Towards a Post Reductionist Science: The Open Universe
July 15, 2009
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Physics
General Physics
In this paper we consider clumped baryonic matter as a spherically symmetric
barotropic fluid associated with a compact four-dimensional Einstein manifold
with a four-radius that is determined by the fluid density. We further
investigate th...
Discrete Linear Groups containing Arithmetic Groups
May 12, 2009
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Mathematics
Group Theory
Group Theory
We prove in a large number of cases, that a Zariski dense discrete subgroup
of a simple real algebraic group G which contains a higher rank lattice is a
lattice in the group G. For example, we show that a Zariski dense subgroup of
$SL_n...
Quantum action, non-locality and coherence from classical perception, a
new facet of Lagrangian formalism for relativistic dynamics
April 14, 2009
Physics
Classical Physics
Classical and quantum mechanical descriptions of physical world are
seamlessly abridged within the framework of Lagrangian formalism which, besides
revealing the essence of nonlocally correlated dynamic evolution, helps
understanding abrupt...
Many-Help-One Problem for Gaussian Sources with a Tree Structure on
their Correlation
January 14, 2009
Computer Science
Mathematics
Information Theory
Information Theory
In this paper we consider the separate coding problem for L+1 correlated
Gaussian memoryless sources. We deal with the case where L separately encoded
data of sources work as side information at the decoder for the reconstruction
of the...
A minimalist two-level foundation for constructive mathematics
November 17, 2008
Mathematics
Logic
We present a two-level theory to formalize constructive mathematics as
advocated in a previous paper with G. Sambin. One level is given by an
intensional type theory, called Minimal type theory. This theory extends the
set-theoretic version...
Proof of the Caratheodory Conjecture
August 6, 2008
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Mathematics
Differential Geometry
Analysis of PDEs
Symplectic Geometry
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. ...