On Direct Product and Quotient of Strongly Connected Automata
April 17, 2011
Computer Science
Mathematics
Formal Languages and Automata Theory
Group Theory
Let A×B be the direct product of a strongly connected
permutation automaton A and a strongly connected synchronizing (reset)
automaton B, then A×B is strongly connected and $$\boldsymbol{A
\cong (A \times B)/\p...
A Simplified and Improved Free-Variable Framework for Hilbert's epsilon
as an Operator of Indefinite Committed Choice
April 13, 2011
Computer Science
Mathematics
Artificial Intelligence
Logic
Free variables occur frequently in mathematics and computer science with ad
hoc and altering semantics. We present the most recent version of our
free-variable framework for two-valued logics with properly improved
functionality, but only t...
Wiring Switches to Light Bulbs
January 25, 2011
|
Mathematics
Combinatorics
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....
From coloured gravity to electromagnetism
December 21, 2010
| |
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...
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 ||...