6,486 research outputs found
Free pluriharmonic majorants and noncommutative interpolation
In this paper, we initiate the study of sub-pluriharmonic curves in
Cuntz-Toeplitz algebras and free pluriharmonic majorants on noncommutative
balls. We are lead to a characterization of the noncommutative Hardy space
in terms of free pluriharmonic majorants, and to a Schur type
description of the unit ball of . These results are used to
solve a multivariable commutant lifting problem and provide a description of
all solutions.Comment: 35 page
From p-adic to real Grassmannians via the quantum
Let F be a local field. The action of GL(n,F) on the Grassmann variety
Gr(m,n,F) induces a continuous representation of the maximal compact subgroup
of GL(n,F) on the space of L^2-functions on Gr(m,n,F). The irreducible
constituents of this representation are parameterized by the same underlying
set both for Archimedean and non-Archimedean fields.
This paper connects the Archimedean and non-Archimedean theories using the
quantum Grassmannian. In particular, idempotents in the Hecke algebra
associated to this representation are the image of the quantum zonal spherical
functions after taking appropriate limits. Consequently, a correspondence is
established between some irreducible representations with Archimedean and
non-Archimedean origin.Comment: 24 pages, final version, to appear in Advances in Mathematic
Extending Functional kriging to a multivariate context
Environmental data usually have a spatio-temporal structure; pollutant concentrations, for example, are recorded along time and space. Generalized Additive Models (GAMs) represent a suitable tool to model spatial and/or temporal trends of this kind of data, that can be treated as functional, although they are collected as discrete observations. Frequently, the attention is focused on the prediction of a single pollutant at an unmonitored site and, at this aim, we extend kriging for functional data to a multivariate context by exploiting the correlation with the other pollutants. In particular, we propose two procedures: the first one (FKED) combines the regression of a variable (pollutant), of primary interest on the other variables, with functional kriging of the regression residuals; the second one (FCK) is based on linear unbiased prediction of spatially correlated multivariate random processes. The performance of the two proposed procedures is assessed by cross validation; data recorded during a year (2011) from the monitoring network of the state of California (USA) are considered
If Archimedes would have known functions
These are notes and slides from a Pecha-Kucha talk given on March 6, 2013.
The presentation tinkered with the question whether calculus on graphs could
have emerged by the time of Archimedes, if the concept of a function would have
been available 2300 years ago. The text first attempts to boil down discrete
single and multivariable calculus to one page each, then presents the slides
with additional remarks and finally includes 40 "calculus problems" in a
discrete or so-called 'quantum calculus' setting. We also added some sample
Mathematica code, gave a short overview over the emergence of the function
concept in calculus and included comments on the development of calculus
textbooks over time.Comment: 31 pages, 36 figure
Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy
We update gamma-ray burst (GRB) luminosity relations among certain spectral
and light-curve features with 139 GRBs. The distance modulus of 82 GRBs at
can be calibrated with the sample at by using the cubic
spline interpolation method from the Union2.1 Type Ia supernovae (SNe Ia) set.
We investigate the joint constraints on the Cardassian expansion model and dark
energy with 580 Union2.1 SNe Ia sample () and 82 calibrated GRBs data
(). In CDM, we find that adding 82 high-\emph{z} GRBs to
580 SNe Ia significantly improves the constrain on
plane. In the Cardassian expansion model, the
best fit is and
, which is consistent with the CDM cosmology in the
confidence region. We also discuss two dark energy models in which
the equation of state is parametrized as and
, respectively. Based on our analysis, we see that our
Universe at higher redshift up to is consistent with the concordance
model within confidence level.Comment: 17 pages, 6 figures, 2 tables; accepted for publication in Advances
in Astronomy, special issue on Gamma-Ray Burst in Swift and Fermi Era. arXiv
admin note: text overlap with arXiv:0802.4262, arXiv:0706.0938 by other
author
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined
- …