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....
Alexandrov meets Kirszbraun
December 27, 2010
| | | | |
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
| |
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
|
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...
A variational and symplectic framework for model-free control:
preliminary results
November 18, 2010
|
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
|
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 ...