Current Algebras from DG Symplectic Pairs in Supergeometry
August 1, 2013
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Physics
Mathematics
Mathematical Physics
High Energy Physics - Theory
Mathematical Physics
Symplectic Geometry
Mathematical Physics
High Energy Physics - Theory
Mathematical Physics
Symplectic Geometry
We propose a new unified formulation of the current algebra theory in terms
of supergeometry. We take a QP-structure, i.e. a differential graded symplectic
structure, on a graded cotangent bundle as a fundamental framework. A Poisson
bracke...
Classification of quasi-affine Generalized Dynkin Diagrams with Rank 4
July 25, 2013
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Mathematics
Quantum Algebra
Quantum Algebra
All quasi-affine connected Generalized Dynkin Diagram with rank =4 are
found. All quasi-affine Nichols (Lie braided) algebras with rank 4 are also
found....
A new graph-based two-sample test for multivariate and object data
July 24, 2013
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Statistics
Methodology
Methodology
Two-sample tests for multivariate data and especially for non-Euclidean data
are not well explored. This paper presents a novel test statistic based on a
similarity graph constructed on the pooled observations from the two samples.
It can b...
Combinatorial data of a free arrangement and the Terao conjecture
July 14, 2013
Mathematics
Combinatorics
We present a combinatorial structure of generators of D(A). This
structure permits us to detect the relationship between the combinatorial
determined property and the singularity of vector field. Consequently, by using
only comb...
Guide to Boundary Value Problems for Dirac-Type Operators
July 11, 2013
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Mathematics
Differential Geometry
Analysis of PDEs
Spectral Theory
We present an introduction to boundary value problems for Dirac-type
operators on complete Riemannian manifolds with compact boundary. We introduce
a very general class of boundary conditions which contains local elliptic
boundary condition...
Impossibility of Local State Transformation via Hypercontractivity
July 10, 2013
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Physics
Computer Science
Mathematics
Quantum Physics
Information Theory
Mathematical Physics
Information Theory
Mathematical Physics
Quantum Physics
Information Theory
Mathematical Physics
Information Theory
Mathematical Physics
Local state transformation is the problem of transforming an arbitrary number
of copies of a bipartite resource state to a bipartite target state under local
operations. That is, given two bipartite states, is it possible to transform an
ar...
Antiglitch Inconsistent With Magnetar Model of AXP
July 2, 2013
Physics
High Energy Astrophysical Phenomena
The recently observed antiglitch of AXP 1E 2259+586 is inconsistent with
magnetar models, but may be explained as the consequence of sudden accretion of
retrograde matter or "propeller" interaction with surrounding matter. AXP/SGR
are expla...
Translational and great Darboux cyclides
June 8, 2013
Mathematics
Algebraic Geometry
Metric Geometry
A surface that is the pointwise sum of circles in Euclidean space is either
coplanar or contains no more than 2 circles through a general point. A surface
that is the pointwise product of circles in the unit-quaternions contains
either 2, 3...
The Attractor-Cycle Notation for Finite Transformations
June 3, 2013
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Mathematics
Computer Science
Group Theory
Formal Languages and Automata Theory
We describe a new notation for finite transformations. This attractor-cycle
notation extends the orbit-cycle notation for permutations and builds upon
existing transformation notations. How the basins of attraction of a finite
transformatio...
Showcasing straight-line programs with memory via matrix Bruhat
decomposition
May 24, 2013
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Computer Science
Mathematics
Data Structures and Algorithms
Group Theory
We suggest that straight-line programs designed for algebraic computations
should be accompanied by a comprehensive complexity analysis that takes into
account both the number of fundamental algebraic operations needed, as well as
memory re...