A multi-Frey approach to Fermat equations of signature (r,r,p)
March 19, 2017
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Mathematics
Number Theory
In this paper, we give a resolution of the generalized Fermat equations x5+y5=3zn and x13+y13=3zn, for all integers n≥2, and all integers n≥2 which are not a multiple of 7, respectively,
using ...
Hasse-Minkowski theorem for quadratic forms on groups
March 17, 2017
Mathematics
Number Theory
Consider groups such as Mordell-Weil groups of abelian varieties over number
fields, odd algebraic K-theory groups of number fields, or finitely generated
subgroups of the multiplicative groups of number fields. They are all equipped
with...
Decompositions of surface flows
March 16, 2017
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Mathematics
Dynamical Systems
Dynamical Systems
Flows on surfaces are one of the most fundamental and classical objects in
dynamical systems, and are studied from various areas (e.g. integrable systems,
differential equations, fluid mechanics). Though hyperbolic flows and recurrent
flows...
Yet another introduction to relativistic astrophysics
March 16, 2017
Physics
High Energy Astrophysical Phenomena
General Relativity and Quantum Cosmology
Late Winter Lecture Notes, Short Course (10 hours) of Relativistic
Astrophysics held at the Department of Physics and Astronomy of the University
of Padova, March 13-17, 2017. Third version....
Shift Aggregate Extract Networks
March 16, 2017
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Computer Science
Statistics
Machine Learning
Machine Learning
We introduce an architecture based on deep hierarchical decompositions to
learn effective representations of large graphs. Our framework extends classic
R-decompositions used in kernel methods, enabling nested part-of-part
relations. Unlike...
An Evolutionary Theory for the Variability Hypothesis
March 12, 2017
Quantitative Biology
Populations and Evolution
An elementary biostatistical theory based on a selectivity-variability
principle is proposed to address a question raised by Charles Darwin, namely,
how one sex of a sexually dimorphic species might tend to evolve with greater
variability t...
On the Origin of Inertia: Implications for Dark Matter and Dark Energy
March 8, 2017
Physics
General Physics
In this paper, we present a new theory explaining the origin of inertia based
on two key ideas: gravity as a spin-1 gauge field theory and the relativity of
all kinds of motion. This theory proposes that inertial mass is influenced by
the d...
Noncommutative-geometry inspired charged wormholes with low tidal forces
March 8, 2017
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Physics
General Relativity and Quantum Cosmology
When Morris and Thorne first proposed that wormholes might be actual physical
structures suitable for interstellar travel, they needed to pay close attention
to certain traversability conditions such as low tidal forces, which placed
severe...
A lower bound for Heilbronn's triangle-problem
March 8, 2017
Mathematics
Number Theory
Metric Geometry
Let n points be placed on a closed convex domain on the plane, no three
points on a straight line. A conjecture by H. A. Heilbronn (before 1950) stated
that on the convex domain of unit area the smallest triangle defined by these
points has...
Rational singularities
March 7, 2017
Mathematics
Algebraic Geometry
A resolution-free definition of rational singularities is introduced, and it
is proved that for a variety admitting a resolution of singularities, so in
particular in characteristic zero, this is equivalent to the usual definition.
It is al...