iosr-Jm   Volume-19 ~ Issue-3 ~ May – June 2023

Abstract : Mathematics is a discipline that closely relates to everyday life, making it essential to align its learning with the reality of students. An approach used to bridge the gap between classroom learning and real-life experiences is Realistic Mathematics Learning (RML). By placing the experiences and reality of students at the forefront, RML allows students to learn this subject through activities that develop mathematical tools to solve problems associated with everyday life. The mathematization process, which starts from the real world and progresses to the symbol world, comprises two stages, namely horizontal and vertical. In the horizontal stage, students use their informal experiences........

Keywords: Horizontal Mathematization, Vertical Mathematization, Realistic Mathematics Learning.

[1]. Begle, E.C. Critical Variables in Mathematics Education. Washington DC: MAA & NCTM (1979)
[2]. De Lange, J. Mathematics Insight and Meaning. CW & OC, Utrecht. (1987)
[3]. Gravemeijer. Developing Realistic Mathematics Education. Utrecht: Freudenthal Institute. (1994)
[4]. Gagne, RM. The Conditions of Learning and Theory of Instruction. New York: Hott, Reinhart and Winston. (1985)
[5]. Herman Hudoyo. Heboh tentang Pengajaran Matematika di SD. Makalah yang disajikan dalam Seminar Regional Matematika kota Malang, 20 September (1990).

Abstract :The concept in which division by zero results in a defined and logically consistent answer as opposed to the currently accepted "undefined" answer sprung forth from a theory that was developed by applying division to infinitesimal numbers in the hyperreal number line, leading to the discovery of sub-infinitesimals, which are an extension of the concept of the number zero, with the latter assuming the role of the data of numbers. Sub-infinitesimals themselves have no magnitude as they are simply zero, however they serve as a system of identification for numbers describing how in certain situations a number will "react" to certain operations. When considering division by three, which results in a never-ending quotient, speculation that division by 3 was an "imperfect" operation that cannot......

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[4]. Carlström, J. (2001, September). Wheels — On Division by Zero (No. 11). Department of Mathematics Stockholm University. https://www2.math.su.se/reports/2001/11/2001-11.pdf
[5]. Britannica, T. Editors of Encyclopaedia (2016, October 17). infinitesimal. Encyclopedia Britannica.

Abstract : The notion introduced in [1] for 𝑆𝜉− Strictly singular operator in Banach spaces. We extend this notion for super strict singular operator in Locally convex spaces (Lcs). Some properties and characterization for these operators are derived in hereditarily indecomposable(HI) complex Banach spaces.

Keywords: Strictly singular operator, Super strictly singular operator, Hereditarily indecomposable(HI).

[1]. G. Androulakis, P. Dodos, G. Sirotkin and V.G. Troitsky, Classes of strictly singular operators and their product, Israel. J. Math. 169: 221-250, 2009.
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[5]. S. Goldberg, Unbounded linear operators theory and application, Mc Graw-Hill, New york, Ny, USA, 1966.

Abstract : This paper presents a deterministic mathematical model on the transmission dynamics of tuberculosis with exogenous reinfection and vaccination control. A non-linear compartmental model for the disease transmission was developed. Stability analysis of disease-free equilibrium point was estimated to be both locally and globally asymptotically stable if 𝑅0<1 and unstable𝑅0>1 using the next-generation matrix and the comparison theorem. The findings indicate that transmission of tuberculosis can be reduced by ensuring adequate intervention by continuous vaccination and sensitization.

Keywords: Tuberculosis, Exogenous Reinfection, Sensitivity and Vaccination

[1]. Birkhof, G. and Rota, G. C. (1989) Ordinary Differential Equations. MIT Press, Boston.
[2]. C.D.C (2000). Report, emergence of mycobacterium tuberculosis with extensive resistance to second-line drugs. JAMA: The Journal of the American Medical Association.
[3]. C.D.C (2010). Infection control and prevention of tuberculosis. Fact sheet.
[4]. Daley, D. and Gani, J. (2005). Epidemic modelling, an introduction; Cambridge University Press .
ISBN 0521640792
[5]. Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R0 in the models of infectious diseases in heterogenous populations. J.Math Biol., 28:365–382.

Abstract : The concept of tracing the pirated copy of Digital content was introduced by Chor, Fiat and Naor [5]in 1994.Then the Strong form of Codes i.e. traceable codes was defined by Staddon and Wei[9]in 2001. Several authors defined different combinatorial structures like Hadamard Codes, t-Designs, and Balanced Incomplete Block Designs in form of frameproof and traceable (TA) codes. Here in this present study we show that Hadamard Codes with parameters (𝑛−1,𝑛,𝑛2) obtained from Hadamard Matrices are not in general 2-TA. We also show that the rows of Hadamard matrices of the type (𝑛,𝑛,𝑛2) do not form 2-TA.

Keywords: Balanced Incomplete Block Design, Hadamard Code and Hadamard Matrix, Traceable (TA) Code

[1]. Anu Kathuria, Sudhir Batra and S.K. Arora " On traceabilty property of Equidistant codes" Discrete Mathematics,Elsevier,vol.340,issue 4,April 2017,pg.713-721
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[3]. D. Boneh and J. Shaw," Collusion –Secure fingerprinting for Digital Data", in Advances in Cryptology-CRYPTO'95, (Lecture Notes in Computer Science)", vol. 963 , pp.453-465, New York, 1995.
[4]. Hongxia Jin, Mario Blaum," Combinatorial Properties of Traceability Codes using Error Correcting Codes" IEEE Transformations on Information Theory,vol.53,no.2, February 07.
[5]. B. Chor, A. Fiat and M. Naor ,"Tracing Traitors", in Advances in Cryptology – CRYPTO 94 ( Lecture Notes in Computer Science)Berlin, Germany, Springer Verlag, vol. 839, pp. 257-270 ,1994.

Abstract : Predicting traffic events is vital for improving road safety. Models for predicting traffic accidents can be used to pinpoint accident causes and lower accident rates. Creating a fuzzy logic model for forecasting traffic accidents in Bangladesh is the goal of this work. The annual average daily traffic (AADT), the road width (RW), the speed (SP), which is measured in distance per unit time, and the roadside market (RM) are the four input variables used in this model. Annual All Accidents (AAA), the model's output, is determined as the total number of accidents that happen on a road in a day for every kilometer of road. This model is used in Bangladesh on the Dhaka-Mymenshingh highway. MATLAB's fuzzy logic toolbox is used here...... 2-TA.

Keywords: Fuzzy Logic; Mamdani Fuzzy Logic; Fuzzy Classification.

[1]. A Study of Membership Functions on Mamdani-Type Fuzzy Inference System for Industrial Decision-Making.
[2]. DEVELOPMENT OF ACCIDENT PREDICTION MODEL.
[3]. Introducing an Intelligent Transportation System Decision Support Model for the Highways in Iran Based on Fuzzy Logic.
[4]. Comparative Analysis of Membership Function on Mamdani Fuzzy Inference System for Decision Making.

Abstract : Blood flow is analyzed for various aneurysmatic arteries of the regular tissue using Oldroyd-B fluid. A finite element method is used to analyze blood flow numerically for the different situations of aneurysmatic arteries. The Oldroyd-B fluid is considered due to the manner of blood viscosity. In this paper, the impact of an aneurysm artery on blood flow in various arterial conditions has been studied. The Oldroyd-B model has been used to study the blood flow characteristics in bulge arteries. The non-linear partial differential equations are converted into dimensionless equations using non-dimensional variables and solved mathematically. The uniqueness of this study is to determine the arterial diseases.....

Keywords: Aneurysmatic artery; Oldroyd-B fluid; Finite element method; Blood flow; Viscoelasticity

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[4] R. Keslerová and K. Kozel, "Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme", J. Phys.: Conf. Ser. 633(2015)012128.
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