Renormalized Four Dimensional Quantum Yang-Mills Theory and Mass Gap
June 16, 2014
Mathematics
General Mathematics
A quantization procedure for the Yang-Mills equations for the Minkowski space
R1,3 is carried out in such a way that field maps satisfying
Wightman axioms of Constructive Quantum Field Theory can be obtained. Moreover,
by remo...
Jump relations for magnetrohydrodynamic shock waves in a dusty gas
atmosphere
June 7, 2014
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Physics
High Energy Astrophysical Phenomena
High Energy Astrophysical Phenomena
In this article, we have derived Rankine-Hugoniot (RH) jump conditions across
a magnetohydrodynamic (MHD) shock front propagating in a dusty gas atmosphere.
The dusty gas atmosphere is assumed to be a mixture of a perfect gas and small
soli...
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...