With a f-left-invariant Riemannian metric on a Lie group G, we mean a
Riemannian metric which is conformally equivalent to a left-invariant
Riemannian metric, with the conformal factor f. In this article, we study the
geometry of such m...
Unsolved Problems in Group Theory. The Kourovka Notebook
January 1, 2014
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Mathematics
Group Theory
This is a collection of open problems in group theory proposed by hundreds of
mathematicians from all over the world. It has been published every 2--4 years
since 1965. This is the 20th edition, which contains 126 new problems and a
number ...
A Potential Definition of Weak ω-Category
December 30, 2013
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Mathematics
Category Theory
Category Theory
We give a potential alternative definition of a weak infinite dimensional
category, in an unbiased fashion, using one one dimensional quiver with
composition and extra structure....
Defining implication relation for classical logic
December 30, 2013
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Mathematics
Computer Science
Logic
Artificial Intelligence
Computation and Language
Logic in Computer Science
Logic
Artificial Intelligence
Computation and Language
Logic in Computer Science
In classical logic, ''P implies Q'' is equivalent to ''not-P or Q''. It is
well known that the equivalence is problematic. Actually, from ''P implies Q'',
''not-P or Q'' can be inferred (''Implication-to-Disjunction'' is valid),
whereas fro...
Implementing a Quantum CNOT and Quantum Memory Using a Quantum-Dot
Cellular Automata Array
December 19, 2013
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Physics
Quantum Physics
In this work, we develop a method to use Quantum- Dot Cellular Automata (QCA)
for universal quantum computing. This method is based conceptually on
refocusing in NMR systems. We show how an array of QCA cells can be used for
isolated single...
Third-order correction to top-quark pair production near threshold I.
Effective theory set-up and matching coefficients
December 17, 2013
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Physics
High Energy Physics - Phenomenology
This is the first in a series of papers, in which we compute the third-order
QCD corrections to top-antitop production near threshold in e+ e- collisions.
The present paper provides a detailed outline of the strategy of computation in
the f...
The Kirby torus trick for surfaces
December 12, 2013
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Mathematics
Geometric Topology
Geometric Topology
This is an expository paper giving a proof of the existence and uniqueness of
smooth structures (hence also PL structures) on topological surfaces. Most
published proofs rely on the topological Schoenflies theorem, but here we use
instead t...
On the Plaque Expansivity Conjecture
November 27, 2013
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Mathematics
Dynamical Systems
Dynamical Systems
It is one of the main properties of uniformly hyperbolic dynamics that points
of two distinct trajectories cannot be uniformly close one to another. This
characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and
Shub, 1...
Categorical Cell Decomposition of Quantized Symplectic Algebraic
Varieties
November 26, 2013
| | |
Mathematics
Algebraic Geometry
Quantum Algebra
Symplectic Geometry
We prove a new symplectic analogue of Kashiwara's Equivalence from D-module
theory. As a consequence, we establish a structure theory for module categories
over deformation quantizations that mirrors, at a higher categorical level, the
Bial...
Well-posedness for a system of quadratic derivative nonlinear
Schr\"odinger equations with low regularity periodic initial data
November 24, 2013
Mathematics
Analysis of PDEs
We consider the Cauchy problem of a system of quadratic derivative nonlinear
Schr\"odinger equations which was introduced by M. Colin and T. Colin (2004) as
a model of laser-plasma interaction. For the nonperiodic case, the author
proved th...