2,252 research outputs found
The Bohr radius of the -dimensional polydisk is equivalent to
We show that the Bohr radius of the polydisk behaves
asymptotically as . Our argument is based on a new
interpolative approach to the Bohnenblust--Hille inequalities which allows us
to prove that the polynomial Bohnenblust--Hille inequality is subexponential.Comment: The introduction was expanded and some misprints correcte
Importance of interlinguistic similarity and stable bilingualism when two languages compete
In order to analyze the dynamics of two languages in competition, one
approach is to fit historical data on their numbers of speakers with a
mathematical model in which the parameters are interpreted as the similarity
between those languages and their relative status. Within this approach, we
show here, on the basis of a detailed analysis and extensive calculations, the
outcomes that can emerge for given values of these parameters. Contrary to
previous results, it is possible that in the long term both languages coexist
and survive. This happens only when there is a stable bilingual group, and this
is possible only if the competing languages are sufficiently similar, in which
case its occurrence is favoured by both similarity and status symmetry.Comment: to appear in New Journal of Physic
When is the Haar measure a Pietsch measure for nonlinear mappings?
We show that, as in the linear case, the normalized Haar measure on a compact
topological group is a Pietsch measure for nonlinear summing mappings on
closed translation invariant subspaces of . This answers a question posed
to the authors by J. Diestel. We also show that our result applies to several
well-studied classes of nonlinear summing mappings. In the final section some
problems are proposed
A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities
The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved
in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet
series. Since then these inequalities have found applications in various fields
of analysis and analytic number theory. The control of the constants involved
is crucial for applications, as it became evident in a recent outstanding paper
of Defant, Frerick, Ortega-Cerd\'{a}, Ouna\"{\i}es and Seip published in 2011.
The present work is devoted to obtain lower estimates for the constants
appearing in the Bohnenblust--Hille polynomial inequality and some of its
variants. The technique that we introduce for this task is a combination of the
Krein--Milman Theorem with a description of the geometry of the unit ball of
polynomial spaces on .Comment: This preprint does no longer exist as a single manuscript. It is now
part of the preprint entitled "The optimal asymptotic hypercontractivity
constant of the real polynomial Bohnenblust-Hille inequality is 2" (arXiv
reference 1209.4632
Low-temperature anomalies of a vapor deposited glass
We investigate the low temperature properties of two-dimensional
Lennard-Jones glass films, prepared in silico both by liquid cooling and by
physical vapor deposition. We identify deep in the solid phase a crossover
temperature , at which slow dynamics and enhanced heterogeneity emerge.
Around , localized defects become visible, leading to vibrational
anomalies as compared to standard solids. We find that on average,
decreases in samples with lower inherent structure energy, suggesting that such
anomalies will be suppressed in ultra-stable glass films, prepared both by very
slow liquid cooling and vapor deposition.Comment: 10 pages including appendices, 8 figures. Version accepted for
Physical Review Material
Multiplicative structures of hypercyclic functions for convolution operators
In this note, it is proved the existence of an infinitely generated
multiplicative group consisting of entire functions that are, except for the
constant function 1, hypercyclic with respect to the convolution operator
associated to a given entire function of subexponential type. A certain
stability under multiplication is also shown for compositional hypercyclicity
on complex domains.Comment: 12 page
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