Recognizing Visibility Graphs of Polygons with Holes and
Internal-External Visibility Graphs of Polygons
April 13, 2018
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Computer Science
Computational Complexity
Computational Geometry
Visibility graph of a polygon corresponds to its internal diagonals and
boundary edges. For each vertex on the boundary of the polygon, we have a
vertex in this graph and if two vertices of the polygon see each other there is
an edge betwee...
Symmetry operators and generation of symmetry transformations of partial
differential equations
April 12, 2018
Mathematics
Analysis of PDEs
The study of symmetries of partial differential equations (PDEs) has been
traditionally treated as a geometrical problem. Although geometrical methods
have been proven effective with regard to finding infinitesimal symmetry
transformations,...
Convex fair partitions into an arbitrary number of pieces
April 9, 2018
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Mathematics
Metric Geometry
Algebraic Topology
Combinatorics
We prove that any convex body in the plane can be partitioned into m convex
parts of equal areas and perimeters for any integer m≥2; this result was
previously known for prime powers m=pk. We also discuss possible
higher-dimension...
Improved effective estimates of P\'olya's Theorem for quadratic forms
April 8, 2018
Mathematics
Algebraic Geometry
Following de Loera and Santos, the P\'olya exponent of a n-ary real form
(i.e. a homogeneous polynomial in n variables with real coefficients) f is
the infimum of the upward closed set of nonnegative integers m such that
$(x_1 + \cd...
Generating Functions in R2n and the Hatcher-Waldhausen map
April 7, 2018
Mathematics
Symplectic Geometry
Algebraic Topology
K-Theory and Homology
In this paper we construct a generating function quadratic at infinity for
any exact Lagrangian in R2n equal to Rn outside a
compact set. This type of Lagrangian is equivalent to a Lagrangian filling in
D2n of t...
ResFrac Technical Writeup
April 5, 2018
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Physics
Geophysics
Computational Physics
ResFrac is a combined hydraulic fracturing, reservoir, and hydraulic
fracturing simulator. It describes multiphase fluid flow (black oil or
compositional), proppant transport, transport of non-Newtonian fluid additives,
and thermal transpor...
Nonexistence of generalized bent functions and the quadratic norm form
equations
April 4, 2018
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Computer Science
Mathematics
Information Theory
Information Theory
Number Theory
Information Theory
Information Theory
Number Theory
We present a new result on the nonexistence of generalized bent functions
(GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is
an odd prime number. By showing certain quadratic norm form equations having no
integr...
Average non-vanishing of Dirichlet L-functions at the central point
April 4, 2018
Mathematics
Number Theory
The Generalized Riemann Hypothesis implies that at least 50% of the central
values L(21,χ) are non-vanishing as χ ranges
over primitive characters modulo q. We show that one may unconditionally go
beyond GR...
Distributed Online Optimization for Multi-Agent Optimal Transport
April 4, 2018
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Mathematics
Optimization and Control
We propose a scalable, distributed algorithm for the optimal transport of
large-scale multi-agent systems. We formulate the problem as one of steering
the collective towards a target probability measure while minimizing the total
cost of tr...
An investigation of the non-trivial zeros of the Riemann zeta function
April 4, 2018
Mathematics
General Mathematics
While many zeros of the Riemann zeta function are located on the critical
line ℜ(s)=1/2, the non-existence of zeros in the remaining part of the
critical strip ℜ(s)∈]0,1[ is the main scope to be proven for the
Riemann hypoth...