Let ABC be an equilateral triangle. For certain triangles T (the "tile")
and certain N, it is possible to cut ABC into N copies of T. It is
known that only certain shapes of T are possible, but until now very little
was known ...
Hamiltonian cubic bipartite graphs
December 16, 2018
Mathematics
General Mathematics
We provide a polynomial time algorithm to determine a cubic bipartite graph
has a hamilton cycle or not....
Points accessible in average by rearrangement of sequences
December 14, 2018
Mathematics
Classical Analysis and ODEs
We investigate the set of limit points of averages of rearrangements of a
given sequence. We study how the properties of the sequence determine the
structure of that set and what type of sets we can expect as the set of such
accessible poin...
Posterior Projection for Inference in Constrained Spaces
December 13, 2018
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Statistics
Methodology
Methodology
Estimation of parameters that obey specific constraints is crucial in
statistics and machine learning; for example, when parameters are required to
satisfy boundedness, monotonicity, or linear inequalities. Traditional
approaches impose the...
Some proofs of the Poincar\'e-Birkhoff-Witt theorem and related matters
December 12, 2018
Mathematics
Rings and Algebras
This expository paper focuses on free Lie K-algebras and the basic PBW
theorem. We argue in various ways that the basic PBW theorem is a quite close
consequence of the Magnus-Witt theorems concerning free Lie algebras....
Solutions to a moving boundary problem on the Boltzmann equation
December 11, 2018
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Mathematics
Analysis of PDEs
Analysis of PDEs
Motivated by the numerical investigation by Aoki et al. [1], we study a
rarefied gas flow between two parallel infinite plates of the same temperature
governed by the Boltzmann equation with diffuse reflection boundaries, where
one plate is...
On the final limit of a transition matrix
December 11, 2018
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Mathematics
Classical Analysis and ODEs
Probability
Classical Analysis and ODEs
Probability
An efficient algorithm is presented for computation of the limit of exp(t A)
for t towards infinity where A denotes an intensity matrix of finite dimension....
Avatars of Margulis invariants and proper actions
December 10, 2018
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Mathematics
Geometric Topology
Differential Geometry
Dynamical Systems
Geometric Topology
Differential Geometry
Dynamical Systems
In this article, we provide a necessary and sufficient criterion for proper
actions on Hn,n−1 in terms of certain special Anosov
representations in SO(n,n). Moreover, we show that affine Anosov
representations of an...
The spectra of generalized Paley graphs of (qℓ+1)-th powers and
applications
December 8, 2018
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Mathematics
Combinatorics
Combinatorics
We consider a special class of generalized Paley graphs over finite fields,
namely the Cayley graphs with vertex set Fqm and connection set
the nonzero (qℓ+1)-th powers in Fqm, as well as their
complement...
Perpetual cutoff method and discrete Ricci curvature bounds with
exceptions
December 6, 2018
Mathematics
Differential Geometry
One of the main obstacles regarding Barky Emery curvature on graphs is that
the results require a global uniform lower curvature bounds where no exception
sets are allowed. We overcome this obstacle by introducing the perpetual cutoff
metho...