A system of polynomial equations related to the Jacobian Conjecture
June 3, 2014
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Mathematics
Algebraic Geometry
Commutative Algebra
We prove that the Jacobian conjecture is false if and only if there exists a
solution to a certain system of polynomial equations. We analyse the solution
set of this system. In particular we prove that it is zero dimensional....
Preserving positivity for rank-constrained matrices
May 30, 2014
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Mathematics
Functional Analysis
Classical Analysis and ODEs
Entrywise functions preserving the cone of positive semidefinite matrices
have been studied by many authors, most notably by Schoenberg [Duke Math. J. 9,
1942] and Rudin [Duke Math. J. 26, 1959]. Following their work, it is
well-known that ...
Unbelievable O(L1.5) worst case computational complexity achieved
by spdspds algorithm for linear programming problem
May 27, 2014
Mathematics
Optimization and Control
The Symmetric Primal-Dual Symplex Pivot Decision Strategy (spdspds) is a
novel iterative algorithm to solve linear programming problems. A symplex
pivoting operation is simply an exchange between a basic variable and a
non-basic variable, i...
On space-time quasiconcave solutions of the heat equation
May 25, 2014
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Mathematics
Analysis of PDEs
In this paper we first obtain a constant rank theorem for the second
fundamental form of the space-time level sets of a space-time quasiconcave
solution of the heat equation. Utilizing this constant rank theorem, we can
obtain some strictly...
Model-Checking PCTL Properties of Stateless Probabilistic Pushdown
Systems
May 19, 2014
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Computer Science
Mathematics
Logic in Computer Science
Formal Languages and Automata Theory
Logic
In this paper, we resolve a longstanding open question in the probabilistic
verification of infinite-state systems. We show that model checking {\em
stateless probabilistic pushdown systems (pBPA)} against {\em probabilistic
computational t...
Explanation of Superluminal Phenomena Based on Wave-Particle Duality and
Proposed Optical Experiments
May 14, 2014
Physics
Quantum Physics
Optics
An explanation for superluminal phenomena based on wave-particle duality of
photons is suggested. A single photon may be regarded as a wave packet, whose
spatial extension is its coherence volume. As a photon propagates as a wave
train in v...
Finite Type Invariants of w-Knotted Objects II: Tangles, Foams and the
Kashiwara-Vergne Problem
May 8, 2014
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Mathematics
Representation Theory
Quantum Algebra
Geometric Topology
This is the second in a series of papers dedicated to studying w-knots, and
more generally, w-knotted objects (w-braids, w-tangles, etc.). These are
classes of knotted objects that are wider but weaker than their "usual"
counterparts. To ge...
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....