Some Connections Between The Arithmetic and The Geometry of Lipschitz
Integers
January 27, 2012
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Mathematics
Number Theory
Some relationships between the arithmetic and the geometry of Lipschitz and
Hurwitz integers are presented. In particular, it is shown that the (ternary)
vector product of a Lipschitz integer α with two other Lipschitz
integers, both...
Identification of transformer overload and new energy planning for
enterprises based on load forecasting
January 11, 2012
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
Mathematical Physics
Mathematical Physics
The new energy system constructed by energy storage and photovoltaic power
generation system can effectively solve the problem of transformer overload
operation in some enterprises. It can not only reduce the cost of electricity,
but also r...
The Fundamental Theorem of Phyllotaxis revisited
January 8, 2012
Quantitative Biology
Tissues and Organs
Jean's `Fundamental Theorem of Phyllotaxis' (\emph{Phyllotaxis: a systematic
study in Plant Morphogenesis}, CUP 1994) describes the relationship between the
count numbers of observed spirals in cylindrical lattices and the horizontal
angle ...
An explicit version of Shimura's reciprocity law for Siegel modular
functions
December 29, 2011
Mathematics
Number Theory
We give an explicit version of Shimura's reciprocity law for singular values
of Siegel modular functions. We use this to construct the first examples of
class invariants of quartic CM fields that are smaller than Igusa invariants.
Our state...
The Extended UCB Policies for Frequentist Multi-armed Bandit Problems
December 8, 2011
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Computer Science
Mathematics
Statistics
Machine Learning
Probability
Statistics Theory
Statistics Theory
The multi-armed bandit (MAB) problem is a widely studied model in the field
of operations research for sequential decision making and reinforcement
learning. This paper mainly considers the classical MAB model with the
heavy-tailed reward d...
On generalized black brane solutions in the model with multicomponent
anisotropic fluid
December 7, 2011
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Physics
High Energy Physics - Theory
General Relativity and Quantum Cosmology
High Energy Physics - Theory
General Relativity and Quantum Cosmology
A family of spherically O(d0+1)-symmetric solutions in the model with
m-component anisotropic fluid is obtained. The metrics are defined on a
manifold which contains a product of n−1 Ricci-flat ``internal'' spaces. The
equation of ...
Vacuum Potentials for the Two Only Permanent Free Particles, Proton and
Electron. Appendix D: QEM Theory of IVBs, Higgs
November 14, 2011
Physics
General Physics
The two only species of isolatable, smallest, or unit charges +e and -e
present in nature interact with the universal vacuum in a polarisable
dielectric representation through two uniquely defined vacuum potential
functions. All of the non-...
Characterizing closed curves on Riemann surfaces via homology groups of
coverings
November 9, 2011
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Mathematics
Algebraic Topology
Group Theory
Let S be a hyperbolic oriented Riemann surface of finite type. The main
purpose of this paper is to show that non-trivial geometric intersection
between closed curves on S is detected by some symplectic submodules they
naturally determi...
On the solution of the Collatz problem
October 16, 2011
Mathematics
General Mathematics
In this paper, we propose a key idea and innovation on the Collatz problem.
Let an odd Collatz's Sequence be Sc(m,t)={n0(m,t),n1(m,t),n2(m,t),…,nm(m,t),nm+1(m,t)} produced by a function $n_{i+1}(m,t)=(3n_{i}(m...