For any α<1/3, we construct weak solutions to the 3D
incompressible Euler equations in the class CtCxα that have nonempty,
compact support in time on R×T3 and therefore
fail to conserve the...
Non-Euclidean Triangle Centers
August 29, 2016
Mathematics
Metric Geometry
Non-Euclidean triangle centers can be described using homogeneous coordinates
that are proportional to the generalized sines of the directed distances of a
given center from the edges of the reference triangle. Identical homogeneous
coordin...
Human Action Recognition without Human
August 28, 2016
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Computer Science
Computer Vision and Pattern Recognition
Multimedia
The objective of this paper is to evaluate "human action recognition without
human". Motion representation is frequently discussed in human action
recognition. We have examined several sophisticated options, such as dense
trajectories (DT) ...
The homotopy type of the PL cobordism category. I
August 22, 2016
Mathematics
Geometric Topology
Algebraic Topology
In this paper, we introduce a bordism category CdPL whose
objects are bundles of closed (d−1)-dimensional piecewise linear manifolds
and whose morphisms are bundles of d-dimensional piecewise linear cobordisms.
In the ma...
Semantics, Specification Logic, and Hoare Logic of Exact Real
Computation
August 20, 2016
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Computer Science
Numerical Analysis
Logic in Computer Science
We propose a simple imperative programming language, ERC, that features
arbitrary real numbers as primitive data type, exactly. Equipped with a
denotational semantics, ERC provides a formal programming language-theoretic
foundation to the a...
Introduction to Cluster Algebras. Chapters 1-3
August 19, 2016
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Mathematics
Combinatorics
Rings and Algebras
Representation Theory
Combinatorics
Rings and Algebras
Representation Theory
This is a preliminary draft of Chapters 1-3 of our forthcoming textbook
"Introduction to Cluster Algebras." This installment contains:
Chapter 1. Total positivity
Chapter 2. Mutations of quivers and matrices
Chapter 3. Clusters and se...
Nonexistence of time-periodic solutions of the Dirac equation in
nonextreme Kerr-Newman-AdS spacetime
August 18, 2016
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Physics
Mathematics
General Relativity and Quantum Cosmology
Classical Analysis and ODEs
In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no
nontrivial Dirac particle which is Lp for 0<p≤34 with
arbitrary eigenvalue λ, and for 34<p≤3−2q4,
0<q<23 with eig...
The high type quadratic Siegel disks are Jordan domains
August 14, 2016
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Mathematics
Dynamical Systems
Let α be an irrational number of sufficiently high type and suppose
Pα(z)=e2πiαz+z2 has a Siegel disk Δα centered
at the origin. We prove that the boundary of Δα is a Jordan curve,
and th...
We consider rough differential equations whose coefficients contain
path-dependent bounded variation terms and prove the existence and a priori
estimate of solutions. These equations include classical path-dependent SDEs
containing running ...
Border Ranks of Monomials
August 8, 2016
Mathematics
Computer Science
Algebraic Geometry
Computational Complexity
Young flattenings, introduced by Landsberg and Ottaviani, give determinantal
equations for secant varieties and their non-vanishing provides lower bounds
for border ranks of tensors and in particular polynomials. We study
monomial-optimal s...