A surface that is the pointwise sum of circles in Euclidean space is either
coplanar or contains no more than 2 circles through a general point. A surface
that is the pointwise product of circles in the unit-quaternions contains
either 2, 3...
The Attractor-Cycle Notation for Finite Transformations
June 3, 2013
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Mathematics
Computer Science
Group Theory
Formal Languages and Automata Theory
We describe a new notation for finite transformations. This attractor-cycle
notation extends the orbit-cycle notation for permutations and builds upon
existing transformation notations. How the basins of attraction of a finite
transformatio...
Showcasing straight-line programs with memory via matrix Bruhat
decomposition
May 24, 2013
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Computer Science
Mathematics
Data Structures and Algorithms
Group Theory
We suggest that straight-line programs designed for algebraic computations
should be accompanied by a comprehensive complexity analysis that takes into
account both the number of fundamental algebraic operations needed, as well as
memory re...
About Asymptotic continuation of Einstein equation
May 22, 2013
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Physics
General Relativity and Quantum Cosmology
General Relativity and Quantum Cosmology
The energy density of the gravitational field is a full-fledged source of the
gravitational field. This principle of Einstein was not implemented by him in
the Einstein equation. Not long ago it was possible to find an energy-momentum
tenso...
Methods to Calculate the Upper Bound of Gini Coefficient Based on
Grouped Data and the Result for China
May 21, 2013
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Statistics
Methodology
Methodology
Determining an upper bound, particularly the optimal upper bound of the Gini
coefficient when dealing with grouped data without specified income brackets,
remains an important and open question. In this paper, we introduce an
efficient algo...
Curvature estimates for the level sets of solutions of the
Monge-Amp\`{e}re equation detD2u=1
May 12, 2013
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Mathematics
Analysis of PDEs
For the Monge-Amp\`{e}re equation detD2u=1, we find new auxiliary
curvature functions which attain respective maximum on the boundary. Moreover,
we obtain the upper bounded estimates for the Gauss curvature and mean
curvature of the l...
On limit set of KdV flow: An extension of Remling theorem
April 24, 2013
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Mathematics
Spectral Theory
Spectral Theory
C. Remling obtained a theorem on limit set of the shift operation on a space
of functions on R when the associated 1-D half line Schr\"odinger operators
have absolutely continuous component in their spectrum. The purpose of the
paper is to ...
On the probability of being synchronizable
April 21, 2013
Computer Science
Mathematics
Formal Languages and Automata Theory
Discrete Mathematics
Combinatorics
We prove that a random automaton with n states and any fixed non-singleton
alphabet is synchronizing with high probability (modulo an unpublished result
about unique highest trees of random graphs). Moreover, we also prove that the
conver...
Commutativity properties of Quinn spectra
April 17, 2013
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Mathematics
Algebraic Topology
We give a simple sufficient condition for Quinn's "bordism-type" spectra to
be weakly equivalent to commutative symmetric ring spectra. We also show that
the symmetric signature is (up to weak equivalence) a monoidal transformation
between ...
Extending the parking space
March 21, 2013
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Mathematics
Combinatorics
The action of the symmetric group Sn on the set Parkn of parking
functions of size n has received a great deal of attention in algebraic
combinatorics. We prove that the action of Sn on Parkn extends to an
action of Sn+1....