Mathematics
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Constrained Bayesian Methods of Hypotheses Testing: A New Philosophy of Hypotheses Testing in Parallel and Sequential Experiments

Author: Kartlos Kachiashvili (Professor of Georgian Technical University, Main Scientific Worker of I. Vekua Institute of Applied Mathematics of Tbilisi State University, Tbilisi, Georgia)

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
The problems of one of the basic branches of mathematical statistics – statistical hypotheses testing – are considered in this book. The intensive development of these methods began at the beginning of the last century. The basic results of modern theory of statistical hypotheses testing belong to the cohort of famous statisticians of this period: Fisher, Neyman-Pearson, Jeffreys and Wald (Fisher, 1925; Neyman and Pearson, 1928, 1933; Jeffreys, 1939; Wald, 1947a,b). Many other bright scientists have brought their invaluable contributions to the development of this theory and practice. As a result of their efforts, many brilliant methods for different suppositions about the character of random phenomena are under study, as well as their applications for solving very complicated and diverse modern problems.

Since the mid-1970s, the author of this book has been engaged in the development of the methods of statistical hypotheses testing and their applications for solving practical problems from different spheres of human activity. As a result of this activity, a new approach to the solution of the considered problem has been developed, which was later named the Constrained Bayesian Methods (CBM) of statistical hypotheses testing. Decades were dedicated to the description, investigation and applications of these methods for solving different problems. The results obtained for the current century are collected in seven chapters and three appendices of this book. The short descriptions of existing basic methods of statistical hypotheses testing in relation to different CBM are examined in Chapter One. The formulations and solutions of conventional (unconstrained) and new (constrained) Bayesian problems of hypotheses testing are described in Chapter Two. The investigation of singularities of hypotheses acceptance regions in CBM and new opportunities in hypotheses testing are presented in Chapter Three. Chapter Four is devoted to the investigations for normal distribution. Sequential analysis approaches developed on the basis of CBM for different kinds of hypotheses are described in Chapter Five. The special software developed by the author for statistical hypotheses testing with CBM (along with other known methods) is described in Chapter Six. The detailed experimental investigation of the statistical hypotheses testing methods developed on the basis of CBM and the results of their comparison with other known methods are given in Chapter Seven. The formalizations of absolutely different problems of human activity such as hypotheses testing problems in the solution – of which the author was engaged in different periods of his life – and some additional information about CBM are given in the appendices.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-103-1
ISBN: 978-1-53613-104-8

Price: $270.00
Price: $270.00


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Uniform Classification of Open Manifolds

Author: Juergen Eichhorn (Institut fuer Mathematik und Informatik, Universitaet Greifswald, Greifswald, Germany)

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
A certain classification of open manifolds has been a continuous problem in geometry, topology and global analysis. The background for this is the fact that in any dimension greater than one, there are innumerous homotopy types. A solution to this problem seemed almost hopeless. In this monograph, the author offers an approach by decomposing the classification into two fundamental steps. This book introduces certain uniform structures in the set of all proper metric spaces under consideration (complexes, Riemannian manifolds, etc.), then considers the components of this uniform space by classifying the components by adapted homology theories (Gromov-Hausdorff and Lipschitz cohomology). The author then moves on to classifying the elements inside a component. For the second step, a geometric bordism theory for open manifolds and geometric generators are introduced. The main achievements include the invariance of a spectral gap under uniform homotopy equivalences and the vanishing of the K-theoretic signature in the geometric bordism theory. Concerning surgery, the absolutely fundamental achievements of Maumary and Taylor are included. Repeated motivations and explanations should make this monograph fairly legible to a vast audience.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53612-939-7
ISBN: 978-1-53612-940-3

Price: $230.00
Price: $230.00


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Optimal Control Engineering with MATLAB: A Solutions Manual

Author: Rami A. Maher (Dean of Scientific Research and Graduate Studies, Isra University Amman, Jordan)

Series: Computational Mathematics and Analysis

Publication Date: 2018

Book Description:
This book is a solution manual of the 110 questions that were presented in the eight chapters throughout the author’s previous book, Optimal Control Engineering with MATLAB. The manual is prepared as an independent book since it includes the problems’ questions, figures, and all necessary equations and formulas in a summarizing fashion and within the given solution frameworks. The idea behind writing this book is to increase significantly the student’s or reader’s knowledge about the optimal control discipline that is found in many engineering fields. Detailed step-by-step hand solutions are carried out while utilizing the MATLAB functions in the toolboxes. Simulink models are presented to simulate and validate the obtained results. Each chapter concludes with the lists of MATLAB programs that are used either to assess or to develop the desired solutions to challenging problems. The reader will discover the importance of using these programs, especially in solving parameter optimization design, different nonlinear TBVP, finite horizon LRQ, DDP and ILRQ problems. In addition, the implementation of the obtained time function optimal control law by a transfer function controller is accomplished for some problems. Among these problems, the reader will find many practical engineering problems in continuous as well as discrete forms. Finally, the reader can easily modify these programs and Simulink models for his or her problems.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-055-3
ISBN: 978-1-53613-056-0

Price: $230.00
Price: $230.00


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New Mathematical Methods for Physics

Author: Jean-Francois Pommaret (CERMICS, Ecole des Ponts ParisTech, Marne-la-Vallee Cedex, France)

Series: Computational Mathematics and Analysis

Publication Date: 2018

Book Description:
The concept of “group” has been introduced in mathematics for the first time by E. Galois (1830) and slowly passed from algebra to geometry with the work of S. Lie on Lie groups (1880) and Lie pseudogroups (1890) of transformations. The concept of a finite length differential sequence, now called the Janet sequence, had been described for the first time by M. Janet (1920). Then, the work of D. C. Spencer (1970) has been the first attempt to use the formal theory of systems of partial differential equations (PDE) in order to study the formal theory of Lie pseudogroups. However, the linear and nonlinear Spencer sequences for Lie pseudogroups, though never used in physics, largely supersede the ”Cartan structure equations ” (1905) and are quite different from the ”Vessiot structure equations ” (1903), introduced for the same purpose but never acknowledged by E. Cartan or successors. Meanwhile, mixing differential geometry with homological algebra, M. Kashiwara (1970) created “algebraic analysis” in order to study differential modules and double duality. By chance, unexpected arguments have been introduced by the brothers E. and F. Cosserat (1909) in order to revisit elasticity and by H. Weyl (1918) in order to revisit electromagnetism through a unique differential sequence only depending on the structure of the conformal group of space-time.
The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of the extension. It has been the dream of many mathematicians at the end of the nineteenth century to generalize these results to systems of linear or algebraic PDE and the corresponding finitely generated differential extensions, in order to be able to add the word differential in front of any classical statement. The achievement of the Picard-Vessiot theory by E. Kolchin and coworkers between 1950 and 1970 is now well-known. However, the work of Vessiot on the differential Galois theory (1904), that is on the possibility to extend the classical Galois theory to systems of algebraic PDE and algebraic Lie pseudogroups, namely groups of transformations solutions for systems of algebraic PDE, has also never been acknowledged. His main idea has been to notice that the Galois theory (old and new) is a study of principal homogeneous spaces (PHS) for algebraic groups or pseudogroups described by what he called ”automorphic systems” of PDE.
The purpose of this book is first to revisit Gauge Theory and General Relativity in light of the latest developments just described and then to apply the differential Galois theory in order to revisit various domains of mechanics (Shell theory, Chain theory, Frenet-Serret formulas, Hamilton-Jacobi equations). All the results presented are new.

Binding: Softcover
Binding: e-Book

ISBN: 978-1-53613-410-0
ISBN: 978-1-53613-411-7

Price: $95.00
Price: $95.00


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Elementary Particles with Internal Structure in External Fields. Vol I. General Theory

Authors: Vasiliy Vasilievich Kisel, Elena Mikhaylovna Ovsiyuk, Olga Vladimirovna Beko, Yana Aleksandrovna Voynova, Vladimir Balan, and Viktor Mikhaylovich Red’kov (Institute of Physics, National Academy of Sciences of Belarus, University Polithechnica of Bucharest

Series: Computational Mathematics and Analysis

Publication Date: 2018

Book Description:
The book represents the systematical development of several rarely used or new mathematical techniques to construct new wave equations for elementary particles. On this ground, it develops the quantum mechanics of the particles with additional electromagnetic structures in the presence of external electromagnetic fields, and, concerning the curved space-time background, it details many new solvable problems in the field. Volume I of this book is devoted to studying the mathematical formalism of the generalized theory of relativistic wave equations, which permits the construction of new equations for particles with an intrinsic spectrum of the spin, mass, and a number of additional electromagnetic characteristics, which lead to additional physical effects in the presence of external fields (electromagnetic and gravitational). The main theoretical tools are: The theory of the Lorentz group; the wave equations and the Gel’fand–Yaglom canonical basis; the Lagrangian formulation of the theory; the minimal polynomials approach; the projective operators technique; and the definiteness of energy and charge. Primary attention is focused on the possibility of constructing different relativistic wave equations for particles with a fixed value of spin and mass, proving that such wave equations describe substantially different objects. These equations possess some intrinsic electromagnetic structures in addition to the electric charge, and this leads to physical effects in the presence of external – electromagnetic and gravitational – fields. Extended models for particles of spins 0, 1/2, 1, 3/2, and 2 are developed.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-108-6
ISBN: 978-1-53613-109-3

Price: $230.00
Price: $230.00


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Elementary Particles with Internal Structure in External Fields. Vol II. Physical Problems

Authors: Vasiliy Vasilievich Kisel, Elena Mikhaylovna Ovsiyuk, Olga Vladimirovna Beko, and Yana Aleksandrovna Voynova (Researcher, Laboratory of Theoretical Physics, Institute of Physics, National Academy of Sciences of Belarus)

Series: Computational Mathematics and Analysis

Publication Date: 2018

Book Description:
The book represents a systematical development of several rarely used or new mathematical techniques to construct new wave equations for elementary particles. On this ground, it develops the quantum mechanics of the particles with additional electromagnetic structures in presence of external electromagnetic fields, and, on the curved space-time background, it details many new exactly solvable problems in the field. In Volume II, the wave equations for particles of spin 0, 1/2, 1 with additional intrinsic structure (such as polarizability, anomalous magnetic moment, quadrupole electric moment, Darwin–Cox structure) are solved for several special types of external electric and magnetic fields, in Minkowski flat space and in spaces with simple non-Euclidean geometry: hyperbolic Lobachevsky and spherical Riemann models. The main attention is focused on new and additional effects which are due to the more general structure of the wave equations in presence of external fields. The following problems are considered: reflection of spin 0 and spin 1 particles by an effective (geometrical) medium; Schrodinger and Dirac particles in electric field on the background of Lobachevsky and Riemann models (LR-models); Dirac-K¨ahler boson in LR-models; spinless particle with polarizability in Coulomb and magnetic fields; spin 1/2 particle with anomalous magnetic moment in homogeneous magnetic and electric fields, and in Coulomb field; spin 1 particle (ordinary and with polarizability) in external magnetic field; spin 1 particle with anomalous magnetic and quadrupole moment in magnetic and electric fields; spinless Darwin–Cox particle with intrinsic structure in external electric and magnetic fields in Euclid, Lobachevsky and Riemann models; fermion with two masses in presence of magnetic field.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-110-9
ISBN: 978-1-53613-111-6

Price: $230.00
Price: $230.00


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Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume I

Authors: Ioannis K. Argyros, Santhosh George, and Narayan Thapa (Cameron University, Department of Mathematical Sciences, Lawton, OK, USA, and National Institute of Technology Karnataka, Department of Mathematical and Computational Sciences, Mangalore, India)

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
This book is dedicated to the approximation of solutions of nonlinear equations using iterative methods. The study about convergence matter of iterative methods is usually based on two categories: semi-local and local convergence analysis. The semi-local convergence category is, based on the information around an initial point, to provide criteria ensuring the convergence of the method; while the local one is, based on the information around a solution, to find estimates of the radii of the convergence balls. The book is divided into two volumes. The chapters in each volume are self-contained so they can be read independently. Each chapter contains semi-local and local convergence results for single, multi-step and multi-point old and new contemporary iterative methods involving Banach, Hilbert or Euclidean valued operators. These methods are used to generate a sequence defined on the aforementioned spaces that converges with a solution of a nonlinear equation, an inverse problem or an ill-posed problem. It is worth mentioning that most problems in computational and related disciplines can be brought in the form of an equation using mathematical modelling. The solutions of equations can be found in analytical form only in special cases. Hence, it is very important to study the convergence of iterative methods.

The book is a valuable tool for researchers, practitioners, graduate students, and can also be used as a textbook for seminars in all computational and related disciplines.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-361-5
ISBN: 978-1-53613-362-2

Price: $230.00
Price: $230.00


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Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume II

Authors: Ioannis K. Argyros, Santhosh George, and Narayan Thapa (Cameron University, Department of Mathematical Sciences, Lawton, OK, USA, and National Institute of Technology Karnataka, Department of Mathematical and Computational Sciences, Mangalore, India)

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
This book is dedicated to the approximation of solutions of nonlinear equations using iterative methods. The study about convergence matter of iterative methods is usually based on two categories: semi-local and local convergence analysis. The semi-local convergence category is, based on the information around an initial point, to provide criteria ensuring the convergence of the method; while the local one is, based on the information around a solution, to find estimates of the radii of the convergence balls. The book is divided into two volumes. The chapters in each volume are self-contained so they can be read independently. Each chapter contains semi-local and local convergence results for single, multi-step and multi-point old and new contemporary iterative methods involving Banach, Hilbert or Euclidean valued operators. These methods are used to generate a sequence defined on the aforementioned spaces that converges with a solution of a nonlinear equation, an inverse problem or an ill-posed problem. It is worth mentioning that most problems in computational and related disciplines can be brought in the form of an equation using mathematical modelling. The solutions of equations can be found in analytical form only in special cases. Hence, it is very important to study the convergence of iterative methods.

The book is a valuable tool for researchers, practitioners, graduate students, and can also be used as a textbook for seminars in all computational and related disciplines.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-309-7
ISBN: 978-1-53613-310-3

Price: $230.00
Price: $230.00


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The Fibonacci Numbers and Integer Structure: Foundations for a Modern Quadrivium

Authors: Anthony G. Shannon and Jean V. Leyendekkers (University of Technology, Sydney, AU)

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
In the study of integers over many centuries, simple but very useful data have often been overlooked or at least sparingly used. The development of modular rings provides a means to shed light on such data.

A modular ring is effectively an array of integers which can be uniquely identified by columns and rows with the aid of linear equations. Thus the modular ring Z4 has 4 columns (or classes), and its first two rows are 0,1,2,3 and 4,5,6,7, respectively. In turn, its columns can be identified by the classes. This notation is suggestive and transparent, and the notation itself becomes a tool of thought.

The book contains a collection of readily accessible classical problems, most of which can be linked to the sequence of Fibonacci integers and explained with integer structure analysis. Modular rings are used to solve, prove and extend a variety of number theory problems associated with generalized Fibonacci numbers, golden ratio families and primes, and distinctions between prime and composite integers, as well as the classical conjectures of Brocard-Ramanujan and Erdös-Strauss. Thus (though mathematically, the golden ratio is a humble surd), replacing its argument shows that it has an infinity for close relatives that can be a source of further exploration, particularly with generalizations of Fibonacci numbers.

Another important structural feature is the right-end-digit (RED) of an integer – its value modulo 10. No matter the sizes of integers, operations with their REDs are stable; for instance, the sum of the integers abcde2 and ghabj5 has a RED of 7. This stability is exploited in several chapters so that powers are reduced to 4 types in the ring modulo 4 which, for example, clarifies Fermat’s Last Theorem for some powers.

The context of this book is the teaching and learning of mathematics. This happens in historical and sociological contexts, and the text has sufficient historical and philosophical allusions for anyone to see that mathematics per se transcends race and religion, history and geography. The topics of number theory in the hands of well-educated teachers can inspire a love of learning in general and in mathematics in particular.

For this reason, the authors have embedded relevant issues on liberal education as a foundation for education in the 21st century, particularly in fostering creativity through the inspiration and passion of teachers. Thus, the authors indicate the role of number theory as an important part of a genuine liberal education, accessible to all students today in a way that education in the ancient quadrivium was confined to a small section of society.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-454-4
ISBN: 978-1-53613-455-1

Price: $195.00
Price: $195.00


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Mathematical Modeling: Methods, Applications and Research

Editor: Seth Sparks and Bill Willis

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
Mathematical Modeling: Methods, Applications and Research reviews recent progress in three different propulsion systems which may offer significant advantages for more efficient, compact and adaptive astronautic vehicles in the mid-21st century: swirling nuclear magneto-hydrodynamic propulsion, biomimetic magneto-rheological propulsion and electro-hydrodynamic propulsion systems. The authors introduce an empirical mathematical model. This model has been developed to describe contrast uptake and washout behavior without use of vascular input functions. Though this approach does not require making assumptions about underlying physiology or anatomy, the primary disadvantage of this approach, is that the parameters obtained by this approach do not correspond directly to identifiable physiological or anatomic features. In closing, the authors aim to express how the mathematical modeling is a valid tool for teaching and learning in a competent way and should be incorporated in academic curricula.

Binding: Softcover
Binding: e-Book

ISBN: 978-1-53613-162-8
ISBN: 978-1-53613-163-5

Price: $95.00
Price: $95.00


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Bayesian Inference: Observations and Applications

Editor: Rosario O. Cardenas

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
Bayesian Inference: Observations and Applications discusses standard Bayesian inference, in which a-priori distributions are standard probability distributions. In some cases, however, a more general form of a-priori distributions (fuzzy a-priori densities) is suitable to model a-priori information. The combination of fuzziness and stochastic uncertainty calls for a generalization of Bayesian inference, i.e. fuzzy Bayesian inference. The authors explain how Bayes’ theorem may be generalized to handle this situation. Next, they present a decision analytic framework for completing selection of optimal parameters for machining process definition. In addition, a discussion section on the subjects of inference, experimental design, and risk aversion is included. The concluding review focuses on the sparse Bayesian methods from their model specifications, interference algorithms, and applications in sensor array signal processing. Sparse and structured sparse Bayesian methods formulate problems in a probabilistic manner by constructing a hierarchical model, allowing for the obtainment of flexible modeling capability and statistical information.

Binding: Softcover
Binding: e-Book

ISBN: 978-1-53613-212-0
ISBN: 978-1-53613-213-7

Price: $82.00
Price: $82.00


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Wavelets: Principles, Analysis and Applications

Editor: Joseph Burgess

Series: Theoretical and Applied Mathematics

Publication Date: 2018

Book Description:
In this book, the authors report the results obtained by the application of wavelet analysis to two physics experiments: the motion of variable mass pendulum and the motion of variable length pendulum. These two motions, which furnish non stationary signals for their motions, are analyzed by means of a comparative Fourier Transform and Wavelet Transform. Afterwards, interval arithmetic extensions for the standard algorithms for the decimated and undecimated unidimensional Haar wavelet transform, as well as the standard and non-standard formulations for the two-dimensional HWT, are presented. In one paper, wavelet analysis and other statistical tools are employed in order to analyse different aspects of Sicily temperature data. Sicily represents one of the hot spots for studying climate change in the Mediterranean area because of its vulnerability to desertification processes. The authors aim to highlight how wavelet transform can be employed to extract information from experimental results obtained by spectroscopic techniques, such as InfraRed, light and neutron scattering spectroscopies. In particular, this book shows how it is possible to characterize the registered spectral profiles by means of Wavelet Cross Correlation to evaluate spectra and the degree of similarity between images. Later, an iterative à trous coarsening algorithm combined with a wavelet extrapolation procedure is presented and analyzed to filter and identify the mean trend of simulated 1D data with non trivial boundary conditions. Results show that the wavelet extrapolation based algorithm considered for the data-driven analysis is robust and reliable, allowing for an increased confidence region of the wavelet transform. In the concluding chapter, the authors aim to show that the wavelet transform has several advantages and benefits over classical methods of spectral analysis and other approches.

Binding: Softcover
Binding: e-Book

ISBN: 978-1-53613-374-5
ISBN: 978-1-53613-375-2

Price: $95.00
Price: $95.00


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The Analytic Hierarchy Process: Advances in Research and Applications

Editor: Rolando Daniel

Series: Mathematics Research Developments

Publication Date: 2018

Book Description:
In this collection, the authors investigate a variety of hazards that drilling operations may be exposed to. Some may be location dependent and some may be activity-dependent and each can pose a different level of risk. The key elements of the framework to assess risk are: a hierarchy of major contributors to risk in two or more levels; a quantification of primary hazard categories with measurable attributes; a graphical representation of risk to aide distinguishing critical hazards; a layered, filtering approach to remove the less important hazards; and a weighted-score method, which is based on the analytic hierarchy process (AHP) approach. Next, the authors seek to develop a multi-criteria decision-making method for the evaluation of railway restructuring models through reviews of practices, alternatives, and criteria of railway restructuring. The development of the tool was based on the combination of the Analytic Hierarchy Process (AHP) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods. A paper is included which aims to present a new way of stakeholder assessment going beyond standard approaches, such as the Gardner Model and the Salience Model of Mitchell, Agle and Wood. The new approach is based on the Advanced Hierarchy Process (AHP) method. Companies applying the method are placed in a position to design and implement their own stakeholder management without any reference to models presented in the literature. Later, an ICT oriented procurement model resulting from a partial re-engineering of the basic procurement process is proposed. This model was obtained by merging the traditional frameworks buygrid and buying centre to provide a consistent choice of procurement alternatives in a multiplicity of Web solutions. Following this, taking into account the suitability of Analytic Hierarchy Process (AHP) for evaluating electronic services or websites, the authors review on the evaluation experiments on e-government that are using the AHP theory. More specifically, the book presents evaluation experiments that use AHP, fuzzy AHP or their combination with other methods for e-government evaluation. The analytic hierarchy process method is employed in the closing chapter to reduce single parameter error and improve the accuracy of the prediction model, combined with the sensitivity and correlation of the characteristic parameters. The aging index of an actual case is assessed, and it is shown that the model is feasible and effective to provide a reference for optimizing maintenance cycle of polymer insulation in power distribution network.

Binding: Hardcover
Binding: e-Book

ISBN: 978-1-53613-333-2
ISBN: 978-1-53613-334-9

Price: $160.00
Price: $160.00