Series: Advances in Mathematics, Vol. 7
2005, XII, 386 p. 27 illus., Hardcover
ISBN: 0-387-24219-8
The textbook literature on ordered sets is still rather limited.
A lot of the material presented in this book is published for the
first time in a textbook.
Order theory works with combinatorial and set-theoretical
methods, depending on whether the sets under consideration are
finite or infinite. In this book the set-theoretical parts
prevail. The book treats in detail lexicographic products and
their connections with universally ordered sets, and also
provides thorough investigations on the structure of power sets.
Other topics dealt with include dimension theory of ordered sets,
well-quasi-ordered sets, trees, combinatorial set theory for
ordered sets, comparison of order types, and comparability graphs.
Table of contents
Preface.- Fundamental Notions of Set Theory.- Fundamental Notions.-
General Relations Between Posets and Their Chains and Antichains.-
Linearly Ordered Sets.- Products of Orders.- Universally Ordered
Sets.- Applications of the Splitting Method.- The Dimension of
Posets.- Well-Founded Posets, pwo-sets, and Trees.- On the Order
Structure of Power Sets.- Comparison of Order Types.-
Comparability.- Graphs.- References.- Index.- List of Symbols.
Series: Advances in Mathematics, Vol. 8
2005, X, 363 p., Hardcover
ISBN: 0-387-24413-1
About this book
This book is about regularity properties of functional equations.
In the second part of his fifth problem, Hilbert asked,
concerning functional equations, "In how far are the
assertions which we can make in the case of differentiable
functions true under proper modifications without this
assumption?" This book contains, in a unified fashion, most
of the modern results about regularity of non-composite
functional equations with several variables. These results show
that "weak" regularity properties, say measurability or
continuity, of solutions imply that they are in C[infinity], and
hence the equation can be reduced to a differential equation. A
long introduction highlights the basic ideas for beginners.
Several applications are also included.
Table of contents
Preface.- Preliminaries.- Steinhaus type theorems.- Boundedness
and continuity of solutions.- Differentiability and analyticity.-
Regularity theorems on manifolds.- Regularity results with fewer
variables.- Applications.- References.- Index.
Series: Encyclopaedia of Mathematical Sciences, Vol. 135
Volume package: Enc.Mathematical Sciences Invariant Theory
2005, XII, 177 p., Hardcover
ISBN: 3-540-24323-2
About this book
Multiplicative invariant theory, as a research area in its own
right within the wider spectrum of invariant theory, is of
relatively recent vintage. The present text offers a coherent
account of the basic results achieved thus far..
Multiplicative invariant theory is intimately tied to integral
representations of finite groups. Therefore, the field has a
predominantly discrete, algebraic flavor. Geometry, specifically
the theory of algebraic groups, enters through Weyl groups and
their root lattices as well as via character lattices of
algebraic tori.
Throughout the text, numerous explicit examples of multiplicative
invariant algebras and fields are presented, including the
complete list of all multiplicative invariant algebras for
lattices of rank 2.
The book is intended for graduate and postgraduate students as
well as researchers in integral representation theory,
commutative algebra and, mostly, invariant theory.
Table of contents
Series: Mathematics and Its Applications, Vol. 576
2005, X, 238 p., Hardcover
ISBN: 0-387-24505-7
About this book
This book presents the author’s new method of two-stage
maximization of likelihood function, which helps to solve a
series of non-solving before the well-posed and ill-posed
problems of pseudosolution computing systems of linear algebraic
equations (or, in statistical terminology, parameters’
estimators of functional relationships) and linear integral
equations in the presence of deterministic and random errors in
the initial data. This book, for the first time, presents a
solution of the problem of reciprocal influence of passive errors
of regressors and of active errors of predictors by computing
point estimators of functional relationships.
Table of contents
Contents.- General Preface.- Labels and Abbreviations.- Chapter I.
Systems of Linear Algebraic Equations.- Chapter II. Systems of
Linear Algebraic Equations.- Chapter III. Linear Integral
Equations.- References.- Application.- Index.- Glossary of
Symbols.
2005, Approx. 1550 p., Hardcover
ISBN: 0-387-23473-X
Due: May 2005
About this book
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