The relative isoperimetric inequality for minimal submanifolds with free
boundary in the Euclidean space
February 3, 2020
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Mathematics
Differential Geometry
Analysis of PDEs
In this paper, we mainly consider the relative isoperimetric inequalities for
minimal submanifolds with free boundary. We first generalize ideas of
restricted normal cones introduced by Choe-Ghomi-Ritor\'e in \cite{CGR06} and
obtain an opti...
Operations on the Hochschild Bicomplex of a Diagram of Algebras
February 3, 2020
Mathematics
Category Theory
Algebraic Topology
Rings and Algebras
A diagram of algebras is a functor valued in a category of associative
algebras. I construct an operad acting on the Hochschild bicomplex of a diagram
of algebras. Using this operad, I give a direct proof that the Hochschild
cohomology of a...
On the Erd\H{o}s distance problem
February 2, 2020
Mathematics
Metric Geometry
Combinatorics
Number Theory
In this paper, using the method of compression, we recover the lower bound
for the Erd\H{o}s unit distance problem and provide an alternative proof to the
distinct distance conjecture. In particular, we show that for sets of points
$\mathbb...
Estimating Welfare Effects in a Nonparametric Choice Model: The Case of
School Vouchers
January 31, 2020
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Economics
Quantitative Finance
General Economics
Econometrics
Economics
We develop new robust discrete choice tools to learn about the average
willingness to pay for a price subsidy and its effects on demand given
exogenous, discrete variation in prices. Our starting point is a nonparametric,
nonseparable model...
Smooth Solutions of the Navier-Stokes Equation in Lp(R3)
January 31, 2020
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Mathematics
General Mathematics
In this paper we prove that if we take to be identically zero and assume that
any initial value satisfies on for any and then the Navier-Stokes initial value
problem (1) have a smooth global solution , with bounded energy....
Macroscopic loops in the loop O(n) model via the XOR trick
January 31, 2020
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Mathematics
Physics
Probability
Mathematical Physics
Mathematical Physics
The loop O(n) model is a family of probability measures on collections of
non-intersecting loops on the hexagonal lattice, parameterized by a loop-weight
n and an edge-weight x. Nienhuis predicts that, for 0≤n≤2, the
model...
A Review of Blockchain-based Smart Grid: Applications,Opportunities, and
Future Directions
January 31, 2020
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Computer Science
Computers and Society
The Smart Grid (SG) concept presented an unprecedented opportunity to move
the energy sector to more availability, reliability, and efficiency to improve
our economic and environmental conditions. Renewable energy sources (Solar &
Wind) are...
Zeta Functions and the (Linear) Logic of Markov Processes
January 31, 2020
Computer Science
Mathematics
Logic in Computer Science
Dynamical Systems
Logic
Probability
The author introduced models of linear logic known as ''Interaction Graphs''
which generalise Girard's various geometry of interaction constructions. In
this work, we establish how these models essentially rely on a deep connection
between ...
Solvability for non-smooth Schr\"{o}dinger equations with singular
potentials and square integrable data
January 31, 2020
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Mathematics
Analysis of PDEs
Classical Analysis and ODEs
We develop a holomorphic functional calculus for first-order operators DB
to solve boundary value problems for Schr\"{o}dinger equations −divA∇u+aVu=0 in the upper half-space R+n+1 with
$n\in\math...
On dp-minimal expansions of the integers
January 30, 2020
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Mathematics
Logic
Logic
We show that if Z is a dp-minimal expansion of (Z,+,0,1) that defines an infinite subset of N, then Z is interdefinable with (Z,+,0,1,<). As a coroll...