Synchrotron radiation of vector bosons at relativistic colliders
July 9, 2014
Physics
High Energy Physics - Phenomenology
Magnetic fields produced in collisions of electrically charged particles at
relativistic energies are strong enough to affect the dynamics of the strong
interactions. In particular, it induces radiation of vector bosons by
relativistic ferm...
The missing proof of Paley's theorem about lacunary coefficients
July 6, 2014
Mathematics
Classical Analysis and ODEs
We modify the standard proof of Paley's theorem about lacunary coefficients
of functions in H1 to work without analytic factorization. This leads to the
first direct proof of the extension of Paley's theorem that we applied to the
former...
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...
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...