2002. XIV, 354 p. Softcover
3-540-43782-7
Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The expose is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.
Keywords: Separable functor, Frobenius functor,
entwined
module, Yetter-Drinfeld module, Nonlinear
equation Mathematics
Subject Classification ( 2000 ): primary
16W30, secondary 16D90,
16W50, 16B50
Contents: Part I: Entwined modules and Doi-Koppinen Hopf modules.- 1. Generalities.- 2. Doi-Koppinen Hopf modules and entwined modules.- 3. Frobenius and separable functors for entwined modules.- 4. Applications.- Part II: Nonlinear equations.- 5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation.- 6. Hopf modules and the pentagon equation.- 7. Long dimodules and the Long equation.- 8. The Frobenius-Separability equation.- References.- Index.
Series: Lecture Notes in Mathematics. VOL. 1787
2002. XVIII, 288 p. Hardcover
3-540-43727-4
In Western Civilization Mathematics and Music
have a long and
interesting history in common, with several
interactions,
traditionally associated with the name of
Pythagoras but also
with a significant number of other mathematicians,
like Leibniz,
for instance. Mathematical models can be
found for almost all
levels of musical activities from composition
to sound production
by traditional instruments or by digital
means. Modern music
theory has been incorporating more and more
mathematical content
during the last decades. This book offers
a journey into recent
work relating music and mathematics. It contains
a large variety
of articles, covering the historical aspects,
the influence of
logic and mathematical thought in composition,
perception and
understanding of music and the computational
aspects of musical
sound processing. The authors illustrate
the rich and deep
interactions that exist between Mathematics
and Music.
Keywords: Music, Mathematics, Ethnomusicology, Ethnomathematics,
2nd ed. 2002. XI, 232 p. Softcover 1-85233-662-5
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.
Series: Springer Undergraduate Mathematics Series.
2002. XI, 421 pp. 172 figs., 4 in color. Hardcover
3-540-43639-1
Multiresolution methods in geometric modelling
are concerned
with the generation, representation, and
manipulation of
geometric objects at several levels of detail.
Applications
include fast visualization and rendering
as well as coding,
compression and digital transmission of 3D
geometric objects.
This book is based on thirteen tutorials
presented during the
European Summer School "Principles of
Multiresolution in
Geometric Modelling", held at the Munich
University of
Technology, Germany, during August 22-30,
2001. The book covers:
subdivision; wavelets; scattered data modelling;
and coding and
data structures.
The tutorials are designed to be introductory
in character, and
include supporting exercises. Other supplementary
material and
software can be downloaded from the Web Site
www.ma.tum.de/primus
2001/.
Keywords: multiresolution, geometric modeling
Series: Mathematics and Visualization.
2002. IX, 211 p. Softcover
3-540-43846-7
The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmuller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmuller spaces.
Keywords: Modulus, Riemann surface, Teichmuller space, conformal and quasiconformal mappings . MSC ( 2000 ): 30C35, 30C55, 30C62, 30C75, 30F10, 30F60
Series: Lecture Notes in Mathematics. VOL. 1788
2002. V, 157 pp. Softcover
3-540-43799-1
Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.
Keywords: Hopf algebra, Yetter-Drinfel '
d module,
classification, Radford Biproduct . MSC (
2000 ): 16W30
Series: Lecture Notes in Mathematics. VOL.
1789
4th ed. 2003. Approx. 1000 pp. Hardcover
3-540-43491-7
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. For the 4th edition, the concept of the book has been completely re-arranged. The new emphasis is on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing.
Keywords: Engineering, Applied Mathematics, Calculus, Reference, For- mulae, Formulas, Tables, Functions, Integrals, Algebra, Ana- lysis, Geometry, Differential Equations, Physics, Computer Science, Numerics, Numerical, Computational, Probability, Statistics .
Ingram "Handbook of Mathematics" contains the fundamental working knowledge of mathematics which is needed as an everyday guide for both students and professionals in the areas of physics, mathematics, and engineering. Covering material from the introductory level through to more advanced applications, this classic handbook also presents tables of many important functions. 95 illus Pub: 5/97.
Contents: Arithmetics.- Functions and their Notion.- Geometry.- Linear Algebra.- Algebra and Discrete Mathematics.- Differentiation.-Infinite Series.- Integral Calculus.- Differential Equations.- Calculus of Variations.- Linear Integral Equations.- Functional Analysis.- Vector Analysis and Vector Fields.- Functional Theory.- Integral Transformations.- Probability Theory and Mathematical Statistics.- Dynamical Systems and Chaos.- Optimization.- Numerical Analysis.- Computer Algebra Systems.- Tables.- Literature.- Index.- Mathematic Symbols.- List of Tables.
2002. V, 235 p. Softcover
3-540-43780-0
A morphism of algebraic varieties (over a
field characteristic
0) is monomial if it can locally be represented
in e'tale
neighborhoods by a pure monomial mappings.
The book gives proof
that a dominant morphism from a nonsingular
3-fold X to a surface
S can be monomialized by performing sequences
of blowups of
nonsingular subvarieties of X and S.
The construction is very explicit and uses
techniques from
resolution of singularities. A research monograph
in algebraic
geometry, it addresses researchers and graduate
students.
Keywords: Monomialization, Algebraic Variety, Morphism, Resolution of Singularities Mathematics Subject Classification ( 2000 ): 14E15, 14D06
Contents: 1. Introduction.- 2. Local Monomialization.- 3. Monomialization of Morphisms in Low Dimensions.- 4. An Overview of the Proof of Monomialization of Morphisms from 3 Folds to Surfaces.- 5. Notations.- 6. The Invariant v.- 7. The Invariant v under Quadratic Transforms.- 8. Permissible Monoidal Transforms Centered at Curves.- 9. Power Series in 2 Variables.- 10. Ar(X).- 11.Reduction of v in a Special Case.- 12. Reduction of v in a Second Special Case.- 13. Resolution 1.- 14. Resolution 2.- 15. Resolution 3.- 16. Resolution 4.- 17. Proof of the main Theorem.- 18. Monomialization.- 19. Toroidalization.- 20. Glossary of Notations and definitions.- References.
Series: Lecture Notes in Mathematics. VOL.
1786