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Advanced Problem Solving Using Maple (TM): Applied Mathematics,
Operations Research, Business Analytics, and Decision Analysis
applies the mathematical modeling process by formulating, building,
solving, analyzing, and criticizing mathematical models. Scenarios
are developed within the scope of the problem-solving process. The
text focuses on discrete dynamical systems, optimization
techniques, single-variable unconstrained optimization and applied
problems, and numerical search methods. Additional coverage
includes multivariable unconstrained and constrained techniques.
Linear algebra techniques to model and solve problems such as the
Leontief model, and advanced regression techniques including
nonlinear, logistics, and Poisson are covered. Game theory, the
Nash equilibrium, and Nash arbitration are also included. Features:
The text's case studies and student projects involve students with
real-world problem solving Focuses on numerical solution techniques
in dynamical systems, optimization, and numerical analysis The
numerical procedures discussed in the text are algorithmic and
iterative Maple is utilized throughout the text as a tool for
computation and analysis All algorithms are provided with
step-by-step formats About the Authors: William P. Fox is an
emeritus professor in the Department of Defense Analysis at the
Naval Postgraduate School. Currently, he is an adjunct professor,
Department of Mathematics, the College of William and Mary. He
received his PhD at Clemson University and has many publications
and scholarly activities including twenty books and over one
hundred and fifty journal articles. William C. Bauldry, Prof.
Emeritus and Adjunct Research Prof. of Mathematics at Appalachian
State University, received his PhD in Approximation Theory from
Ohio State. He has published many papers on pedagogy and
technology, often using Maple, and has been the PI of several
NSF-funded projects incorporating technology and modeling into math
courses. He currently serves as Associate Director of COMAP's Math
Contest in Modeling (MCM).
Problem Solving is essential to solve real-world problems. Advanced
Problem Solving with Maple: A First Course applies the mathematical
modeling process by formulating, building, solving, analyzing, and
criticizing mathematical models. It is intended for a course
introducing students to mathematical topics they will revisit
within their further studies. The authors present mathematical
modeling and problem-solving topics using Maple as the computer
algebra system for mathematical explorations, as well as obtaining
plots that help readers perform analyses. The book presents cogent
applications that demonstrate an effective use of Maple, provide
discussions of the results obtained using Maple, and stimulate
thought and analysis of additional applications. Highlights: The
book's real-world case studies prepare the student for modeling
applications Bridges the study of topics and applications to
various fields of mathematics, science, and engineering Features a
flexible format and tiered approach offers courses for students at
various levels The book can be used for students with only algebra
or calculus behind them About the authors: Dr. William P. Fox is an
emeritus professor in the Department of Defense Analysis at the
Naval Postgraduate School. Currently, he is an adjunct professor,
Department of Mathematics, the College of William and Mary. He
received his Ph.D. at Clemson University and has many publications
and scholarly activities including twenty books and over one
hundred and fifty journal articles. William C. Bauldry, Prof.
Emeritus and Adjunct Research Prof. of Mathematics at Appalachian
State University, received his PhD in Approximation Theory from
Ohio State. He has published many papers on pedagogy and
technology, often using Maple, and has been the PI of several
NSF-funded projects incorporating technology and modeling into math
courses. He currently serves as Associate Director of COMAP's Math
Contest in Modeling (MCM). *Please note that the Maple package,
"PSM", is now on the public area of the Maple Cloud. To access it:
* From the web: 1. Go to the website https://maple.cloud 2. Click
on "packages" in the left navigation pane 3. Click on "PSM" in the
list of packages. 4. Click the "Download" button to capture the
package. * From Maple: 1. Click on the Maple Cloud icon (far right
in the Maple window toolbar). Or click on the Maple Cloud button on
Maple's Start page to go to the website. 2. Click on the "packages"
in the navigation pane 3. Click on "PSM" in the list of packages.
The package then downloads into Maple directly.
This text presents a wide variety of common types of models found
in other mathematical modeling texts, as well as some new types.
However, the models are presented in a very unique format. A
typical section begins with a general description of the scenario
being modeled. The model is then built using the appropriate
mathematical tools. Then it is implemented and analyzed in Excel
via step-by-step instructions. In the exercises, we ask students to
modify or refine the existing model, analyze it further, or adapt
it to similar scenarios.
Mathematical modeling is a powerful craft that requires practice.
The more practice the better one will become in executing the art.
The authors wrote this book to develop the craft of mathematical
modeling and to foster a desire for lifelong learning, habits of
mind and develop competent and confident problem solvers and
decision makers for the 21st century. This book offers a
problem-solving approach. The authors introduce a problem to help
motivate the learning of a particular mathematical modeling topic.
The problem provides the issue or what is needed to solve using an
appropriate modeling technique. Then principles are applied to the
problem and present the steps in obtaining an appropriate model to
solve the problem. Modeling Change and Uncertainty: Covers both
linear and nonlinear models of discrete dynamical systems.
Introduces statistics and probability modeling. Introduces critical
statistical concepts to handle univariate and multivariate data.
Establishes a foundation in probability modeling. Uses ordinary
differential equations (ODEs) to develop a more robust solution to
problems. Uses linear programming and machine learning to support
decision making. Introduces the reality of uncertainty and
randomness that is all around us. Discusses the use of linear
programing to solve common problems in modern industry. Discusses
he power and limitations of simulations. Introduces the methods and
formulas used in businesses and financial organizations. Introduces
valuable techniques using Excel, MAPLE, and R. Mathematical
modeling offers a framework for decision makers in all fields. This
framework consists of four key components: the formulation process,
the solution process, interpretation of the solution in the context
of the actual problem, and sensitivity analysis. Modeling Change
and Uncertainty will be of interest to mathematics departments
offering advanced mathematical modeling courses focused on decision
making or discrete mathematical modeling and by undergraduate,
graduate students and practitioners looking for an opportunity to
develop, practice, and apply the craft of mathematical modeling.
Table of Contents 1. Perfect Partners: Combining Models of Change
and Uncertainty with Technology 2. Modeling Change: Discrete
Dynamical Systems (DDS) and Modeling Systems of DDS 3. Statistical
and Probabilistic Models 4. Modeling with Probability 5.
Differential Equations 6. Forecasting with Linear Programming and
Machine Learning 7. Stochastic Models and Markov Chains 8. Linear
Programming 9. Simulation of Queueing Models 10. Modeling of
Financial Analysis 11. Reliability Models 12. Machine Learning and
Unconstrained Optimal Process Dr. William P. Fox is currently a
visiting professor of Computational Operations Research at the
College of William and Mary. He is an emeritus professor in the
Department of Defense Analysis at the Naval Postgraduate School and
teaches a three-course sequence in mathematical modeling for
decision making. He received his Ph.D. in Industrial Engineering
from Clemson University. He has taught at the United States
Military Academy for twelve years until retiring and at Francis
Marion University where he was the chair of mathematics for eight
years. He has many publications and scholarly activities including
twenty plus books and one hundred and fifty journal articles.
Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor
in the Defense Analysis Department of the Naval Postgraduate School
(NPS) and the Director of the NPS' Wargaming Center. He holds a
Ph.D. in Operations Research from the Air Force Institute of
Technology. He is a retired logistics Army Colonel with more than
thirty years of military experience in leadership, advanced
analytics, decision modeling, and logistics operations who served
as an Army Operations Research analyst at the Naval Postgraduate
School, TRADOC Analysis Center, United States Military Academy, and
the United States Army Recruiting Command. Other book by William P.
Fox and Robert E. Burks: Advanced Mathematical Modeling with
Technology, 2021, CRC Press. Other books by William P. Fox from CRC
Press: Mathematical Modeling in the Age of the Pandemic, 2021, CRC
Press. Advanced Problem Solving Using Maple: Applied Mathematics,
Operations Research, Business Analytics, and Decision Analysis
(w/William Bauldry), 2020, CRC Press. Mathematical Modeling with
Excel (w/Brian Albright), 2020, CRC Press. Nonlinear Optimization:
Models and Applications, 2020, CRC Press. Advanced Problem Solving
with Maple: A First Course (w/William Bauldry), 2019. CRC Press.
Mathematical Modeling for Business Analytics, 2018, CRC Press.
One cannot watch or read about the news these days without hearing
about the models for COVID-19 or the testing that must occur to
approve vaccines or treatments for the disease. The purpose of
Mathematical Modeling in the Age of a Pandemic is to shed some
light on the meaning and interpretations of many of the types of
models that are or might be used in the presentation of analysis.
Understanding the concepts presented is essential in the entire
modeling process of a pandemic. From the virus itself and its
infectious rates and deaths rates to explain the process for
testing a vaccine or eventually a cure, the author builds,
presents, and shows model testing. This book is an attempt, based
on available data, to add some validity to the models developed and
used, showing how close to reality the models are to predicting
"results" from previous pandemics such as the Spanish flu in 1918
and more recently the Hong Kong flu. Then the author applies those
same models to Italy, New York City, and the United States as a
whole. Modeling is a process. It is essential to understand that
there are many assumptions that go into the modeling of each type
of model. The assumptions influence the interpretation of the
results. Regardless of the modeling approach the results generally
indicate approximately the same results. This book reveals how
these interesting results are obtained.
One cannot watch or read about the news these days without hearing
about the models for COVID-19 or the testing that must occur to
approve vaccines or treatments for the disease. The purpose of
Mathematical Modeling in the Age of a Pandemic is to shed some
light on the meaning and interpretations of many of the types of
models that are or might be used in the presentation of analysis.
Understanding the concepts presented is essential in the entire
modeling process of a pandemic. From the virus itself and its
infectious rates and deaths rates to explain the process for
testing a vaccine or eventually a cure, the author builds,
presents, and shows model testing. This book is an attempt, based
on available data, to add some validity to the models developed and
used, showing how close to reality the models are to predicting
"results" from previous pandemics such as the Spanish flu in 1918
and more recently the Hong Kong flu. Then the author applies those
same models to Italy, New York City, and the United States as a
whole. Modeling is a process. It is essential to understand that
there are many assumptions that go into the modeling of each type
of model. The assumptions influence the interpretation of the
results. Regardless of the modeling approach the results generally
indicate approximately the same results. This book reveals how
these interesting results are obtained.
Mathematical modeling is both a skill and an art and must be
practiced in order to maintain and enhance the ability to use those
skills. Though the topics covered in this book are the typical
topics of most mathematical modeling courses, this book is best
used for individuals or groups who have already taken an
introductory mathematical modeling course. Advanced Mathematical
Modeling with Technology will be of interest to instructors and
students offering courses focused on discrete modeling or modeling
for decision making. Each chapter begins with a problem to motivate
the reader. The problem tells "what" the issue is or problem that
needs to be solved. In each chapter, the authors apply the
principles of mathematical modeling to that problem and present the
steps in obtaining a model. The key focus is the mathematical model
and the technology is presented as a method to solve that model or
perform sensitivity analysis. We have selected , where applicable
to the content because of their wide accessibility. The authors
utilize technology to build, compute, or implement the model and
then analyze the it. Features: MAPLE (c), Excel (c), and R (c) to
support the mathematical modeling process. Excel templates, macros,
and programs are available upon request from authors. Maple
templates and example solution are also available. Includes
coverage of mathematical programming. The power and limitations of
simulations is covered. Introduces multi-attribute decision making
(MADM) and game theory for solving problems. The book provides an
overview to the decision maker of the wide range of applications of
quantitative approaches to aid in the decision making process, and
present a framework for decision making. Table of Contents 1.
Perfect Partners: Mathematical Modeling and Technology 2. Review of
Modeling with Discrete Dynamical Systems and Modeling Systems of
DDS 3. Modeling with Differential Equations 4. Modeling System of
Ordinary Differential Equation 5. Regression and Advanced
Regression Methods and Models 6. Linear, Integer and Mixed Integer
Programming 7. Nonlinear Optimization Methods 8. Multivariable
Optimization 9. Simulation Models 10. Modeling Decision Making with
Multi-Attribute Decision Modeling with Technology 11. Modeling with
Game Theory 12. Appendix Using R Index Biographies Dr. William P.
Fox is currently a visiting professor of Computational Operations
Research at the College of William and Mary. He is an emeritus
professor in the Department of Defense Analysis at the Naval
Postgraduate School and teaches a three-course sequence in
mathematical modeling for decision making. He received his Ph.D. in
Industrial Engineering from Clemson University. He has taught at
the United States Military Academy for twelve years until retiring
and at Francis Marion University where he was the chair of
mathematics for eight years. He has many publications and scholarly
activities including twenty plus books and one hundred and fifty
journal articles. Colonel (R) Robert E. Burks, Jr., Ph.D. is an
Associate Professor in the Defense Analysis Department of the Naval
Postgraduate School (NPS) and the Director of the NPS' Wargaming
Center. He holds a Ph.D. in Operations Research form the Air Force
Institute of Technology. He is a retired logistics Army Colonel
with more than thirty years of military experience in leadership,
advanced analytics, decision modeling, and logistics operations who
served as an Army Operations Research analyst at the Naval
Postgraduate School, TRADOC Analysis Center, United States Military
Academy, and the United States Army Recruiting Command.
Optimization is the act of obtaining the "best" result under given
circumstances. In design, construction, and maintenance of any
engineering system, engineers must make technological and
managerial decisions to minimize either the effort or cost required
or to maximize benefits. There is no single method available for
solving all optimization problems efficiently. Several optimization
methods have been developed for different types of problems. The
optimum-seeking methods are mathematical programming techniques
(specifically, nonlinear programming techniques). Nonlinear
Optimization: Models and Applications presents the concepts in
several ways to foster understanding. Geometric interpretation: is
used to re-enforce the concepts and to foster understanding of the
mathematical procedures. The student sees that many problems can be
analyzed, and approximate solutions found before analytical
solutions techniques are applied. Numerical approximations: early
on, the student is exposed to numerical techniques. These numerical
procedures are algorithmic and iterative. Worksheets are provided
in Excel, MATLAB (R), and Maple (TM) to facilitate the procedure.
Algorithms: all algorithms are provided with a step-by-step format.
Examples follow the summary to illustrate its use and application.
Nonlinear Optimization: Models and Applications: Emphasizes process
and interpretation throughout Presents a general classification of
optimization problems Addresses situations that lead to models
illustrating many types of optimization problems Emphasizes model
formulations Addresses a special class of problems that can be
solved using only elementary calculus Emphasizes model solution and
model sensitivity analysis About the author: William P. Fox is an
emeritus professor in the Department of Defense Analysis at the
Naval Postgraduate School. He received his Ph.D. at Clemson
University and has taught at the United States Military Academy and
at Francis Marion University where he was the chair of mathematics.
He has written many publications, including over 20 books and over
150 journal articles. Currently, he is an adjunct professor in the
Department of Mathematics at the College of William and Mary. He is
the emeritus director of both the High School Mathematical Contest
in Modeling and the Mathematical Contest in Modeling.
examines engineering examples and applications, while also
including social sciences and more examples. presents a course can
be tailored for students at all levels and background. explains
projects and labs to instructors and students to make the course
more interesting for both. Features labs that can be used for group
work, in class, or for self-directed study.
This text presents a wide variety of common types of models found
in other mathematical modeling texts, as well as some new types.
However, the models are presented in a very unique format. A
typical section begins with a general description of the scenario
being modeled. The model is then built using the appropriate
mathematical tools. Then it is implemented and analyzed in Excel
via step-by-step instructions. In the exercises, we ask students to
modify or refine the existing model, analyze it further, or adapt
it to similar scenarios.
Advanced Problem Solving Using Maple (TM): Applied Mathematics,
Operations Research, Business Analytics, and Decision Analysis
applies the mathematical modeling process by formulating, building,
solving, analyzing, and criticizing mathematical models. Scenarios
are developed within the scope of the problem-solving process. The
text focuses on discrete dynamical systems, optimization
techniques, single-variable unconstrained optimization and applied
problems, and numerical search methods. Additional coverage
includes multivariable unconstrained and constrained techniques.
Linear algebra techniques to model and solve problems such as the
Leontief model, and advanced regression techniques including
nonlinear, logistics, and Poisson are covered. Game theory, the
Nash equilibrium, and Nash arbitration are also included. Features:
The text's case studies and student projects involve students with
real-world problem solving Focuses on numerical solution techniques
in dynamical systems, optimization, and numerical analysis The
numerical procedures discussed in the text are algorithmic and
iterative Maple is utilized throughout the text as a tool for
computation and analysis All algorithms are provided with
step-by-step formats About the Authors: William P. Fox is an
emeritus professor in the Department of Defense Analysis at the
Naval Postgraduate School. Currently, he is an adjunct professor,
Department of Mathematics, the College of William and Mary. He
received his PhD at Clemson University and has many publications
and scholarly activities including twenty books and over one
hundred and fifty journal articles. William C. Bauldry, Prof.
Emeritus and Adjunct Research Prof. of Mathematics at Appalachian
State University, received his PhD in Approximation Theory from
Ohio State. He has published many papers on pedagogy and
technology, often using Maple, and has been the PI of several
NSF-funded projects incorporating technology and modeling into math
courses. He currently serves as Associate Director of COMAP's Math
Contest in Modeling (MCM).
Based on many years of applied research, modeling and educating
future decision makers, the authors have selected the critical set
of mathematical modeling skills for decision analysis to include in
this book. The book focuses on the model formulation and modeling
building skills, as well as the technology to support decision
analysis. The authors cover many of the main techniques that have
been incorporated into their three-course sequence in mathematical
modeling for decision making in the Department of Defense Analysis
at the Naval Postgraduate School. The primary objective of this
book is illustrative in nature. It begins with an introduction to
mathematical modeling and a process for formally thinking about
difficult problems, illustrating many scenarios and illustrative
examples. The book incorporates the necessary mathematical
foundations for solving these problems with military applications
and related military processes to reinforce the applied nature of
the mathematical modeling process.
Problem Solving is essential to solve real-world problems. Advanced
Problem Solving with Maple: A First Course applies the mathematical
modeling process by formulating, building, solving, analyzing, and
criticizing mathematical models. It is intended for a course
introducing students to mathematical topics they will revisit
within their further studies. The authors present mathematical
modeling and problem-solving topics using Maple as the computer
algebra system for mathematical explorations, as well as obtaining
plots that help readers perform analyses. The book presents cogent
applications that demonstrate an effective use of Maple, provide
discussions of the results obtained using Maple, and stimulate
thought and analysis of additional applications. Highlights: The
book's real-world case studies prepare the student for modeling
applications Bridges the study of topics and applications to
various fields of mathematics, science, and engineering Features a
flexible format and tiered approach offers courses for students at
various levels The book can be used for students with only algebra
or calculus behind them About the authors: Dr. William P. Fox is an
emeritus professor in the Department of Defense Analysis at the
Naval Postgraduate School. Currently, he is an adjunct professor,
Department of Mathematics, the College of William and Mary. He
received his Ph.D. at Clemson University and has many publications
and scholarly activities including twenty books and over one
hundred and fifty journal articles. William C. Bauldry, Prof.
Emeritus and Adjunct Research Prof. of Mathematics at Appalachian
State University, received his PhD in Approximation Theory from
Ohio State. He has published many papers on pedagogy and
technology, often using Maple, and has been the PI of several
NSF-funded projects incorporating technology and modeling into math
courses. He currently serves as Associate Director of COMAP's Math
Contest in Modeling (MCM). *Please note that the Maple package,
"PSM", is now on the public area of the Maple Cloud. To access it:
* From the web: 1. Go to the website https://maple.cloud 2. Click
on "packages" in the left navigation pane 3. Click on "PSM" in the
list of packages. 4. Click the "Download" button to capture the
package. * From Maple: 1. Click on the Maple Cloud icon (far right
in the Maple window toolbar). Or click on the Maple Cloud button on
Maple's Start page to go to the website. 2. Click on the "packages"
in the navigation pane 3. Click on "PSM" in the list of packages.
The package then downloads into Maple directly.
This textbook and guide focuses on methodologies for bias analysis
in epidemiology and public health, not only providing updates to
the first edition but also further developing methods and adding
new advanced methods. As computational power available to analysts
has improved and epidemiologic problems have become more advanced,
missing data, Bayes, and empirical methods have become more
commonly used. This new edition features updated examples
throughout and adds coverage addressing: Measurement error
pertaining to continuous and polytomous variables Methods
surrounding person-time (rate) data Bias analysis using missing
data, empirical (likelihood), and Bayes methods A unique feature of
this revision is its section on best practices for implementing,
presenting, and interpreting bias analyses. Pedagogically, the text
guides students and professionals through the planning stages of
bias analysis, including the design of validation studies and the
collection of validity data from other sources. Three chapters
present methods for corrections to address selection bias,
uncontrolled confounding, and measurement errors, and subsequent
sections extend these methods to probabilistic bias analysis,
missing data methods, likelihood-based approaches, Bayesian
methods, and best practices.
Bias analysis quantifies the influence of systematic error on an
epidemiology study's estimate of association. The fundamental
methods of bias analysis in epi- miology have been well described
for decades, yet are seldom applied in published presentations of
epidemiologic research. More recent advances in bias analysis, such
as probabilistic bias analysis, appear even more rarely. We suspect
that there are both supply-side and demand-side explanations for
the scarcity of bias analysis. On the demand side, journal
reviewers and editors seldom request that authors address
systematic error aside from listing them as limitations of their
particular study. This listing is often accompanied by explanations
for why the limitations should not pose much concern. On the supply
side, methods for bias analysis receive little attention in most
epidemiology curriculums, are often scattered throughout textbooks
or absent from them altogether, and cannot be implemented easily
using standard statistical computing software. Our objective in
this text is to reduce these supply-side barriers, with the hope
that demand for quantitative bias analysis will follow.
Offering a solid introduction to the entire modeling process, A
FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an
excellent balance of theory and practice, and gives you relevant,
hands-on experience developing and sharpening your modeling skills.
Throughout, the book emphasizes key facets of modeling, including
creative and empirical model construction, model analysis, and
model research, and provides myriad opportunities for practice. The
authors apply a proven six-step problem-solving process to enhance
your problem-solving capabilities -- whatever your level. In
addition, rather than simply emphasizing the calculation step, the
authors first help you learn how to identify problems, construct or
select models, and figure out what data needs to be collected. By
involving you in the mathematical process as early as possible --
beginning with short projects -- this text facilitates your
progressive development and confidence in mathematics and modeling.
Based on many years of applied research, modeling and educating
future decision makers, the authors have selected the critical set
of mathematical modeling skills for decision analysis to include in
this book. The book focuses on the model formulation and modeling
building skills, as well as the technology to support decision
analysis. The authors cover many of the main techniques that have
been incorporated into their three-course sequence in mathematical
modeling for decision making in the Department of Defense Analysis
at the Naval Postgraduate School. The primary objective of this
book is illustrative in nature. It begins with an introduction to
mathematical modeling and a process for formally thinking about
difficult problems, illustrating many scenarios and illustrative
examples. The book incorporates the necessary mathematical
foundations for solving these problems with military applications
and related military processes to reinforce the applied nature of
the mathematical modeling process.
The updated second edition of Cutaneous Manifestations of Infection
in the Immunocompromised Host is an invaluable reference for
physicians and ancillary medical professionals involved in the care
of patients with impaired immune systems due to cancer,
chemotherapy, systemic steroids and other immunosuppressive drugs,
HIV/AIDS or organ transplantation. This volume will help you
recognize skin lesions and diagnose their infectious cause.
Textbook features include: * Over 350 color images demonstrating
pathognomonic, atypical, rare and routine skin lesions * Tables for
differential diagnosis of different skin lesions in the
immunocompromised host * Complete coverage of infectious pathogens
with the patterns of infection and the likely causes in different
clinical settings (HIV/AIDS versus solid organ transplantation
versus neutropenia post-chemotherapy versus bone marrow recovery
post hematopoietic stem cell transplantation ) * New chapter
discussing the role of viruses causing malignancies with cutaneous
signs in the immunocompromised patient Written by dermatologists,
the new edition is an indispensable diagnostic tool intended for
use by all clinicians who care for immunocompromised patients.
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This book contains the papers presented at the Parallel
Computational Fluid Dynamics 1998 Conference.
The book is focused on new developments and applications of
parallel technology. Key topics are introduced through contributed
papers and invited lectures. These include typical algorithmic
developments, such as: distributed computing, domain decomposition
and parallel algorithm. Some of the papers address the evaluations
of software and machine performance and software tool environments.
The application of parallel computers to complex fluid dynamics
problems are also conveyed through sessions such as DNS/LES,
combustion and reacting flows, industrial applications, water
resources and environmental flows.
The editors believe this book will provide many researchers, much
beyond those contributing to this volume, with fresh information
and reference.
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