Advances in Mathematics Research. Volume 28


Albert R. Baswell (Editor)

Series: Advances in Mathematics Research
BISAC: MAT000000

This compilation first outlines a stochastic multicriteria modelling-to-generate-alternatives approach for waste management planning that can generate maximally different sets using a modified version of the computationally efficient Firefly Algorithm.

The authors present reduced-order models to pattern formations occurring in the activator-inhibitor FitzHugh-Nagumo equation, parametrized Allen-Cahn equation, non-linear Schrödinger equation, Ginzburg-Landau equation and Swift-Hohenberg equation.

The subsequent chapter deals with the singularly perturbed semilinear convection-diffusion problem, serving as an introduction to the model problems which arise frequently in counterflow flames modeling, modeling in mathematical biology, semi-conductor device simulations based on the so-called drift diffusion modeling, fluid dynamics and heat conduction.

The authors present a linear integer programming approach to construct efficient incomplete block designs forgiven v, b and k. The proposed approach is illustrated by constructing an A-efficient incomplete block design, and the strengths and weaknesses of this algorithm are also discussed.

One included work is devoted to the issue of the Green functions that are related to some three-point boundary and eigenvalue problems. A detailed definition is given for the Green functions provided that the considered three-point boundary value problems are governed by a class of ordinary differential equations which are associated with homogeneous boundary and continuity conditions.
A review on the methods of mathematical modeling used to calculate irreversible loss of capacity in polymer lithium-ion batteries is provided.

In closing, the authors consider the corpus of mathematical theorems that admit formulations in natural language and offer some explanations of the existence of several types of theorems.



Table of Contents


Chapter 1. A Stochastic, Multicriteria, Firefly Algorithm-Based Approach for Waste Management Decision-Making
(Julian Scott Yeomans, Schulich School of Business, York University, Toronto, Canada)

Chapter 2. Discontinuous Galerkin Model Order Reduction for Semi-linear Parabolic Equations
(Bülent Karasözen and Murat Uzunca, Institute of Applied Mathematics and Department of Mathematics
Middle East Technical University, Ankara, Turkey, and others)

Chapter 3. A Rigorous Analysis of a Hybrid Numerical Method for Singularly Perturbed Semilinear Problems
(Varsha Srivastava, PhD, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India)

Chapter 4. Construction of Efficient Incomplete Block Designs Using Linear Integer Programming Approach
(B. N. Mandal and Rajender Parsad, ICAR-Indian Agricultural Statistics Research Institute, New Delhi, India)

Chapter 5. Green Functions for Three-Point Boundary Value Problems with Applications to Beams
(György Szeidl and László Péter Kiss, Institute of Applied Mechanics, University of Miskolc, Miskolc, Hungary)

Chapter 6. Mathematical Modeling of Capacity Loss of Polymer Lithium-Ion Batteries: A Review
(Andressa Leseux, Airam Sausen, Mauricio de Campos and Paulo Sérgio Sausen, Masters and Doctoral Program in Mathematical Modeling, Regional University of Northwestern, Rio Grande do Sul State [UNIJUÍ], Ijuí, RS, Brazil)

Chapter 7. Mathematical Theorems in Natural Languages
(Grigory Kreydlin and George Shabat, Department of Russian at Institute of Linguistics, Russia State University for the Humanities, Moscow, Russia, and others)


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