2003XII, 351 p. Softcover
0-387-95470-8
This volume will deal with the constructions
of block designs.
Tadeusz Calin'ski taught statistics, biometry
and experimental
design at the Agricultural University of
Poznan' from 1953 to
1988. He obtained the title of Professor
of Natural Sciences in
1974. He was head of the Department of Mathematical
and
Statistical Methods from 1968 to 1984 and
is now Professor
Emeritus. In 1998 Professor Calin'ski was
awarded the doctoral
Degree honoris causa by the Agricultural
University of Poznan'.
He has published over 140 articles in scientific
journals. He has
served on the editorial boards of the Journal
of Statistical
Planning and Inference, Biometrics, and several
Polish scientific
journals. Sanpei Kageyama has been Professor
of Statistics and
Discrete Mathematics in the Department of
Mathematics, Hiroshima
University, Japan, since 1992. He has published
over 240 articles
in scientific journals. Professor Kageyama
is a Foundation Fellow
of the Institute of Combinatorics and its
Applications, and a
council member of the Mathematical Society
of Japan. He has
served on the editorial boards of the Journal
of Japan
Statistical Society, Utilitas Mathematics,
and the Journal of
Statistical Planning and Inference.
Contents: Constructional Approaches and Methods.-
Designs with
Full Efficiency for Some Contrasts.- Designs
with No Full
Efficiency.- Resolvable Designs.- Special
Designs.
Series: Lecture Notes in Statistics. Volume.
170
2002IX,197 Softcover
3-540-44196-4
This self-contained monograph is the first
to feature the
intersection of the structure theory of noncommutative
associative algebras and the algorithmic
aspect of Groebner basis
theory. A double filtered-graded transfer
of data in using
noncommutative Groebner bases leads to effective
exploitation of
the solutions to several structural-computational
problems, e.g.,
an algorithmic recognition of quadric solvable
polynomial
algebras, computation of GK-dimension and
multiplicity for
modules, and elimination of variables in
noncommutative setting.
All topics included deal with algebras of
(q-)differential
operators as well as some other operator
algebras, enveloping
algebras of Lie algebras, typical quantum
algebras, and many of
their deformations.
Keywords: Filtered ring, Gradedring, Groebner
basis, Monomial
ordering, Solvable polynomial algebra
Contents: Introduction.- Chapter I: Basic
Structural Tricks and
Examples.- Chapter II: Grobner Bases in Associative
Algebras.-
Chapter III: Grobner Bases and Basic Algebraic-Algorithmic
Structures.- Chapter IV: Filtered-Graded
Transfer of Grobner
Bases.- Chapter V: GK-dimension of Modules
over Quadric Solvable
Polynomial Algebras and Elimination of Variables.-
Chapter VI:
Multiplicity Computation of Modules over
Quadric Solvable
Polynomial Algebras.- Chapter VII: (partial-)Holonomic
Modules
and Functions over Quadric Solvable Polynomial
Algebras.- Chapter
VII: Regularity and Ko-group of Quadric Solvable
Polynomial
Algebras.- References.- Index.
Series: Lecture Notes in Mathematics. Volume.
1795
2003XIV, 332 p. Softcover
3-540-44201-4
Many partial differential equations arising
in practice are
parameter-dependent problems that are of
singularly perturbed
type. Prominent examples include plate and
shell models for small
thickness in solid mechanics, convection-diffusion
problems in
fluid mechanics, and equations arising in
semi-conductor device
modelling. Common features of these problems
are layers and, in
the case of non-smooth geometries, corner
singularities. Mesh
design principles for the efficient approximation
of both
features by the hp-version of the finite
element method (hp-FEM)
are proposed in this volume. For a class
of singularly perturbed
problems on polygonal domains, robust exponential
convergence of
the hp-FEM based on these mesh design principles
is established
rigorously.
Keywords: FEM, Finite element method, elliptic
regularity, high
order method, non-smooth domains, singular
perturbation, spectral
method
Contents: 1.Introduction.- Part I: Finite
Element Approximation.-
2. hp-FEM for Reaction Diffusion Problems:
Principal Results.- 3.
hp Approximation.- Part II: Regularity in
Countably Normed Spaces.-
4. The Countably Normed Spaces blb, epsilon.-
5. Regularity
Theory in Countably Normed Spaces.- Part
III: Regularity in Terms
of Asymptotic Expansions.- 6. Exponentially
Weighted Countably
Normed Spaces.- Appendix.- References.- Index.
Series: Lecture Notes in Mathematics. Volume.
1796
2003Approx. 265 pp. Hardcover
0-387-95520-8
This book provides a systematic and comprehensive
account of
asymptotic sets and functions from which
a broad and useful
theory emerges in the areas of optimization
and variational
inequalities. Mainly it is concerned with
the existence of
solutions of a given problem in these classes,
whenever for
example standard compacity hypothesis is
not present. Thus it
addresses the central problem of handling
unbounded situations.
This book will be useful to advanced graduate
students,
researchers, and practitioners in the fields
of optimization
theory, nonlinear programming, and applied
mathematical sciences.
Keywords: asymptotic cones, asymptotic functions,
asymptotic
sets, nonlinear programming, optimization,
optimization theory
Contents: Convex Analysis and Set Valued
Maps: A Review.-
Asymptotic Cones and Functions.- Existence
and Stability in
Optimization Problems.- Minimizing and Stationary
Sequences.-
Duality in Optimization Problems.- Maximal
Monotone Maps and
Variational Inequalities.
Series: Springer Monographs in Mathematics.
2003Approx. 330 p. Hardcover
3-540-43403-8
In modern financial practice, asset prices
are modelled by means
of stochastic processes, and continuous-time
stochastic calculus
thus plays a central role in financial modelling.
This approach
has its roots in the foundational work of
the Nobel laureates
Black, Scholes and Merton. Asset prices are
further assumed to be
rationalizable, that is, determined by equality
of demand and
supply on some market. This approach has
its roots in the
foundational work on General Equilibrium
of the Nobel laureates
Arrow and Debreu and in the work of McKenzie.
This book has four
parts. The first brings together a number
of results from
discrete-time models. The second develops
stochastic continuous-time
models for the valuation of financial assets
(the Black-Scholes
formula and its extensions), for optimal
portfolio and
consumption choice, and for obtaining the
yield curve and pricing
interest rate products. The third part recalls
some concepts and
results of general equilibrium theory, and
applies this in
financial markets. The last part is more
advanced and tackles
market incompleteness and the valuation of
exotic options in a
complete market.
Keywords: complete and incomplete markets,
equilibrium,
investment, optimisation of consumption,
pricing
Contents: The Discrete Case.- Dynamic Models
in Discrete Time.-
The Black-Scholes Formula.- Portfolios Optimizing
Wealth and
Consumption.- The Yield Curve.- Equilibrium
of Financial Markets
in Discrete Time.- Equilibrium of Financial
Markets in Continuous
Time. The Complete Markets Case.- Incomplete
Markets.- Exotic
Options.- Appendix A: Brownian Motion.- Appendix
B: Numerical
Methods.
Series: Springer Finance.