The gravitational field of an isolated, axisymmetric flat disk of spinning
dust is calculated approximately in the weak-field limit of quasi-metric
gravity. Boundary conditions single out the exponential disk as a "preferred"
physical surfa...
A numeral system for the middle-levels graphs
December 5, 2010
Mathematics
Combinatorics
The middle-levels graph Mk (0<k∈Z) has a dihedral quotient
pseudograph Rk whose vertices are the k-edge ordered trees T, each T
encoded as a (2k+1)-string F(T) formed via →DFS by: {\bf(i)}
($\leftarr...
A variational and symplectic framework for model-free control:
preliminary results
November 18, 2010
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Computer Science
Mathematics
Systems and Control
Optimization and Control
Systems and Control
Optimization and Control
The model-free control approach is an advanced control law that requires few
information about the process to control. Since its introduction in 2008,
numerous applications have been successfully considered, highlighting
attractive robustne...
Introduction to Normed *-Algebras and their Representations, 7th ed
November 6, 2010
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Mathematics
Operator Algebras
Operator Algebras
This book treats: - spectral theory of Banach *-algebras, - basic
representation theory of normed *-algebras, - spectral theory of
representations of commutative *-algebras. A novel feature of the book is the
construction of the enveloping ...
Heegaard Floer homology and integer surgeries on links
November 4, 2010
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Mathematics
Geometric Topology
Let L be a link in an integral homology three-sphere. We give a description
of the Heegaard Floer homology of integral surgeries on L in terms of some data
associated to L, which we call a complete system of hyperboxes for L. Roughly,
a com...
Mathematical analysis without gaps
October 5, 2010
Mathematics
Classical Analysis and ODEs
This is a draft of my textbook on mathematical analysis and the areas of
mathematics on which it is based. The idea is to fill the gaps in the existing
textbooks. Any remarks from readers are welcome....
An inverse theorem for the Gowers U^{s+1}[N]-norm
September 21, 2010
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Mathematics
Combinatorics
Dynamical Systems
We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >=
3; this is new for s > 3, and the cases s<3 have also been previously
established. More precisely, we establish that if f : [N] -> [-1,1] is a
function with || f ||...
Exploring Mount Neverest
September 12, 2010
Mathematics
History and Overview
Optimization and Control
The problem `Exploring Mount Neverest' by Henry Ernest Dudeney is solved.
Dudeney formulated the problem in the beginning of the 20th century and gave a
non-optimal solution (without estimating the non-optimality)....
The surface parametrizing cuboids
September 2, 2010
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Mathematics
Algebraic Geometry
Algebraic Geometry
We study the surface Sˉ parametrizing cuboids: it is defined by the
equations relating the sides, face diagonals and long diagonal of a rectangular
box. It is an open problem whether a `rational box' exists, i.e., a rectangular
box a...
Quantum-classical phase transition with spontaneous superposition
breaking (basic characteristics)
July 15, 2010
Physics
Quantum Physics
In this work we consider basic characteristics of a quantum-classical
continuous phase transition with spontaneous (non-dynamical) unitary symmetry
(superposition) breaking (effective hiding). We clearly demonstrate that
collapse (transitio...