ISBN: 048645021X
Page Count: 256
Dimensions: 6 1/8 x 9 1/4
Offering classroom-proven results, Differential Topology presents
an introduction to point set topology via a naive version of
nearness space. Its treatment encompasses a general study of
surgery, laying a solid foundation for further study and greatly
simplifying the classification of surfaces. This self-contained
treatment features 88 helpful illustrations. Its subjects include
topological spaces and properties, some advanced calculus,
differentiable manifolds, orientability, submanifolds and an
embedding theorem, and tangent spaces. Additional topics comprise
vector fields and integral curves, surgery, classification of
orientable surfaces, and Whitney's embedding theorem. 1982 ed.
Table of Contents
1. What Is Topology?
2. Topological Spaces
3. Some Topological Properties
4. Some Advanced Calculus
5. Differentiable Manifolds
6. Orientability
7. Submanifolds and an Embedding Theorem
8. Tangent Spaces
9. Critical Points Again
10. Vector Fields and Integral Curves
11. Surgery
12. The Trace of a Surgery
13. Surgery on a Surface
14. Classification of Orientable Surfaces
15. Whitneyfs Embedding Theorem
Appendix A. The Unproved Theorems
Appendix B. Further Topics
Notation
Bibliography
Index
Included in series
Contributions to Economic Analysis, 276
Description
The business cycle has long been the focus of empirical economic
research. Until recently statistical analysis of macroeconomic
fluctuations was dominated by linear time series methods. Over
the past 15 years, however, economists have increasingly applied
tractable parametric nonlinear time series models to business
cycle data; most prominent in this set of models are the classes
of Threshold AutoRegressive (TAR) models, Markov-Switching
AutoRegressive (MSAR) models, and Smooth Transition
AutoRegressive (STAR) models. In doing so, several important
questions have been addressed in the literature, including:
1. Do out-of-sample (point, interval, density, and turning point)
forecasts obtained with nonlinear time series models dominate
those generated with linear models?
2. How should business cycles be dated and measured?
3. What is the response of output and employment to oil-price and
monetary shocks?
4. How does monetary policy respond to asymmetries over the
business cycle?
5. Are business cycles due more to permanent or to transitory
negative shocks?
6. Is the business cycle asymmetric, and does it matter?
Accordingly, we have compiled and edited a book for the Elsevier
economics program comprising 15 original papers on these and
related themes.
Audience
Economists: Academics, Professionals and Students
Contents
Contents: Introduction. 1. Dating business cycle turning points (M.
Chauvet, J.D. Hamilton). 2. Combining predictors & combining
information in modelling: forecasting U.S. recession
probabilities and output growth (M.P. Clements, A.B.C. Galvo). 3.
The importance of nonlinearity in reproducing business cycle
features (J. Morley, J. Piger). 4. The vector floor and ceiling
model (G. Koop, S.M. Potter). 5. A new framework to analyze
business cycle synchronization (M. Camacho, G. Perez-Quiros). 6.
Non-linearity and instability in the EURO area (M. Marcellino). 7.
Nonlinear modelling of autoregressive structural breaks in some
US macroeconomic series (G. Kapetanios, E. Tzavalis). 8. Trend-cycle
decomposition models with smooth - Transition parameters:
Evidence from US economic time series (S.J. Koopman, K.M. Lee, S.Y.
Wong). 9. Modeling inflation and money demand using a fourier-series
approximation (R. Becker, W. Enders, S. Hurn). 10. Random walk
smooth transition autoregressive models (H. Anderson, C.N. Low).
11. Nonlinearity and structural change in interest rate reaction
functions for the U.S., U.K. and Germany (M. Kesriyeli, D.
Osborn, M. Sensier). 12. State asymmetries in the effects of
monetary-policy shocks on output: Some new evidence for the EURO-area
(J.J. Dolado, R.M. Dolores). 13. Non-linear dynamics in output,
real exchange rates and real money balances: Norway, 1830-2003 (Q.F.
Akram, ?. Eitrheim, L. Sarno). 14. A predictive comparison of
some simple long memory and short memory models of daily U.S.
stock returns, with emphasis on business cycle effects (G.
Bhardwaj, N.R. Swanson). 15. Nonlinear modeling of the changing
lag structure in US housing construction (C.M. Dahl, T.
Kulaksizoglu).
Hardbound, ISBN: 0-444-51838-X, 460 pages, publication date: 2006
Summary
When it comes to mathematics, paper isnft just for pen and
pencil any more! Origami, the art and science of paper folding,
can be used to explain concepts and solve problems in mathematics-and
not just in the field of geometry. The origami activities
collected here also relate to topics in calculus, abstract
algebra, discrete mathematics, topology, and more.
Using origami, learn about:
Solving Cubic Equations
Bucky Balls and PHiZZ units
Matrix models for folds
Gaussian Curvature and much more!
These activities, which can enhance the classroom experience,
also make great independent student projects and are perfect for
math clubs or math circles.
Details
ISBN: 1-56881-258-2
Year: 2006
Format: Paperback
Pages: 272
Learn about the boy who
could read and add numbers when he was three years old,
thwarted his teacher by finding a quick and easy way to sum the
numbers 1-100,
attracted the attention of a Duke with his genius,
and became the man whoc
predicted the reappearance of a lost planet,
discovered basic properties of magnetic forces,
invented a surveying tool used by professionals until the
invention of lasers.
Based on extensive research of original and secondary sources,
this historical narrative will inspire young readers and even
curious adults with its touching story of personal achievement.
Details
ISBN: 1-56881-261-2
Year: 2006
Format: Hardcover
Pages: 264
Distributed for the Center for the Study of Language and
Information.
200 p. 6 x 9 Series:
(CSLI-LN) Center for the Study of Language and Information -
Lecture Notes
Cloth 1-57586-509-2 Fall 2005
Paper 1-57586-510-6 Fall 2005
What does it mean to have visual intuition? Can we gain
geometrical knowledge by using visual reasoning? And if we can,
is it because we have a faculty of intuition? In After Euclid,
Jesse Norman reexamines the ancient and long-disregarded concept
of visual reasoning and reasserts its potential as a formidable
tool in our ability to grasp various kinds of geometrical
knowledge. The first detailed philosophical case study of its
kind, this text is essential reading for scholars in the fields
of mathematics and philosophy.
Series: Information Science and Knowledge Management , Vol. 10
2006, XIV, 358 p., Hardcover
ISBN: 1-4020-4112-8
About this book
This book is an extension of the discussions presented in Blairfs
1990 book Language and Representation in Information Retrieval,
which was selected as the "Best Information Science Book of
the Year" by the American Society for Information Science (ASIS).
That work stated that the Philosophy of Language had the best
theory for understanding meaning in language, and within the
Philosophy of Language, the work of philosopher Ludwig
Wittgenstein was found to be most perceptive. The success of that
book provided an incentive to look more deeply into Wittgensteinfs
philosophy of language, and how it can help us to understand how
to represent the intellectual content of information. This is
what the current title does, and by using this theory it creates
a firm foundation for future Information Retrieval research.
The work consists of four related parts. Firstly, a brief
overview of Wittgensteinfs philosophy of language and its
relevance to information systems. Secondly, a detailed
explanation of Wittgensteinfs late philosophy of language and
mind. Thirdly, an extended discussion of the relevance of his
philosophy to understanding some of the problems inherent in
information systems, especially those systems which rely on
retrieval based on some representation of the intellectual
content of that information. And, fourthly, a series of detailed
footnotes which cite the sources of the numerous quotations and
provide some discussion of the related issues that the text
inspires.
Contents
The theory of shadows of 3 and 4-manifolds represents a bridge
between combinatorics of polyhedra and low-dimensional topology.
On one side, it allows a purely combinatorial approach to the
study of smooth 4-manifolds and, on the other side, it indicates
relations between old-standing problems in group theory and
recent topological results on 4-dimensional manifolds.
The present Ph.D. Thesis is devoted to further develop these
connections and to ?nd new applications to low-dimensional
topology. The results proved, for the most part, seem to
strengthen the idea that topology of 3-manifolds can be used as a
guide to study the 4-dimensional case and that polyhedra can be
used as a gbridgeh: in many cases the 4-dimensional results
based on shadows restrict through the theory of spines to results
about 3-dimensional topology and geometry.
On the 3-dimensional side, a new notion of gshadow-complexityh
of 3-manifolds is de?ned.
The study of this complexity clari?es how hyperbolic geometry of
3-manifolds is intimately connected with the combinatorial
structure of the polyhedra used to describe the manifolds.
On the 4-dimensional side, the notion of branched shadow is
introduced in order to study, through a purely combinatorial
approach, differentiable objects as Spinc and almost complex
structures on smooth 4 manifolds.
Combinatorial suf?cient conditions based on these objects are
proved assuring that grefinedh structures on 4-manifolds
exist such as integrable complex structures and Stein domain
structures.
Francesco Costantino, Shadows and branched shadows of 3 and 4-manifolds,
Pisa, Edizioni della Normale 2005, pp. XX-208, ISBN 88-7642-154-8,
This volume deals with the regularity theory for elliptic
systems. We may find the origin of such a theory in two of the
problems posed by David Hilbert in his celebrated lecture
delivered on the occasion of the International Congress of
Mathematicians in 1900 in Paris:
- 19th problem: are the solutions to regular problems in the
Calculus of Variations always necessarily analytic?
- 20th problem: does any variational problem have a solution,
provided that certain assumptions regarding the given boundary
conditions are satisfied, and provided that the notion of a
solution is suitably extended?
During the last century these two problems have generated a great
deal of work, usually referred to as is in regularity theory,
which makes this topic quite relevant in many fields and still
very active for research.
However, the purpose of this volume, addressed mainly to
students, is much more limited. We aim to illustrate only some of
the basic ideas and techniques introduced in this context,
confining ourselves to important but simple situations and
refraining from completeness. In fact some relevant topics are
omitted.
Topics include: harmonic functions, direct methods, Hilbert space
methods and Sobolev spaces, energy estimates, Schauder and Lp-theory
both with and without potential theory, including the Calderon
Zygmund theorem, Harnackfs and De Giorgi-Moser-Nash theorems in
the scalar case and partial regularity theorems in the vector
valued case; finally, harmonic maps and minimal graphs in
codimension 1 and greater than 1.
Mariano Giaquinta, Luca Martinazzi, An introduction to the
regularity theory for elliptic systems, harmonic maps and minimal
graphs, Pisa, Edizioni della Normale 2005, pp. 300, ISBN 88-7642-168-8