A well-known conjecture of Caratheodory states that the number of umbilic
points on a closed convex surface in E3 must be greater than one.
In this paper we prove this for C3+α-smooth surfaces. The Conjecture
is first...
Static Universe: Infinite, Eternal and Self-Sustainable
July 7, 2008
Physics
General Physics
In this work, we present a study like a "stellar dynamics" model of an
infinite Universe, in which the matter distribution follow a relationship
inversely proportional to the square power with respect to the distance from
the center of rota...
A proof of the Riemann hypothesis
July 1, 2008
Mathematics
General Mathematics
By studying the trace of an integral operator on a L2 space of complex
valued functions, we prove in this paper the positivity of Li's criterion. This
implies that all nontrivial zeros of the Riemann zeta-function lie on the
critical lin...
Summing the curious series of Kempner and Irwin
June 27, 2008
Mathematics
Number Theory
Classical Analysis and ODEs
In 1914, Kempner proved that the series 1/1 + 1/2 + ... + 1/8 + 1/10 + 1/11 +
... + 1/18 + 1/20 + 1/21 + ... where the denominators are the positive integers
that do not contain the digit 9, converges to a sum less than 90. The actual
sum i...
On the length of lemniscates
May 15, 2008
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Mathematics
Complex Variables
We show that for a monic polynomial p of degree d, the length of the level
set {z: |p(z)|=1} is at most 9.2 d, which improves an earlier estimate due to
P. Borwein. For d=2 we show that the extremal level set is the Bernoullis'
Lemniscate. ...
Strings in five-dimensional anti-de Sitter space with a symmetry
April 1, 2008
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Physics
General Relativity and Quantum Cosmology
The equation of motion of an extended object in spacetime reduces to an
ordinary differential equation in the presence of symmetry. By properly
defining of the symmetry with notion of cohomogeneity, we discuss the method
for classifying all...
Large deviations principles of Non-Freidlin-Wentzell type
March 13, 2008
Physics
Mathematics
Mathematical Physics
Mathematical Physics
Generalized Large deviation principles was developed for Colombeau-Ito SDE
with a random coefficients. We is significantly expand the classical theory of
large deviations for randomly perturbed dynamical systems developed by Freidlin
and We...
A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped
Robots in a Quadratic Number of Moves
February 22, 2008
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Computer Science
Computational Geometry
Multiagent Systems
Robotics
In the modular robot reconfiguration problem, we are given n cube-shaped
modules (or robots) as well as two configurations, i.e., placements of the n
modules so that their union is face-connected. The goal is to find a sequence
of moves...
n-Groupoids and Stacky Groupoids
January 14, 2008
Mathematics
Differential Geometry
Category Theory
We discuss two generalizations of Lie groupoids. One consists of Lie
n-groupoids defined as simplicial manifolds with trivial πk≥n+1.
The other consists of stacky Lie groupoids \cG\rra M with \cG a
differentiable stack. We ...
Data Tables for Lorentz and CPT Violation
January 1, 2008
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Physics
High Energy Physics - Phenomenology
General Relativity and Quantum Cosmology
High Energy Physics - Experiment
High Energy Physics - Theory
High Energy Physics - Phenomenology
General Relativity and Quantum Cosmology
High Energy Physics - Experiment
High Energy Physics - Theory
This work tabulates measured and derived values of coefficients for Lorentz
and CPT violation in the Standard-Model Extension. Summary tables are extracted
listing maximal attained sensitivities in the matter, photon, neutrino, and
gravity ...