Algebraic structure of knot modules
Author(s)
Bibliographic Information
Algebraic structure of knot modules
（Lecture notes in mathematics, 772）
Springer-Verlag, 1980
- : Berlin
- : New York
Available at 73 libraries
-
Library & Science Information Center, Osaka Prefecture University
: BerlinNDC8:410.8||||10007177409
Note
Includes bibliographical references and index
Description and Table of Contents
- Volume
-
: New York ISBN 9780387097398
Description
Classical circuit theory is a mathematical theory of linear, passive circuits, namely, circuits composed of resistors, capacitors and inductors. Like many a thing classical, it is old and enduring, structured and precise, simple and elegant. It is simple in that everything in it can be deduced from ?rst principles based on a few physical laws. It is enduring in that the things we can say about linear, passive circuits are universally true, unchanging. No matter how complex a circuit may be, as long as it consists of these three kinds of elements, its behavior must be as prescribed by the theory. The theory tells us what circuits can and cannot do. As expected of any good theory, classical circuit theory is also useful. Its ulti mate application is circuit design. The theory leads us to a design methodology that is systematic and precise. It is based on just two fundamental theorems: that the impedance function of a linear, passive circuit is a positive real function, and that the transfer function is a bounded real function, of a complex variable.
Table of Contents
Fundamentals.- Circuit Dynamics.- Properties in the Frequency Domain.- The Impedance Function.- Synthesis of Two-Element-Kind Impedances.- Synthesis of RLC Impedances.- Scattering Matrix.- Synthesis of Transfer Functions.- Filter Design.- Circuit Design by Optimization.- All-Pass Circuits.
- Volume
-
: Berlin ISBN 9783540097396
Table of Contents
The derived exact sequences.- Finite modules.- Realization of finite modules.- ?i of finite modules.- Product structure on finite modules.- Classification of derived product structure.- Rational invariants.- Z-torsion-free modules.- ?-only torsion.- Statement of realization theorem.- Inductive construction of derived sequences.- Inductive recovery of derived sequences.- Homogeneous and elementary modules.- Realization of elementary modules.- Classification of elementary modules.- Completion of proof.- Classification of ?-primary modules.- Classification fails in degree 4.- Product structure on ?-primary modules.- Classification of product structure.- Realization of product structure on homogeneous modules.- Product structure on semi-homogeneous modules.- A non-semi-homogeneous module.- Rational classification of product structure.- Non-singular lattices over a Dedekind domain.- Norm criterion for a non-singular lattice.- Dedekind criterion: p-adic reduction.- A computable Dedekind criterion.- Computation of low-degree cases.- Determination of ideal class group.- The quqdratic symetric case.
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