Series: Springer Texts in Statistics,
2005, XIII, 221 p. 59 illus., Hardcover
ISBN: 1-85233-882-2
About this textbook
Most data sets collected by researchers are multivariate, and in
the majority of cases the variables need to be examined
simultaneously to get the most informative results. This requires
the use of one or other of the many methods of multivariate
analysis, and the use of a suitable software package such as S-PLUS
or R.
In this book the core multivariate methodology is covered along
with some basic theory for each method described. The necessary R
and S-PLUS code is given for each analysis in the book, with any
differences between the two highlighted.
Graduate students, and advanced undergraduates on applied
statistics courses, especially those in the social sciences, will
find this book invaluable in their work, and it will also be
useful to researchers outside of statistics who need to deal with
the complexities of multivariate data in their work.
Table of contents
Multivariate Data and Multivariate Analysis.- Looking at
Multivariate Data.- Principal Components Analysis.- Exploratory
Factor Analysis.- Multidimensional Scaling and Correspondence
Analysis.- Cluster Analysis.- Grouped Multivariate Data:
Multivariate Analysis of Variance and Discriminant Function
Analysis.- Multiple Regression and Canonical Correlation.- The
Analysis of Repeated Measures Data.- Appendix.
Series: Advances in Complex Analysis and Its Applications, Vol.
4
2005, XVI, 196 p. 4 illus., Hardcover
ISBN: 0-387-23625-2
About this book
This is a unique book related to the theory of functions of a-bounded
type in the half-plane of the complex plane, which is constructed
by application of the Liouville integro-differential operator.
In addition, the book contains improvements of several results
such as the Phragmen-Lindelof Principle and Nevanlinna
Factorization in the Half-Plane, and offers a new, equivalent
definition of the classical Hardy spaces in the half-plane.
The last chapter of the book presents an application of the
constructed theory as well as M.M.Djrbashianfs theory of
Nevanlinna type classes in the disc in the spectral theory of
linear operators. This is a solution of a problem repeatedly
stated by M.G.Krein and being of special interest for a long time.
Table of contents
Preface.- Intro.- The Liouville Operator.- Blaschke Type Products.-
Equilibrium Relations and Factorization.- Meromorphic Functions.-
Boundary Values.- Uniform Approximations.- Subharmonic Functions.-
Weighted Classes of Subharmonic Functions.- Functions of a-Bounded
Type in Spectral Theory.- References.- Index.
Series: Lecture Notes in Mathematics, Vol. 1862
2005, X, 209 p., Softcover
ISBN: 3-540-24200-7
About this book
There has recently been a renewal of interest in Fokker-Planck
operators, motivated by problems in statistical physics, in
kinetic equations, and differential geometry. Compared to more
standard problems in the spectral theory of partial differential
operators, those operators are not self-adjoint and only
hypoelliptic. The aim of the analysis is to give, as generally as
possible, an accurate qualitative and quantitative description of
the exponential return to the thermodynamical equilibrium. While
exploring and improving recent results in this direction, this
volume proposes a review of known techniques on: the
hypoellipticity of polynomial of vector fields and its global
counterpart, the global Weyl-Hormander pseudo-differential
calculus, the spectral theory of non-self-adjoint operators, the
semi-classical analysis of Schrodinger-type operators, the Witten
complexes, and the Morse inequalities.
Table of contents
Series: Lecture Notes in Mathematics, Vol. 1863
2005, X, 193 p., Softcover
ISBN: 3-540-24259-7
About this book
This volume contains a systematic discussion of wavelet-type
inversion formulae based on group representations, and their
close connection to the Plancherel formula for locally compact
groups. The connection is demonstrated by the discussion of a toy
example, and then employed for two purposes: Mathematically, it
serves as a powerful tool, yielding existence results and
criteria for inversion formulae which generalize many of the
known results. Moreover, the connection provides the starting
point for a ? reasonably self-contained ? exposition of
Plancherel theory. Therefore, the volume can also be read as a
problem-driven introduction to the Plancherel formula.
Table of contents
Series: Lecture Notes in Mathematics, Vol. 1864
2005, IX, 149 p., Softcover
ISBN: 3-540-24316-X
About this book
Modern notions and important tools of classical mechanics are
used in the study of concrete examples that model physically
significant molecular and atomic systems. The parametric nature
of these examples leads naturally to the study of the major
qualitative changes of such systems (metamorphoses) as the
parameters are varied. The symmetries of these systems, discrete
or continuous, exact or approximate, are used to simplify the
problem through a number of mathematical tools and techniques
like normalization and reduction. The book moves gradually from
finding relative equilibria using symmetry, to the Hamiltonian
Hopf bifurcation and its relation to monodromy and, finally, to
generalizations of monodromy.
Table of contents
2005, Approx. 140 p., Hardcover
ISBN: 1-85233-916-0
About this book
Wavelets are mathematical functions that divide data into
different frequency components, and then study each component
with a resolution matched to its scale.
First generation wavelets have proved useful in many applications
in engineering and computer science. However they cannot be used
with non-linear, data-adaptive decompositions and non-equispaced
data
Second Generation Wavelets and their Applications introduces
"second generation wavelets" and the lifting transform
that can be used to apply the traditional benefits of wavelets
into a wide range of new areas in signal processing, data
processing and computer graphics.
This book details the mathematical fundamentals of the lifting
transform and illustrates the latest applications of the
transform in signal and image processing, numerical analysis,
scattering data smoothing and rendering of computer images.
Table of contents
The classical wavelet transform for continous time and discrete
time signals - second generation wavelets - nonlinear and
adaptive lifting - numerical condition - applications of
nonlinear lifting in imaging