Third Order Newton's Method for Zernike Polynomial Zeros
May 9, 2007
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
The Zernike radial polynomials are a system of orthogonal polynomials over
the unit interval with weight x. They are used as basis functions in optics to
expand fields over the cross section of circular pupils. To calculate the roots
of Zer...
A survey of debris trails from short-period comets
April 17, 2007
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We observed 34 comets using the 24 micron camera on the Spitzer Space
Telescope. Each image contains the nucleus and covers at least 10^6 km of each
comet's orbit. Debris trails due to mm-sized or larger particles were found
along the orbit...
"Discrete" vacuum geometry as a tool for Dirac fundamental quantization
of Minkowskian Higgs model
January 10, 2007
Physics
High Energy Physics - Theory
Superconductivity
We demonstrate that assuming the "discrete" vacuum geometry in the
Minkowskian Higgs model with vacuum BPS monopole solutions can justify the
Dirac fundamental quantization of that model. The important constituent of this
quantization is ge...
Metrically Stationary, Axially Symmetric, Isolated Systems in
Quasi-Metric Gravity
October 18, 2005
Physics
General Relativity and Quantum Cosmology
The gravitational field exterior respectively interior to an axially
symmetric, metrically stationary, isolated spinning source made of perfect
fluid is examined within the quasi-metric framework. (A metrically stationary
system is defined ...
Cryptography and Encryption
October 3, 2005
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Mathematics
Category Theory
In cryptography, encryption is the process of obscuring information to make
it unreadable without special knowledge. This is usually done for secrecy, and
typically for confidential communications. Encryption can also be used for
authentica...
An Introduction to Zoli Numbers
October 3, 2005
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Mathematics
General Mathematics
Category Theory
There have been many theories about the paradoxes of numbers, but this is far
and away more paradoxical than most. In this paper we will present the Zoli
Numbers which have some innovative characteristics. The basic concept of these
numbers...
Stabilization phenomena in Kac-Moody algebras and quiver varieties
May 30, 2005
Mathematics
Representation Theory
Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X_0 a
subgraph with all vertices of degree 1 or 2. Using the crystal structure on the
components of quiver varieties for X, we show that if we expand X by extending
X_0, ...
Energy Complexity of Software in Embedded Systems
May 2, 2005
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Physics
Adaptation and Self-Organizing Systems
The importance of low power consumption is widely acknowledged due to the
increasing use of portable devices, which require minimizing the consumption of
energy. The energy in a computational system depends heavily on the software
being exe...
On Gracefully Labeling Trees
March 23, 2005
Mathematics
General Mathematics
In this paper, we propose an algorithm to generate all possible graceful
graphs (including trees) containing n vertices as lattice paths in a certain
triangular lattice defined below. This lattice that corresponds to graphs
containing n ver...
Classical Electrodynamics in Quasi-Metric Space-Time
March 26, 2003
Physics
General Relativity and Quantum Cosmology
The quasi-metric manifold N is equipped with two one-parameter
families of metric tensors gˉt and gt, each
parametrized by the global time function t. Moreover, in (N,gˉt) one must defi...