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...
The Fractal and The Recurrence Equations Concerning The Integer
Partitions
July 2, 2013
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Mathematics
Combinatorics
Dynamical Systems
Number Theory
Combinatorics
Dynamical Systems
Number Theory
This paper introduced a way of fractal to solve the problem of taking count
of the integer partitions, furthermore, using the method in this paper some
recurrence equations concerning the integer partitions can be deduced,
including the pen...
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...
About Asymptotic continuation of Einstein equation
May 22, 2013
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Physics
General Relativity and Quantum Cosmology
General Relativity and Quantum Cosmology
The energy density of the gravitational field is a full-fledged source of the
gravitational field. This principle of Einstein was not implemented by him in
the Einstein equation. Not long ago it was possible to find an energy-momentum
tenso...
Methods to Calculate the Upper Bound of Gini Coefficient Based on
Grouped Data and the Result for China
May 21, 2013
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Statistics
Methodology
Methodology
Determining an upper bound, particularly the optimal upper bound of the Gini
coefficient when dealing with grouped data without specified income brackets,
remains an important and open question. In this paper, we introduce an
efficient algo...