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Mathematics in Computational Science and Engineering


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wind speed) whereas only 3.9% of the variability of the dependent variable PM2.5 is explained by AOD alone as explanatory variable.

      Chapter 6 In this chapter we would see inventory systems and learn to manage it with simulation technique. We would study simulation which is performed manually for better understanding of the topic. Then some merits and demerits of it, Monte Carlo simulation technique and its application in a real life problem would be delved in. We would use Excel software to generate random numbers and perform simulation with it. Inventory sales for a confectionary bakery shop would be predicted for next few days. At the end we would compare and plot a graph so as to see and understand simulation better.

      Chapter 7 The chapter gives an idea about change in characteristics of cement mortar while adding some nano admixtures and polymer PVA. Workability of mortar is measured in terms of flow value that is necessary to know how the mortar will behave with these additives. Final strength is dependent on various factors out of which workability is one factor. Also the handling with mortar in the field while mixing, transporting, pouring and compacting the workability plays important role hence various additives are added to achieve proper workability. In this article various nano materials like nano alumina, nano silica, nano zinc oxide, and polyvinyl alcohol has been tried for changing the workability.

      Chapter 9 In this chapter, we establish a new common fixed point theorem satisfying the digital topology with Contractive mappings in fuzzy sets. Rather than focussing on mathematical details, we will concentrate on making the concepts as clear as possible. There are several useful technical introductions in fuzzy sets and fuzzy logic with digital space. fuzzy set theory is an analytic framework for handling concepts that are simultaneously categorical and dimensional. starting with a rational for fuzzy sets. in this chapter we provide some basic definitions and results for fuzzy sets. In this chapter we shall discuss two important categories of fuzzy logic with linear applications “digital” and “contractions “ with respect to fuzzy digital applications.

      Chapter 10 This chapter discusses the bond between mathematics & Artificial intelligence. Mathematics helps to solve the challenging task of hypothetical problems in artificial intelligence using traditional methods and techniques. In the first part the main concern is to demonstrate the mathematical concepts like Linear Algebra in dimensionality reduction of large datasets, Eigen Vectors in ranking of features of dataset, Calculus in optimization task, Statistics for data visualization and so on. The later part discusses the work flow of artificial intelligence and the application areas where Artificial Intelligence is using now a days.

      Chapter 11 In this chapter three mathematical models have been used. One is model based on Geometric Progression (G.P.). The second is SIR model and the third one is constructed using differential equations. The model based on G.P. shows how coronavirus is spread using tree chart, assuming that an infected person is capable of infecting two persons who come in contact with the former. It can also be observed that there is a significant difference between the number of covid patients with and without the lockdown.

      Chapter 13 This chapter explores the different types of recommender techniques with its mathematical foundation and also discusses some of the problems in the prevailing system. It discusses use of sequential patterns of web navigation along with the content information and is based on set and sequence similarity measure (S3M), principle of upper approximation and singular value decomposition for generating recommendations on web data. This chapter makes use of mathematics involved in finding the set and sequence similarity for recommendation to user on CTI news dataset.

      Chapter 14 The adhesive anchors are usually installed into un-cracked hardened concrete. The Artificial Intelligence methodology of Neural Network (NN) and Genetic Expression Programming (GEP) are used to develop an explicit equation for estimating and predicting the shear capacity of a single adhesive anchor post. The main objective in this chapter is to provide a mathematical tool to predict shear capacity or shear strength of an anchor without any expansive laboratory testing. The Artificial Intelligence (AI) techniques are well-suited for assessment and prediction purposes.

      Chapter 15 Genetic Algorithms is an easy form of learning and improvising design of Algorithm. The foundation of the principle is Darwin’s Natural selection, which states survival of the fittest. It offers solutions to various problems and helps to evaluate the value and also permits to combine with each other. This chapter gives confidence to reproduce good solutions, it will steadily produce enhanced solutions. It proves that any range of problem can be supported and solved. Gene is generally made up of a cells which represents individual problems and it represents individual solution of the problem.

      Chapter 17 This chapter focuses on the control of Plasmodium parasite by studying the stages in the cycle. Backstepping control technique is applied to breakup the life cycle of plasmodium parasites. Lyapunov function is derived for the recursive procedure for the entire system to reduce the energy rate of reproduction among plasmodium parasites. Depending upon the concerned state in the system, ‘pseudo controls’ are introduced so as to achieve global stability of plasmodium life cycle.

      Chapter 18 The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation.