Classification of abelian complex structures on 6-dimensional Lie
algebras
August 21, 2009
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Mathematics
Rings and Algebras
Differential Geometry
We classify the 6-dimensional Lie algebras that can be endowed with an
abelian complex structure and parameterize, on each of these algebras, the
space of such structures up to holomorphic isomorphism....
Quantum Zeno, Hamlet and similar effects
August 10, 2009
Physics
Quantum Physics
Simply speaking quantum Zeno effect for an unstable quantum system represents
total decay probability decrease by frequent decay detection. Analogously
simply speaking quantum anti-Zeno effect for an unstable quantum system
represents total...
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...