Search results for ""Author Albert R. Baswell""

The opening chapter aims 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 generalisations of the Möbius function emphasising 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.

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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 modelling 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 analyses 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.

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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.

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Advances in Mathematics Research. Volume 27 first 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|â 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|â 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.

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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.

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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 Schrodinger 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.

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