ISBN: 0-471-72070-4
Hardcover
504 pages
November 2005
Partial Differential Equations and the Finite Element Method
provides a much-needed, clear, and systematic introduction to
modern theory of partial differential equations (PDEs) and finite
element methods (FEM). Both nodal and hierachic concepts of the
FEM are examined. Reflecting the growing complexity and
multiscale nature of current engineering and scientific problems,
the author emphasizes higher-order finite element methods such as
the spectral or hp-FEM.
A solid introduction to the theory of PDEs and FEM contained in
Chapters 1?4 serves as the core and foundation of the publication.
Chapter 5 is devoted to modern higher-order methods for the
numerical solution of ordinary differential equations (ODEs) that
arise in the semidiscretization of time-dependent PDEs by the
Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs
rooted in the bending of elastic beams and plates and
approximates their solution by means of higher-order Hermite and
Argyris elements. Finally, Chapter 7 introduces the reader to
various PDEs governing computational electromagnetics and
describes their finite element approximation, including modern
higher-order edge elements for Maxwell's equations.
The understanding of many theoretical and practical aspects of
both PDEs and FEM requires a solid knowledge of linear algebra
and elementary functional analysis, such as functions and linear
operators in the Lebesgue, Hilbert, and Sobolev spaces. These
topics are discussed with the help of many illustrative examples
in Appendix A, which is provided as a service for those readers
who need to gain the necessary background or require a refresher
tutorial. Appendix B presents several finite element computations
rooted in practical engineering problems and demonstrates the
benefits of using higher-order FEM.
Numerous finite element algorithms are written out in detail
alongside implementation discussions. Exercises, including many
that involve programming the FEM, are designed to assist the
reader in solving typical problems in engineering and science.
Specifically designed as a coursebook, this student-tested
publication is geared to upper-level undergraduates and graduate
students in all disciplines of computational engineeringand
science. It is also a practical problem-solving reference for
researchers, engineers, and physicists.
Table of Contents
ISBN: 0-471-74583-9
Hardcover
568 pages
November 2005
An easy-to-grasp introduction to nonparametric regression
This book's straightforward, step-by-step approach provides an
excellent introduction to the field for novices of nonparametric
regression. Introduction to Nonparametric Regression clearly
explains the basic concepts underlying nonparametric regression
and features:
Thorough explanations of various techniques, which avoid complex
mathematics and excessive abstract theory to help readers
intuitively grasp the value of nonparametric regression methods
Statistical techniques accompanied by clear numerical examples
that further assist readers in developing and implementing their
own solutions
Mathematical equations that are accompanied by a clear
explanation of how the equation was derived
The first chapter leads with a compelling argument for studying
nonparametric regression and sets the stage for more advanced
discussions. In addition to covering standard topics, such as
kernel and spline methods, the book provides in-depth coverage of
the smoothing of histograms, a topic generally not covered in
comparable texts.
With a learning-by-doing approach, each topical chapter includes
thorough S-PlusR examples that allow readers to duplicate the
same results described in the chapter. A separate appendix is
devoted to the conversion of S-Plus objects to R objects. In
addition, each chapter ends with a set of problems that test
readers' grasp of key concepts and techniques and also prepares
them for more advanced topics.
This book is recommended as a textbook for undergraduate and
graduate courses in nonparametric regression. Only a basic
knowledge of linear algebra and statistics is required. In
addition, this is an excellent resource for researchers and
engineers in such fields as pattern recognition, speech
understanding, and data mining. Practitioners who rely on
nonparametric regression for analyzing data in the physical,
biological, and social sciences, as well as in finance and
economics, will find this an unparalleled resource.
Table of Contents
ISBN: 0-471-45592-X
Hardcover
302 pages
December 2005
This volume represents a comprehensive treatment of a model
sometimes referred to as latent curve or growth curve models.
Latent Curve Models analyzes LTMs from the perspective of
structural equation modeling (SEM) with latent variables.
Although the authors discuss simple regression-based procedures
that are helpful in the early stages of LTM, most of the
presentation will use SEMs as a driving tool throughout the text.
Table of Contents
PART ONE: INTRODUCTION.
1. Introduction.
2. The Conceptualization and Analysis of Trajectories.
3. Three Initial Questions About Trajectories.
4. A Brief History of Latent Curve Models.
5. Organization of the Remainder of the Book.
PART TWO: UNCONDITIONAL LATENT CURVE MODEL.
1. Introduction.
2. Repeated Measures.
3. General Model and Assumptions.
4. Identification.
5. Case-By-Case Approach.
6. Structural Equation Model (SEM) Approach.
7. Alternative Approaches to the Sem.
8. Conclusions.
9. Appendix: Test Statistics, Nonnormality, and Statistical Power.
PART THREE: MISSING DATA AND ALTERNATIVE METRICS OF TIME.
1. Missing Data.
2. Missing Data and Alternative Metrics of Time.
3. Conclusions.
PART FOUR: NONLINEAR TRAJECTORIES AND THE CODING OF TIME.
1. Modeling Nonlinear Functions of Time.
2. Nonlinear Curve Fitting: Estimated Factor Loadings.
3. Piecewise Linear Trajectory Models.
4. Alternative Parametric Functions.
5. Linear Transformations of the Metric of Time.
6. Conclusion.
7. Appendix : Identification of Quadratic and Piecewise Latent
Curve Models.
PART FIVE: CONDITIONAL LATENT CURVE MODELS.
1. Conditional Model and Assumptions.
2. Identification.
3. Structural Equation Modeling Approach.
4. Interpretation of Conditional Model Estimates.
5. Empirical Example.
6. Conclusion.
PART SIX: THE ANALYSIS OF GROUPS.
1. Dummy Variable Approach.
2. Multiple Group Analysis.
3. Unknown Group Member.
4. Conclusion.
5. Appendix: Case-by-Case Approach to Analysis of Different
Groups.
PART SEVEN: MULTIVARIATE LATENT CURVE MODELS.
1. Time-Invariant Covariates.
2. Time-Varying Covariates.
3. Simultaneous Inclusion of Time-Invariant & Time-Varying
Covariates.
4. Multivariate Latent Curve Models.
5. Autoregressive Latent Trajectory (ALT) Model.
6. General Equation for All Models.
7. Implied Moment Matrices.
8. Conclusion.
ISBN: 0-470-01689-2
Hardcover
424 pages
February 2006
The book is an introduction to actuarial mathematics and will
cover the material on the modeling examinations of the Society of
Actuaries and the Casualty Actuarial Society (SOA exam M and CSA
exam 3). The text is unique with heavy emphasis on the
deterministic methods and combines interest theory and life
contingencies in a unified manner. It included a complete
treatment of multiple decrement theory: first covering the basic
ideas in the deterministic case in the associated single
decrement tables, and later returning to discuss multiple
decrement theory when dealing with the stochastic model.
Fractional durations are covered by beginning with a strictly
annual model, and introducing premium and reserve calculations in
that framework and then covering the fractional duration
consideration in a separate chapter.
Basic introduction to actuarial mathematics.
Covers all the material on the modeling examinations of the
Society of Actuaries and the Casualty Actuarial Society (SOA exam
M and CSA exam 3).
Takes a deterministic approach to allow the student to master new
concepts and notation in as simple a setting as possible.
Includes modern methods and computational techniques such as
Martingale stochastic processes and spreadsheets.
Written by a well-respected academic with extensive teaching
experience.
Includes exercises and solutions, enabling use for self-study or
as a course text
Supported by a Website featuring full solutions to exercises,
further examples, Excel spreadsheets.
Table of Contents
Series: Fundamental Theories of Physics, Vol. 148
2005, Approx. 455 p., Hardcover
ISBN: 1-4020-4003-2
Due: November 2005
About this book
A main theme of the book outlines the role of the quantum
potential in quantum mechanics and general relativity and one of
its origins via fluctuations formulated in terms of Fisher
information. Another theme is the description of various
approaches to Bohmian mechanics and their role in quantum
mechanics and general relativity. Along the way various
approaches to, for instance, the Dirac equation, the Einstein
equations, the Klein-Gordon equation, the Maxwell equations and
the Schrodinger equations are described. Statistics and geometry
are intertwined in various ways and, among other matters, the
aether, cosmology, entropy, fractals, quantum Kaehler geometry,
the vacuum and the zero point field are discussed. There is also
some speculative material and some original work along with
material extracted from over 1000 references and the work is
current up to April 2005.
Table of contents
Preface. 1: The Schrodinger Equation. 1.1. Diffusion and
Stochastic Processes. 1.2. Scale Relativity. 1.3. Remarks on
Fractal Spacetime. 1.3.1. Comments on cantor Sets. 1.3.2.
Comments on Hydrodynamics. 1.4. Remarks on Fractal Calculus. 1.5.
A Bohmian Approach to Quantum Fractals. 2: DeBroglie-Bohm in
Various Contexts. 2.1. The Klein-Gordon and Dirac Equations. 2.1.1.
Electromagnetism and the Dirac Equations. 2.2. Bertoldi-Faraggi-Matone
Theory. 2.3. Field Theory Models. 2.3.1. Emergence of Particles.
2.3.2. Bosonic Bohmian Theory. 2.3.3. Fermionic Theory. 2.4.
DeDonder, Weyl and Bohm. 2.5. QFT and Stochastic Jumps. 2.6.
Bohmian Mechanics in QFT. 3: Gravity and the Quantum Potential. 3.1.
Introduction. 3.2. Sketch of DeBroglie-Bohm-Weyl Theory. 3.2.1.
Dirac-Weyl Action. 3.2.2. Remarks on Conformal Gravity. 3.3. The
Schrodinger Equation in Weyl Space. 3.3.1. Fisher Information
Revisited. 3.3.2. The KG Equation. 3.4. Scale relativity and KG.
3.5. Quantum Measurement and Geometry. 3.5.1. Measurement on a
Biconformal Space. 4: Geometry and Cosmology. 4.1. Dirac-Weyl
Geometry. 4.2. Remarks on Cosmology. 4.3. WDW Equation. 4.3.1.
Constraints in Ashtekar Variables. 4.4. Remarks on Regularization.
4.5. Pilot Wave Cosmology. 4.5.1. Euclidan Quantum Gravity. 4.6.
Bohm and Noncommutative Geometry. 4.7. Exact Uncertainty and
Gravity. 5: Fluctuations and Geometry. 5.1. The Zero Point Field.
5.1.1. Remarks on the Aether and Vacuum. 5.1.2. A Version of the
Dirac Aether. 5.1.3. Massless Particles. 5.1.4. Einstein Aether
Waves. 5.2. Stochastic Electrodynamics. 5.3. Photons and EM. 5.4.
Quantum Geometry. 5.4.1. Probability Aspects. 6: Information and
Entropy. 6.1. The Dynamics of Uncertainty. 6.1.1. Informaion
Dynamics. 6.1.2. Information Measures for QM. 6.1.3. Phase
Transitions. 6.1.4. Fisher Information and Hamilton’s Equations.
6.1.5. Uncertainty and Fluctuations. 6.2. A Touch of Chaos. 6.2.1.
Chaos and the Quantum Potential. 6.3. Generalized
Thermostatistics. 6.3.1. Nonextensive Statistical Thermodynamics.
6.4. Fisher Physics. 6.4.1. Legendre Thermodynamics. 6.4.2. First
and Second Laws. 7: On the Quantum Potential. 7.1. Resume. 7.1.1.
The Schrodinger Equation. 7.1.2. DeBroglie-Bohm. 7.1.3. Geometry,
Gravity, and QM. 7.1.4. Geometric Phases. 7.1.5. Entropy and
Chaos. 7.2. Hydrodynamics and Geometry. 7.2.1. Particle and wave
Pictures. 7.2.2. Electromagnetism and the SE. 7.3. Some
Speculations on the Aether. 7.3.1. Discussion of a Putative PSI
Aether. 7.4. Remarks on Trajectories. 8: Remarks on QFT and Tau
Functions. 8.1. Introduction and Background. 8.1.1. Wick’s
Theorem and Renormalization. 8.1.2. Products and Relations to
Physics. 8.2. Quantum Fields and Quantum Groups. 8.3.
Renormalization and Algebra. 8.3.1. Various Algebras. 8.4. Tau
Function and Free Fermions. 8.4.1. Symmetric Functions. 8.4.2.
PSDO on a Circle. 8.5. Intertwining. 8.6. Vertex Operators and
Symmetric Functions.