Unique continuation for many-body Schr\"odinger operators and the
Hohenberg-Kohn theorem. II. The Pauli Hamiltonian
January 10, 2019
Physics
Mathematics
Mathematical Physics
Analysis of PDEs
Mathematical Physics
Quantum Physics
We prove the strong unique continuation property for many-body Pauli
operators with external potentials, interaction potentials and magnetic fields
in L^p\loc(\R^d), and with magnetic potentials in {L^{q}\loc(\R^d)}, where
${p > \max(2d...
Understanding the Topology and the Geometry of the Space of Persistence
Diagrams via Optimal Partial Transport
January 10, 2019
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Computer Science
Mathematics
Computational Geometry
Geometric Topology
Despite the obvious similarities between the metrics used in topological data
analysis and those of optimal transport, an optimal-transport based formalism
to study persistence diagrams and similar topological descriptors has yet to
come. I...
Private Information Retrieval from Locally Repairable Databases with
Colluding Servers
January 9, 2019
Computer Science
Mathematics
Information Theory
Information Theory
We consider information-theoretical private information retrieval (PIR) from
a coded database with colluding servers. We target, for the first time, locally
repairable storage codes (LRCs). We consider any number of local groups g,
loca...
Internet of Things Security, Device Authentication and Access Control: A
Review
January 8, 2019
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Computer Science
Cryptography and Security
Distributed, Parallel, and Cluster Computing
Cryptography and Security
Distributed, Parallel, and Cluster Computing
The Internet of Things (IoT) is one of the emerging technologies that has
grabbed the attention of researchers from academia and industry. The idea
behind Internet of things is the interconnection of internet enabled things or
devices to ea...
Normalized ground states for the NLS equation with combined
nonlinearities: the Sobolev critical case
January 7, 2019
|
Mathematics
Analysis of PDEs
Analysis of PDEs
We study existence and properties of ground states for the nonlinear
Schr\"odinger equation with combined power nonlinearities −Δu=λu+μ∣u∣q−2u+∣u∣2∗−2uin RN, N≥3, having p...
Square function inequality for oscillatory integral operators satisfying
homogeneous Carleson-Sj\"olin type conditions
January 5, 2019
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Mathematics
Analysis of PDEs
In this paper, we establish an improved variable coefficient version of
square function inequality, by which the local smoothing estimate
Lαp→Lp for the Fourier integral operators satisfying
cinematic curvature conditio...
Regularity, singularities and h-vector of graded algebras
January 4, 2019
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Mathematics
Commutative Algebra
Algebraic Geometry
Let R be a standard graded algebra over a field. We investigate how the
singularities of R affect its h-vector, which is the coefficients of the
numerator of its Hilbert series. The most concrete consequences of our work
asserts that ...
Online Monitoring of Metric Temporal Logic using Sequential Networks
January 1, 2019
Computer Science
Logic in Computer Science
Formal Languages and Automata Theory
Metric Temporal Logic (MTL) is a popular formalism to specify temporal
patterns with timing constraints over the behavior of cyber-physical systems
with application areas ranging in property-based testing, robotics,
optimization, and learni...
On the zeros of sum from n=1 to 00 of lambda_P(n)/n^s
December 31, 2018
|
Mathematics
Number Theory
Our main result is to answer a question of Michel Balazard by giving a
Dirichlet series with only one zero in its half-plane of convergence. At the
end of the paper we also give several sufficient conditions for the Generalized
Riemann Hypo...
Lattice of the dual of an Anderson t-motive in terms of Siegel
matrices of its flag variety
December 30, 2018
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Mathematics
Number Theory
Number Theory
Let M be an uniformizable Anderson t-motive. We can describe its lattice
as an element of the maximal Schubert cell of a (generalized) flag variety.
This element (called a Siegel element) is a set of matrices parametrized by
integer poi...