Simulating dynamic systems using Linear Time Calculus theories
May 7, 2014
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Computer Science
Logic in Computer Science
To appear in Theory and Practice of Logic Programming (TPLP).
Dynamic systems play a central role in fields such as planning, verification,
and databases. Fragmented throughout these fields, we find a multitude of
languages to formally sp...
Discrete Noether Currents
May 6, 2014
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Physics
General Physics
General Physics
A simple implementation of Noether's theorem for discrete symmetries in
relativistic continuum field theories is presented. The conserved current is
exemplified by charge conjugation and a cyclic symmetry. In addition, the
quantum version o...
The Vandermonde determinant identity in higher dimension
May 5, 2014
Mathematics
Commutative Algebra
We generalise the Vandermonde determinant identity to one which tests whether
a family of hypersurfaces in Pn has an unexpected intersection
point....
A General Homogeneous Matrix Formulation to 3D Rotation Geometric
Transformations
April 24, 2014
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Computer Science
Computer Vision and Pattern Recognition
We present algebraic projective geometry definitions of 3D rotations so as to
bridge a small gap between the applications and the definitions of 3D rotations
in homogeneous matrix form. A general homogeneous matrix formulation to 3D
rotatio...
On free stable distributions
April 10, 2014
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Mathematics
Probability
We investigate analytical properties of free stable distributions and
discover many connections with their classical counterparts. Our main result is
an explicit formula for the Mellin transform, which leads to explicit series
representatio...
Quantum Painlev\'e II solution and Approximated analytic solution of the
Yukawa Potential
March 27, 2014
Physics
Mathematics
Mathematical Physics
Mathematical Physics
We show that one dimensional non-stationary Schr\"odi-nger equation with a
specific choice of potential reduces to the quantum Painlev\'e II equation and
the solution of its Riccati form appears as a dominant term of that potential.
Further...
Comparison of spectral invariants in Lagrangian and Hamiltonian Floer
theory
March 25, 2014
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Mathematics
Symplectic Geometry
We compare spectral invariants in periodical orbits and Lagrangian Floer
homology case, for closed symplectic manifold P and its closed Lagrangian
submanifolds L, when ω∣π2(P,L)=0, and μ∣π2(P,L)=0.
From this resul...
Cluster Before You Hallucinate: Approximating Node-Capacitated Network
Design and Energy Efficient Routing
March 24, 2014
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Computer Science
Data Structures and Algorithms
We consider the following node-capacitated network design problem. The input
is an undirected graph, set of demands, uniform node capacity and arbitrary
node costs. The goal is to find a minimum node-cost subgraph that supports all
demands ...
The calculation of air filtration efficiency through the visual basic
programming language
March 20, 2014
Computer Science
Computational Engineering, Finance, and Science
The present article describes the development of a software which was written
in visual basic programming language. The software calculates the particle
collection efficiency and penetration of a fibrous filter medium for given
values of pa...
A constructive proof of the Wedderburn-Artin theorem
March 19, 2014
Mathematics
Representation Theory
In this short note, we use the idempotent decomposition to give an explicit
isomorphism from a semisimple Artinian ring to an external direct sum of finite
full matrix rings over division rings....