2006, XII, 206 p. 70 illus., Softcover
ISBN: 0-8176-4384-2
About this textbook
The study of curves and surfaces forms an important part of
classical differential geometry. Differential Geometry of Curves
and Surfaces: A Concise Guide presents traditional material in
this field along with important ideas of Riemannian geometry. The
reader is introduced to curves, then to surfaces, and finally to
more complex topics. Standard theoretical material is combined
with more difficult theorems and complex problems, while
maintaining a clear distinction between the two levels.
Table of contents
Chapter 1 Curves in a 3-dimensional Euclidean space and in the
plane: Preliminaries.- Definition and methods of curves
presentation.- Tangent line and an osculating plane.- Length of a
curve.- Problems: plane convex curves.- Curvature of a curve.-
Problems: curvature of plance curves.- Torsion of a curve.-
Frenet formulas and the natural equation of a curve.- Problems:
space curves- Phase length of a curve and Fenchel-Reshetnyak
inequality.- Exercises Chapter 2 Extrinsic geometry of surfaces
in a 3-dimensional Euclidean space.- Definition and methods of
generating surfaces.- Tangent plane.- First fundamental form of a
surface.- Second fundamental form of a surface.- The third
fundamental form of a surface.- Classes of surfaces.- Some
classes of curves on a surface.- The main equations of the
surfaces theory.- Appendix: Indicatrix of a surface of revolution.-
Exercises Chapter 3 Intrinsic geometry of surfaces.- Introducing
notions.-Covariant derivative of a vector field.- Parallel
translation of a vector along a curve on a surface.- Geodesics.-
Shortest paths and geodesics.- Special coordinate system.- Gauss-Bonet
theorem and comparison theorem for the angles of a triangle.-
Local comparison theorems for triangle.- Alexandrov comparison
theorem for the angles of a triangle.- Problems.- Bibliography.-
Index
Series: Probability and its Applications
2006, X, 328 p., Hardcover
ISBN: 0-8176-4215-3
About this textbook
This text offers a mathematically rigorous exposition of the
basic theory of marked point processes developing randomly over
time, and shows how this theory may be used to treat piecewise
deterministic stochastic processes in continuous time.
The focus is on point processes that generate only finitely many
points in finite time intervals, resulting in piecewise
deterministic processes with "few jumps". The point
processes are constructed from scratch with detailed proofs and
their distributions characterized using compensating measures and
martingale structures. Piecewise deterministic processes are
defined and identified with certain marked point processes, which
are then used in particular to construct and study a large class
of piecewise deterministic Markov processes, whether time
homogeneous or not.
The second part of the book addresses applications of the just
developed theory. This analysis of various models in applied
statistics and probability includes examples and exercises in
survival analysis, branching processes, ruin probabilities,
sports (soccer), finance and risk management (arbitrage and
portfolio trading strategies), and queueing theory.
Table of contents
* Preface
Part I: Theory
* Introduction
* Simple and Marked Point Processes
* Construction of SPPs and MPPs
* Compensators and Mrtingales
* Likelihood Processes
* Independence
* Piecewise Deterministic Markov Processes (PDMPs)
Part II: Applications
* Survival Analysis
* Branching, Ruin, Soccer
* A Model from Finance
* Examples of Queueing Models
Part III: Appendices
* Appendix A: Differentiation of Cadlag Functions
* Appendix B: Filtrations, Processes, Martingales
* Bibliographical Notes
* References
* Notation Index
* Index
2005, XII, 382 p., Softcover
ISBN: 0-387-26127-3
About this book
This book contains 116 exercises of sampling methods solved in
detail. The exercises are grouped into chapters and are preceded
by a brief theoretical review specifying the notation and the
principal results that are useful for understanding the solutions.
Some exercises develop the theoretical aspects of surveys, while
others deal with more applied problems.
Intended for instructors, graduate students and survey
practitioners, this book addresses in a lively and progressive
way the techniques of sampling, the use of estimators and the
methods of appropriate calibration, and the understanding of
problems pertaining to non-response.
Table of contents
Series: Discrete Mathematics and Its Applications Volume: 37
ISBN: 1584884568
Publication Date: 12/9/2005
Number of Pages: 368
Contains over 100 exercises to facilitate comprehension
Presents a proof of Szemeredi's theorem
Discusses how the modern theory of modular forms complements the
classical fundamental results
Includes applications to fields such as cryptography,
crystallography, and thermal radiation
Sums of Squares of Integers covers topics in combinatorial number
theory as they relate to counting representations of integers as
sums of a certain number of squares. The book introduces a
stimulating area of number theory where research continues to
proliferate. It is a book of "firsts" - namely it is
the first book to combine Liouville's elementary methods with the
analytic methods of modular functions to study the representation
of integers as sums of squares. It is the first book to tell how
to compute the number of representations of an integer n as the
sum of s squares of integers for any s and n. It is also the
first book to give a proof of Szemeredi's theorem, and is the
first number theory book to discuss how the modern theory of
modular forms complements and clarifies the classical fundamental
results about sums of squares.
The book presents several existing, yet still interesting and
instructive, examples of modular forms. Two chapters develop
useful properties of the Bernoulli numbers and illustrate
arithmetic progressions, proving the theorems of van der Waerden,
Roth, and Szemeredi. The book also explains applications of the
theory to three problems that lie outside of number theory in the
areas of cryptanalysis, microwave radiation, and diamond cutting.
The text is complemented by the inclusion of over one hundred
exercises to test the reader's understanding.
Table of contents
Series: Biostatistics Volume: 14
ISBN: 0824754697
Publication Date: 9/28/2005
Number of Pages: 504
Provides updated material in every chapter to reflect the massive
growth and change over the past decade
Includes new chapters on topics such as testosterone replacement
therapy trials and active-controlled equivalence trials
Addresses the most current and emerging statistical issues
involved in HIV/AIDS research and anti-cancer trials
Presents a global view of pharmaceutical development in pertinent
chapters by authors from ICH major global regions
The growth of the pharmaceutical industry over the past decade is
astounding, but the impact of this growth on statistics is
somewhat confusing. While software has made analysis easier and
more efficient, regulatory bodies now demand deeper and more
complex analyses, and pharmacogenetic/genomic studies serve up an
entirely new set of challenges. For more than two decades,
Statistics in the Pharmaceutical Industry has been the definitive
guide to sorting through the challenges in the industry, and this
Third Edition continues that tradition.
Updated and expanded to reflect the most recent trends and
developments in the field, Statistics in the Pharmaceutical
Industry, Third Edition presents chapters written by experts from
both regulatory agencies and pharmaceutical companies who discuss
everything from experimental design to post-marketing studies.
This approach sheds light on what regulators consider acceptable
methodologies and what methods have proven successful for
industrial statisticians. Both new and revised chapters reflect
the increasingly global nature of the industry as represented by
authors from Japan and Europe, the increasing trend toward non-inferiority/equivalence
testing, adaptive design in clinical trials, global harmonization
of regulatory standards, and multiple comparison studies. The
book also examines the latest considerations in anti-cancer
studies.
Statistics in the Pharmaceutical Industry, Third Edition
demystifies the approval process by combining regulatory and
industrial points of view, making it a must-read for anyone
performing statistical analysis at any point in the drug approval
process.
Table of contents