Series on Knots and Everything
Every hundred years or so, a unique groundbreaking Copernican class volume arises unexpectedly. From ashes long thought cold of Einstein痴 static universe model, for the first time technically viable alternative interpretations to all pillars of Big Bang cosmology are presented in the context of a profound new 田ontinuous-state・cosmological paradigm able to elucidate many contemporary problems plaguing the standard model of particle physics. The cosmology provides an alternative derivation of the string/brane tension formalism derived from large-scale additional dimensions that leads to a putative unique background-independent string vacuum without requiring the Higgs mechanism or SUSY superpartners. Breakthroughs presented, arising from the broad spectrum of explanatory power, include an empirical protocol for violation of the quantum uncertainty principle that provides a viable model for the implementation of universal bulk quantum computing. Other developments naturally arising from utility of the new regime include a design for constructing de Broglie-type matter-wave projectile defense shields with far-reaching consequences.
Revamping Cosmology:
Demise of the Big Bang ・A Philosophical Conundrum
Extending the Standard Model ・The Ultimate Evolution of String Theory
Fundamental Parameters for a Holographic Anthropic Multiverse
An Alternative Derivation of the String/Brane Tension Formalism
Formalizing the Geometry of Ultimate Reality
Explanatory Power ・Empirical Protocols:
Integration of Gravity & EM in Terms of a Dirac Covariant Polarized Vacuum
A Blackbody Equilibrium Cavity-QED Model of CMBR/Redshift Complementarity
The Physical Implications of Multidimensional Geometries and Measurement
An Empirical Protocol for Surmounting Uncertainty
Applications of the Model:
The Origin Quasar Luminosity in Gravitational Shock Waves
The Implementation of Universal Bulk Quantum Computing
Defense Shield Technologies ・Coherent Control of Matter-Waves
A New Protocol for Success in SETI Research
Readership: Graduate students and researchers in astrophysics, cosmology, universal quantum computing and string theory.
400pp (approx.) Pub. date: Scheduled Fall 2009
ISBN 978-981-283-930-5
The present monograph on matrix partial orders, appearing for the first time, is a unique presentation of many partial orders on matrices that have fascinated mathematicians for their beauty and applied scientists for their wide-ranging application potential. Except for the Lner order, the partial orders considered are relatively new and came into being in the late 1970s. After a detailed introduction to generalized inverses and decompositions, the three basic partial orders ・namely, the minus, the sharp and the star ・and the corresponding one-sided orders are presented using various generalized inverses. The authors then give a unified theory of all these partial orders. This is followed by a study of the Lner order and a limited treatment of majorization (there is an abundance of literature available on majorization). The authors also study the parallel sums and shorted matrices, the latter being studied at great length. Partial orders of modified matrices are a new addition. Finally, applications are given in statistics and electrical network theory.
Introduction
Decompositions and Generalized Inverses
Minus Order
Sharp Order
Star Order
One-Sided Orders
Lner Order and Majorization
Unified Theory of Matrix Partial Orders through Generalized Inverses
Parallel Sums
Schur Complements and Shorted Operators
Shorted Operators II
Supremum and Infimum for a Pair of Matrices
Partial Orders for Modified Matrices
Statistics
Electrical Network Theory
Readership: Graduate students in mathematics; researchers in mathematics, statistics and electrical engineering.
300pp (approx.) Pub. date: Scheduled Winter 2009
ISBN 978-981-283-844-5