7,308 research outputs found
Some extremal functions in Fourier analysis, II
We obtain extremal majorants and minorants of exponential type for a class of
even functions on which includes and , where . We also give periodic versions of these results in which the
majorants and minorants are trigonometric polynomials of bounded degree. As
applications we obtain optimal estimates for certain Hermitian forms, which
include discrete analogues of the one dimensional Hardy-Littlewood-Sobolev
inequalities. A further application provides an Erd\"{o}s-Tur\'{a}n-type
inequality that estimates the sup norm of algebraic polynomials on the unit
disc in terms of power sums in the roots of the polynomials.Comment: 40 pages. Accepted for publication in Trans. Amer. Math. So
Gaussian Subordination for the Beurling-Selberg Extremal Problem
We determine extremal entire functions for the problem of majorizing,
minorizing, and approximating the Gaussian function by
entire functions of exponential type. This leads to the solution of analogous
extremal problems for a wide class of even functions that includes most of the
previously known examples (for instance \cite{CV2}, \cite{CV3}, \cite{GV} and
\cite{Lit}), plus a variety of new interesting functions such as
for ; \,, for
;\, ; and \,, for . Further applications to number theory include optimal
approximations of theta functions by trigonometric polynomials and optimal
bounds for certain Hilbert-type inequalities related to the discrete
Hardy-Littlewood-Sobolev inequality in dimension one
Tunable pinning of a superconducting vortex a by a magnetic vortex
The interaction between a straight vortex line in a superconducting film and
a soft magnetic nanodisk in the magnetic vortex state in the presence of a
magnetic field applied parallel to the film surfaces is studied theoretically.
The superconductor is described by London theory and the nanodisk by the
Landau-Lifshitz continuum theory of magnetism, using the approximation known as
the rigid vortex model. Pinning of the vortex line by the nanodisk is found to
result, predominantly, from the interaction between the vortex line and the
changes in the nanodisk magnetization induced by the magnetic field of the
vortex line and applied field. In the context of the rigid vortex model, these
changes result from the displacement of the magnetic vortex. This displacement
is calculated analytically by minimizing the energy, and the pinning potential
is obtained. The applied field can tune the pinning potential by controlling
the displacement of the magnetic vortex. The nanodisk magnetization curve is
predicted to change in the presence of the vortex lineComment: 9 pages, 8 figures. Submitted to Phys. Rev.
A Note on Tachyon Moduli and Closed Strings
The collective behavior of the SL(2,R) covariant brane states of non-critical
c=1 string theory found in a previous work, is studied in the Fermi liquid
approximation. It is found that such states mimick the coset WZW model, whereas
only by further restrictions one recovers the double-scaling limit which was
purported to be equivalent to closed string models. Another limit is proposed,
inspired by the tachyon condensation ideas, where the spectrum is the same of
two-dimensional string theory. We close by noting some strange connections
between vacuum states of the theory in their different interpretations.Comment: PDFLaTeX, 17 pages, 2 figures; Section 2 rewritten, several fixes
throughout the text to improve clarit
Quantification of reachable attractors in asynchronous discrete dynamics
Motivation: Models of discrete concurrent systems often lead to huge and
complex state transition graphs that represent their dynamics. This makes
difficult to analyse dynamical properties. In particular, for logical models of
biological regulatory networks, it is of real interest to study attractors and
their reachability from specific initial conditions, i.e. to assess the
potential asymptotical behaviours of the system. Beyond the identification of
the reachable attractors, we propose to quantify this reachability.
Results: Relying on the structure of the state transition graph, we estimate
the probability of each attractor reachable from a given initial condition or
from a portion of the state space. First, we present a quasi-exact solution
with an original algorithm called Firefront, based on the exhaustive
exploration of the reachable state space. Then, we introduce an adapted version
of Monte Carlo simulation algorithm, termed Avatar, better suited to larger
models. Firefront and Avatar methods are validated and compared to other
related approaches, using as test cases logical models of synthetic and
biological networks.
Availability: Both algorithms are implemented as Perl scripts that can be
freely downloaded from http://compbio.igc.gulbenkian.pt/nmd/node/59 along with
Supplementary Material.Comment: 19 pages, 2 figures, 2 algorithms and 2 table
Toward in vitro fertilization in Brachiaria spp.
Brachiaria are forage grasses widely cultivated in tropical areas. In vitro pollination was applied to accessions of Brachiaria spp. by placing pollen of non-dehiscent anthers on a solid medium near isolated ovaries. Viability and in vitro germination were tested in order to establish good conditions for pollen development. Comparing sexual to apomictic plants, apomictic pollen has more abortion after meiosis during the microspore stage and a lower viability and, of both types, only some plants have sufficient germination in a high sugar concentration. Using in vitro pollination with the sexual plant, the pollen tube penetrates into the nucellus and micropyle, but the embryo sac degenerates and collapses. In the apomictic B. decumbens, in vitro pollination leads to the transfer of the sperm nuclei into the egg cell and the central cell. The results are discussed according to normal fertilization and barriers in sexual and apomictic plants
On Useful Conformal Tranformations In General Relativity
Local conformal transformations are known as a useful tool in various
applications of the gravitational theory, especially in cosmology. We describe
some new aspects of these transformations, in particular using them for
derivation of Einstein equations for the cosmological and Schwarzschild
metrics. Furthermore, the conformal transformation is applied for the
dimensional reduction of the Gauss-Bonnet topological invariant in to the
spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical
purposes and represents a collection of exercises concerning local conformal
transformations and dimensional reduction. To be published in "Gravitation
and Cosmology
Developing intelligent environments with OSGi and JADE
Series: IFIP International Federation for Information ProcessingThe development of intelligent environments poses complex
challenges, namely at the level of device heterogeneity and environment
dynamics. In fact, we still lack supporting technologies and development
approaches that can efficiently integrate different devices and technologies. In
this paper we present how a recent integration of two important technologies,
OSGi and Jade, can be used to significantly improve the development process,
making it a more dynamic, modular and configurable one. We also focus on the
main advantages that this integration provides to developers, from the Ambient
Intelligence point of view. This work results from the development of two
intelligent environments: VirtualECare, which is an intelligent environment for
the monitorization of elderly in their homes and UMCourt, a virtual
environment for dispute resolution.The work described in this paper is included in TIARAC -
Telematics and Artificial Intelligence in Alternative Conflict Resolution Project
(PTDC/JUR/71354/2006), which is a research project supported by FCT (Science &
Technology Foundation), Portugal
Equality of opportunity and educational achievement in Portugal
Portugal has one of the highest levels of income inequality in Europe, and low wages and unemployment are concentrated among low skill individuals. Education is an important determinant of inequality. However, there are large differences in the educational attainment of different individuals in the population, and the sources of these differences emerge early in the life-cycle when families play a central role in individual development. We estimate that most of the variance of school achievement at age 15 is explained by family characteristics. Observed school inputs explain very little of adolescent performance. Children from highly educated parents benefit of rich cultural environments in the home and become highly educated adults. Education policy needs to be innovative: (1) it needs to explicitly recognize the fundamental long run role of families on child development; (2) it needs to acknowledge the failure of traditional input based policies
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