Albert R. Baswell – författare

This book commences with an introduction to the solution attractor theory of local search systems. Here, a local search algorithm is treated as a discrete dynamical system and its search behavior is studied from the perspective of dynamical systems. Following this, this collection examines the three-year period of 1966 to 1968 when the invariant integral of fracture mechanics became popular, as well as 2015 to 2016 when the neoclassic cosmology based on the invariant integral came about. The authors go on to argue how, in the history of philosophy, the meaning of the term “to be” has been disputed between two research programmes: The Platonic-Aristotelian and the Pythagorean- Parmenidean-Democritean programmes through Hobbes and Boole up to Peano. The history of science and philosophy goes hand in hand with the question of the nature of mathematical objects. By implication, this was known by the Pythagoreans, even though it was not expressed in the plane of a directly named problem. The authors propose that that strict Platonism in mathematics is not possible, though may be considered in many cases. Also in this collection, perform building-scale analysis is performed, and the use of a convex map is considered. However, partitioning an architectural space is not easy due to its ambiguity. As such, an analysis method is proposed which may decompose the space with moderate granularity. One study sets out to determine the feasibility of using a hidden Markov model to assess whether goats were in estrus. Mammalian behavior has typically been studied based on observations, but direct observation requires substantial time and effort if the number of mammals observed is high or the observations are obtained over a long period of time. Thus, a machine-learning method such as a hidden Markov model may be suitable. A literature review of electric circuits and mathematical models of electric power transmission lines is provided, approaching a classification of the models regarding the nature of their parameters and frequency dependence. These models are important in predicting the voltage and current available, which aids in meeting safety and quality demands. The authors conclude with a summary of some results concerning the problem of computing a proper rational parametrization Q from P. In particular, they present an algorithm that computes a parametrization Q of V such that deg(-Q) ≤ deg(-P). If deg(-Q) = 1, then Q is proper and the reparametrization problem is solved.

This book opens to show the importance of mathematical means associated with the role of Pythagorean musical tradition in mathematical and architectural contexts up to the Renaissance. The following chapter proposes a formalism which enables us to separate fields of investigation from the epistemological questions in philosophy and to consider models as parts of hierarchical model families. Continuity of the modulus and phase degrees-of-freedom of molecular electronic states is commented upon in the next section, and the resultant entropy/information descriptors of electronic states, combining the probability and current contributions, are applied to classical issues in chemical-reactivity theory. Additionally, the authors study the categorical generalizations of the Möbius function emphasizing the geometric meaning of these constructions, and discuss the relations between the various approaches. The final chapter introduces the PWP method as a technique for measuring indirect influences in complex networks.

This book aims to approach the dynamical systems analysis from a new standpoint: feedback linearization — a method with a lot of applications. For both linear and non-linear dynamic systems, this method offers an interesting perspective from the qualitative approach stance. The authors examine the implementation of gas-assisted electrical discharge machining of D3 die steel. One of the fundamental disadvantages of the traditional EDM machining process is poor material removal rate. Numerical results for a wide range of Reynolds numbers are presented, including moderate and high Reynolds numbers, and two different numerical schemes to solve this kind of problem are described. For the analysis and interpretation of probabilistic engineering calculations, including those concerning the estimation of the safety of structures, symmetrical normal distribution is often used. In one study, the authors propose that such a distribution may be a linear combination of normal distribution and Gumbel distribution. This compilation goes on to present the problems that arise from the M|G|∞ queue system busy period and busy cycle, an idle period followed by a busy period. The renewal function is calculated, as well as the “peakedness” and the “modified peakedness” for the M|G|∞ busy period and busy cycle time length. Based on earlier research and using new mathematical methods, the authors present a theory using functional integrals for obtaining probability distributions of phase invariants in which N (the number of atoms in the asymmetric unit) doesn''t appear anymore. Also proposed is a numerically realizable explicit formula for the solution to the Cauchy problem for a linear elliptic equation. In closing, a mathematical model assessing the effect of tobacco smoking on the dynamics of tuberculosis transmission is formulated and analyzed. In the absence and presence of smokers, theoretical results indicate the possibility of the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. However, the analysis of the associated reproduction thresholds of the model with smokers shows that tobacco smoking has a detrimental effect on tuberculosis dynamics.

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.

"Advances in Mathematics Research" presents original research results on the leading edge of mathematics research. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed herein include multivariate differences and summation formulae; hybrid contractive maps; generalized games; affine and fundamental vector fields; and Newton''s method for matrix polynomials.

This compilation contains seven chapters, each detailing a particular advancement in mathematics research. Chapter One presents labeled paths as methods for encryption and decryption. Chapter Two presents the possibilities of risk assessment and management assistance built around Bayesian tools. Chapter Three analyzes in detail the Lie point symmetries of the second-order scalar ordinary differential equations appearing in the Painlevé–Gambier classification. Chapter Four focuses on the application of Adomian decomposition method (ADM) for solving singular and non-singular ordinary and partial differential equations with initial and boundary conditions. Chapter Five describes the structure of compact global attractor (Levinson center) for monotone Bohr/Levitan almost periodic dynamical systems. Chapter Six presents the mathematical modeling from the PI model of three real segments derived from the electric power network of two concessionaires located in the city of Ijuí, Brazil. Finally, Chapter Seven presents a study of the mathematical aspects of the theory of error-detecting/correcting codes based on coding theory.

This volume includes some of the latest advancements in mathematics research. Chapter One aims to increase the certainty and reliability of G index through different examples and show that G index can be reached by two different paths. Chapter Two focuses on deriving exact trigonometric ratios using equations. Chapter Three presents a review of rough set theory-based feature selection approaches for small to large scale machine learning tasks. Chapter Four delivers an analytic approach to the Riemann hypothesis. Chapter Five aims to present a comparative analysis of mathematical models of transmission lines applied to two short lines of medium voltage. Finally, Chapter Six focuses on the numerical investigation of the one and two dimensional semi-linear scale-invariant wave equation with damping, mass and power non-linearity.

This volume includes six chapters that detail recent advancements in mathematics research. Chapter One presents various capabilities of the Maple computer algebra system. Chapter Two uses data from the Children of Immigrants Longitudinal Study to demonstrate how to perform multilevel structural equation modeling to investigate if academic aspiration of immigrant youths in late adolescence mediates both the effects of family socioeconomic status and school location at individual and school levels in early adolescence on their later successful college graduation in young adulthood. Chapter Three proves the existence and regularity of solutions in α-norm for some partial functional integrodifferential equations in Banach spaces. Chapter Four discusses a method for obtaining exact solutions of nonlinear partial differential equations. Chapter Five analyzes the linear and nonlinear stability of modons and We-Verkley waves, which are weak solutions of the barotropic vorticity equation. Lastly, Chapter Six provides an explicit representation of the maps interconnecting the sets of solutions to the special double confluent Heun equation and the equation of the RSJ model of overdamped Josephson junction in case of shifted sinusoidal bias.

Chapter 1 is an introduction to meta-regression analysis. The authors demonstrate that meta-regression analysis is a methodological framework that allows modeling and correcting problems of publication bias while explaining the variability of results usually found in social sciences literature. In Chapter 2, a new model order reduction technique for the simplification of the complex large-scale stable linear dynamic systems is presented. Chapter 3 discusses the importance of identifying variables, scales, and methods for the sensory analysis of novel food products. Chapter 4 focuses on structural stability and dynamic quantum models. Chapter 5 is an introduction to linear difference equations. Chapter 6 includes a survey of various measures used in cohort analysis with alternative multifaceted indices used in theory and often by practitioners. The chapter is intended to offer a concise description of these measures and elaborate where and how they may be used in different cohort analysis. In Chapter 7, two mixed initial-boundary value problems describing motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are analytically investigated. In Chapter 8, new permanent solutions for Stokes’ second problem of incompressible burgers fluids and their applications is explored. Next, for the first time, the authors propose the definitions of the fractional sum and fractional difference on non-uniform lattices in two different ways. Chapter 10 focuses on the Carleman linearization method for boundary value problems. In the last chapter, Chapter 11, the authors review some of the recent work on pattern packing, superpatterns, and pattern avoidance when colored or circular patterns/permutations are considered.

This volume includes eight chapters that discuss recent advancements in mathematics research. Chapter One introduces hybrid direction, which is a new method for solving linear programming problems. Chapter Two reviews the theory of p-adic Galois representations and analyzes examples of the ones arriving from elliptic curves. Chapter Three investigates the structure of bicyclic rings and describes some of their properties. Chapter Four presents a numerical simulation of the atmospheric boundary layer related to experiments for stable atmospheric conditions. Chapter Five explains the Extreme Physical-Information (EPI) principle of physics. Chapter Six introduces numerical methods for solving ordinary differential equations with fractional derivatives. Chapter Seven provides a deeper understanding of the phase of the quaternion number and its relation to fluctuation. Lastly, Chapter Eight discusses pension funds, specifically ones that are not auto financed.

This volume contains eight chapters that detail advances in mathematics research. Chapter One discusses the development and analysis of heuristic and metaheuristic methods for solving optimization problems of cutting and packing. Chapter Two details virial energy components, extreme physical information, and property flows in communication networks. Chapter Three explores two functions of molecular information systems, consecutive (cascade) and simultaneous (combination). Chapter Four considers the expressions of a digital-to-analog piezo converter-actuator using the equations of reverse piezo effect and the ordinary linear differential equation of the second order. Chapter Five discusses large regression modeling under Lp-Norm loss function. Chapter Six explains cyclic evolutions in nonrelativistic quantum mechanics and geometric phases. Chapter Seven investigates the HIV/AIDS epidemic model using stability and Lie symmetry analysis. Lastly, Chapter Eight examines a SIRD (Susceptible, Infected, Recovered,Dead) epidemic model via the lens of Lie symmetry analysis.

This volume contains nine chapters that detail advances in mathematics research. In chapter one, the author presents new spectral sufficient conditions for the Hamiltonian and traceable graphs. In chapter two, the authors examine the Green’s function in an acoustic gradient interface model of the monotonic Epstein. In chapter three, asymptotic formulae are presented for solutions and Green’s functions of Sturm-Liouville eigenvalue problem having eigen parameter both in differential equation and in one boundary condition. The focus of chapter four is the representation of Sum of Products in Boolean cubes. The author in chapter five explains the value of ontological logic in mathematical research. Chapter six proves that mathematical results using Riemannian geometry deeply question the origin and existence of gravitational waves. In chapter seven the author considers the problem of solving strongly nonlinear oscillators making use of averaging methods. In chapter eight, the authors study the existence and regularity of solutions in the α-norm for some second order partial neutral functional differential equations with infinite delay in Banach spaces. The last chapter probes the complexities of the frequency-amplitude formula, illuminating its integral role across both linear and nonlinear oscillatory contexts.