Interdisciplinary sciences include various challenging problems of engineering and computational science along with different physical, biological, and many other sciences. Computational, mathematical, and machine intelligence are the bridge to handle various interdisciplinary problems. In recent years, correspondingly increased dialog between the disciplines has led to this new book. The purpose of this book is to meet the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of mathematics on the other hand. It may be challenging to know the ways that mathematics may be applied in traditional areas and innovative steps of applications.

This book deals with recent developments on mathematical methods on theoretical as well as applied science and engineering. It focuses mainly on subjects based on mathematical methods with concepts of modeling, simulation, waves and dynamics, machine intelligence, uncertainty, and pure mathematics that are written clearly and well organized. The idea has been to bring together the leading‐edge research on mathematics combining various fields of science and engineering to present the original work with high quality. This perspective acknowledges the inherent characteristic of current research on mathematics operating in parallel over different subject fields.

In view of the above, the present book consists of 18 chapters. Chapters 1–4 include different problems of connectionist learning methods. As such, Chapter 1 contains the solution of various types of differential and integral equations by using single‐layer artificial neural network (ANN) and functional link artificial neural network (FLANN) models. Multilayer perceptron‐based deep learning architecture has been used in population genetics – specifically selection in Drosophila melanogaster in Chapter 2. Chapter 3 provides an overview of different classification models used in speech emotion recognition (SER) research. Prominent classification techniques are discussed in the SER context with brief mathematical elaborations. Latest deep learning architecture and its implementation to solve the SER problem is also discussed here. Deep learning fundamentals and related applications are addressed in Chapter 4.

Chapters 5–9 incorporate data processing and fuzzy uncertainty problems. A new approach to time‐wise complex representation and processing of multimodal data based on the algebraic system of aggregates have been investigated in Chapter 5. In Chapter 5, authors proposed mathematical models of data synchronization for most possible cases for both crisp and fuzzy synchronization. In Chapter 6, various thermal and chemical diffusion problems have been handled with uncertain bounded parameters. The involved parameters are taken as interval/fuzzy. Fuzzy finite element method (FFEM) based on limit form of arithmetic rules and explicit finite difference method (EFDM) are included. In order to handle the incomplete information under fuzzy uncertainty in the mathematical modeling, some generalization has been proposed for arbitrary order differential equations of Riemann–Liouville type with respect to another function in Chapter 7. Chapter 8 addresses nanofluid flow between two inclined planes known as Jeffery–Hamel problem in an uncertain environment. Here nanoparticle volume fraction is taken as an uncertain parameter in terms of fuzzy number. Further, Chapter 9 presents a review of the several techniques for attribute reduction based on fuzzy rough set theory. Degree of dependency and discernibility matrix‐based approaches are widely discussed for supervised, semisupervised, and unsupervised information systems. Applications of such techniques in different areas such as image processing, signal processing, and bioinformatics are also presented in Chapter 9.

Chapters 10 and 11 include interval and affine‐based research. As regards, Chapter 10 is devoted to theoretical and practical aspects of interval mathematics. The theories of classical intervals and parametric intervals are formally constructed and their mathematical structures are uncovered. Moreover, with a view to treating some problems of the present interval theories, a new alternate theory of intervals, namely, the “theory of universal intervals,” is presented and proved to have a nice S‐field algebra, which extends the ordinary field of the reals. Further, homotopy perturbation method (HPM) based on affine contractor has been developed in Chapter 11 for evaluating the solution bounds of nonlinear dynamical problems in uncertain environments. Different application problems, viz., Rayleigh equation, Van der Pol Duffing equation, and nonhomogeneous Lane–Emden equation are taken into consideration.

Nano‐ and microstructural problems are studied in Chapters 12 and 13, respectively. Accordingly, Chapter 12 considers dynamical behavior (free vibration) of Euler–Bernoulli nanobeam under the framework of the strain gradient model. The differential transform method (DTM) is applied to investigate the dynamic behavior of SS and CC boundary conditions. Effects of small‐scale parameter and length‐scale parameter on frequency parameters are reported. Lie Symmetry Groups approach is implemented in Chapter 13 for analyzing the response of a very nonlinear system represented by a stiff differential equation. The problem under discussion has been the dynamic performance of a microcantilever beam subjected to an electrostatic force, which acts very close to the pull‐in potential.

Advanced numerical methods with respect to numerical and application problems are investigated in Chapters 14 and 15 and optimization method in Chapter 16. In this respect, Chapter 14 discusses the mathematical fundamentals and performances of some innovative numerical approaches, namely, the generalized differential quadrature (GDQ) and the generalized integral quadrature (GIQ), while illustrating the procedure to evaluate the weighting coefficients, principal types of discretization, and some applications to simple functions. The accuracy of the GDQ and the GIQ methods are demonstrated through convergence analyses, which can be of great interest for many engineering problems of practical interest. An efficient method is provided in Chapter 15 for solving a nonlinear multidimensional inverse problem. This inverse problem is concerning the diffusion equation with an unknown source control parameter. The proposed method is based on applying the θ‐weighted finite difference scheme for time discretization and Chebyshev collocation method for spatial approximation. Chapter 16 deals with the problem of optimal resource allocation when designing control strategies for infectious diseases in developing countries, subject to budgetary constraints. A binary integer programming formulation is developed for this purpose. Different objectives such as minimizing the total risk are considered in the same context, and it is briefly described how to meet the expected objectives by using a goal programming approach.

Artificial intelligence understanding with respect to different application problems is defined and discussed in Chapter 17. The last chapter, viz., Chapter 18, considered the problem to find the zeros of monotone operators. Both direct and iterative methods have been proposed to solve such types of issues. Proximal point algorithm and its different modified form along with their convergence behavior have been studied. In this respect, various numerical and application problems are also addressed.

It is worth mentioning that the present book incorporates a systematic understanding of theory related to the multidiscipline area and the applications. This may prove to be a benchmark for graduate and postgraduate students, teachers, engineers, and researchers in the mentioned subject areas. The book provides comprehensive results up to date and self‐contained review of the topic along with application‐oriented treatment of the use of newly developed methods of different modeling, simulation, and computation in various domains of engineering and sciences. It is believed that the readers will find this book as an excellent source to have a variety of application problems concerning mathematical models in one place, which may be fruitful and challenging for the future direction of research.

Rourkela, March 2020

Snehashish Chakraverty