Augmented Lagrangian Functions for Cone Constrained Optimization: the
Existence of Global Saddle Points and Exact Penalty Property
July 18, 2017
Mathematics
Optimization and Control
In the article we present a general theory of augmented Lagrangian functions
for cone constrained optimization problems that allows one to study almost all
known augmented Lagrangians for cone constrained programs within a unified
framework...
A chronology of continued square roots and other continued compositions,
through the year 2016
July 17, 2017
Mathematics
History and Overview
Classical Analysis and ODEs
An infinite continued composition is an expression of the form
\begin{equation*} \lim_{n\to\infty}t_0\circ t_1 \circ t_2 \circ \cdots \circ
t_n(c)\;, \end{equation*} where the ti are maps from a set D to itself,
the initial value c i...
An extension of the Erd\H{o}s-Tur\'{a}n additive base conjecture via
generalized circles of partition
July 16, 2017
Mathematics
Number Theory
This paper is an extension program of the notion of circle of partition
developed in our first paper \cite{CoP}. As an application we prove the
Erd\H{o}s-Tur\'{a}n additive base conjecture....
A technique for solving the polygon inclusion problems
July 13, 2017
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Computer Science
Computational Geometry
We propose a technique called Rotate-and-Kill for solving the polygon
inclusion and circumscribing problems. By applying this technique, we obtain
O(n) time algorithms for computing (1) the maximum area triangle in a given
n-sided conve...
Phonon and electronic properties of semiconducting silicon nitride
bilayers
July 10, 2017
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Physics
Materials Science
The two-dimensional (2D) IV-V semiconductors have attracted much attention
due to their fascinating electronic and optical properties. In this work, we
predicted three phases of silicon nitrides, denoted α-Si2N2,
β-Si...
Ramsey expansions of metrically homogeneous graphs
July 9, 2017
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Mathematics
Computer Science
Combinatorics
Discrete Mathematics
Logic
We investigate Ramsey expansions, the coherent extension property for partial
isometries (EPPA), and the existence of a stationary independence relation for
all classes of metrically homogeneous graphs from Cherlin's catalogue. We show
that...
Facilitated exclusion process
July 6, 2017
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Mathematics
Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
We study the Facilitated TASEP, an interacting particle system on the one
dimensional integer lattice. We prove that starting from step initial
condition, the position of the rightmost particle has Tracy Widom GSE
statistics on a cube root ...
Anomaly cancellation by generalised cohomology
July 4, 2017
Physics
High Energy Physics - Theory
Supersymmetric states in M-theory are mapped after compactification to
perturbatively non-supersymmetric states in type IIA string theory, with the
supersymmetric parts being encoded in the non-perturbative section of the
string theory. An ...
Utility maximization in constrained and unbounded financial markets:
Applications to indifference valuation, regime switching, consumption and
Epstein-Zin recursive utility
July 1, 2017
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Mathematics
Quantitative Finance
Probability
Mathematical Finance
This memoir presents a systematic study of utility maximization problems for
an investor in constrained and unbounded financial markets. Building upon the
foundational work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a
bound...
Schubert puzzles and integrability I: invariant trilinear forms
June 30, 2017
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Mathematics
Physics
Combinatorics
Mathematical Physics
Algebraic Geometry
Mathematical Physics
The puzzle rules for computing Schubert calculus on d-step flag manifolds,
proven in [Knutson Tao 2003] for 1-step, in [Buch Kresch Purbhoo Tamvakis
2016] for 2-step, and conjectured in [Coskun Vakil 2009] for 3-step, lead
to vector...