Given n buttons and n bulbs so that the ith button toggles the ith bulb and
at most two other bulbs, we compute the sharp lower bound on the number of
bulbs that can be lit regardless of the action of the buttons....
Alexandrov meets Kirszbraun
December 27, 2010
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Mathematics
Differential Geometry
Differential Geometry
We give a simplified proof of the generalized Kirszbraun theorem for
Alexandrov spaces, which is due to Lang and Schroeder. We also discuss related
questions, both solved and open....
From coloured gravity to electromagnetism
December 21, 2010
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Physics
General Relativity and Quantum Cosmology
The gauge formalism in telepalallel gravity provides an interesting viewpoint
to describe interactions according to an anholonomic observer's tetrad basis.
Without going into assessing the complete viability of quantization in an early
stag...
Rationality of instanton moduli
December 18, 2010
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Mathematics
Algebraic Geometry
Tikhomirov (2009) proved the irreducibility of the moduli space of
mathematical instantons on the projective 3-space for all odd charges. The
irreducibility for charges between 1 and 5 was known before. In the present
paper, the rationality...
Dark Matter Explanation from Quasi-Metric Gravity
December 14, 2010
Physics
General Relativity and Quantum Cosmology
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...
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 ||...