kind of generalized number theoretical Mobius function", The
Mathematical Scientist 25 (2000), no. 2, 72–77.
[3]. Eckford Cohen, Trignometric Sums in Elementary Number theory, American Mathematical Monthly, 1959, pp 105-117.
[4]. Eckford Cohen, Arithmetical Inversion Formulas, Canadian J. Math., 12 (1960), pp 399-409.
[5]. McCarthy, P.J. Some Remarks on Arithmetical Identities, Amerrican Math., Monthly, 67 (1956) pp 539-548

Abstract : The use of Catastrophic Mortality (CATM) Bonds (CMBs) as an alternative risk transfer (ART) mechanism is well established in the insurance and reinsurance fields. However pricing of these bonds is a complex problem and no closed form solution can be found in the existing literature. In this paper, we introduce an interesting model-independent upper bound for the price of the Swiss Re Mortality Bond 2003 by employing Lagrangian Optimization Technique. Swiss Re mortality bond was indeed the first catastrophic mortality bond to be launched in the insurance market. The bond mechanism relies upon the behaviour of a well-defined mortality index to generate......

Keywords:- Mortality Risk, Catastrophic Mortality Bonds, model-independent bound, Asian options

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Abstract : The outbreak of the Coronavirus COVID-19 has taken the lives of several thousands worldwide and locked out many countries and regions, with yet unpredictable global consequences. In this work, we propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of symptomatic, asymptomatic or super-spreaders individuals. We estimate the basic reproduction number to our propose model using general and exponential growth rate formula. A case study of transmission of Covid-19 in Bangladesh has been done by our proposed model. The efficiency and some limitations of our model also explained in the paper.

Keywords: Covid-19 Coronavirus, Mathematical Modeling, Basic Reproduction Number, SEIR Model, Exponential Growth Rate, Case Study

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Abstract : Tamil literature, one of the oldest and richest literary traditions in the world, dating back over two thousand years, is renowned for its rich depiction of natural phenomena, including detailed observations of weather and climate. This essay explores the references to weather prediction found in Tamil literature, delves into the hymns related to weather forecasting, categorizes the climate into distinct parts as described in these texts, and introduces a modern mathematical modeling approach using network theory principles to predict weather patterns based on ancient Tamil knowledge. By integrating ancient Tamil knowledge with contemporary scientific methods, we aim to enhance the accuracy and reliability of weather forecasts.

[1]. Dr. R. N. Vijayalakshmi, "Weather and Climate in Sangam Literature," Journal of Tamil Studies, 2005, Vol. 47, pp. 34-45.
[2]. Prof. S. Kalyanasundaram, "Environmental Insights from Ancient Tamil Texts," Indian Journal of History of Science, 2008, Vol. 43, No. 3, pp. 245-260.
[3]. Dr. V. S. Rajalakshmi, "Ecological and Meteorological Concepts in Tamil Literature," Tamil Civilization, 2010, Vol. 18, No. 2, pp. 98-112.
[4]. Dr. P. S. Subramanian, "Climate Patterns in Ancient Tamil Nadu: An Analysis," South Indian Studies, 2012, Vol. 21, pp. 55-67.
[5]. Prof. R. K. Narayanasamy, "Traditional Knowledge of Weather Forecasting in Tamil Culture," Asian Folklore Studies, 2015, Vol. 74, No. 1, pp. 73-85.