208 research outputs found
Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type
theorem) for homogeneous polynomials on , and improve bounds on
the number in the analogous conjecture for odd degrees (this case
is known as the Birch theorem) and complex polynomials. We also consider a
stronger conjecture on the homogeneous polynomial fields in the canonical
bundle over real and complex Grassmannians. This conjecture is much stronger
and false in general, but it is proved in the cases of (for 's of
certain type), odd , and the complex Grassmannian (for odd and even and
any ). Corollaries for the John ellipsoid of projections or sections of a
convex body are deduced from the case of the polynomial field conjecture
First principles simulations of direct coexistence of solid and liquid aluminium
First principles calculations based on density functional theory, with
generalised gradient corrections and ultrasoft pseudopotentials, have been used
to simulate solid and liquid aluminium in direct coexistence at zero pressure.
Simulations have been carried out on systems containing up to 1000 atoms for 15
ps. The points on the melting curve extracted from these simulations are in
very good agreement with previous calculations, which employed the same
electronic structure method but used an approach based on the explicit
calculation of free energies [L. Vo\v{c}adlo and D. Alf\`e, Phys. Rev. B, {\bf
65}, 214105 (2002).]Comment: To appear in Phys. Rev.
Elliptic curves of large rank and small conductor
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the
smallest conductor known, improving on the previous records by factors ranging
from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search
methods, and tabulate, for each r=5,6,...,11, the five curves of lowest
conductor, and (except for r=11) also the five of lowest absolute discriminant,
that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the
Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after
comments by J.Silverman on the previous draft, and again to get the correct
page break
Regulator constants and the parity conjecture
The p-parity conjecture for twists of elliptic curves relates multiplicities
of Artin representations in p-infinity Selmer groups to root numbers. In this
paper we prove this conjecture for a class of such twists. For example, if E/Q
is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p
extension, then the p-parity conjecture holds for twists of E by all orthogonal
Artin representations of Gal(K^\infty/Q). We also give analogous results when
K/Q is non-abelian, the base field is not Q and E is replaced by an abelian
variety. The heart of the paper is a study of relations between permutation
representations of finite groups, their "regulator constants", and
compatibility between local root numbers and local Tamagawa numbers of abelian
varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat
Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve
{\em Ab initio} techniques based on density functional theory in the
projector-augmented-wave implementation are used to calculate the free energy
and a range of other thermodynamic properties of liquid iron at high pressures
and temperatures relevant to the Earth's core. The {\em ab initio} free energy
is obtained by using thermodynamic integration to calculate the change of free
energy on going from a simple reference system to the {\em ab initio} system,
with thermal averages computed by {\em ab initio} molecular dynamics
simulation. The reference system consists of the inverse-power pair-potential
model used in previous work. The liquid-state free energy is combined with the
free energy of hexagonal close packed Fe calculated earlier using identical
{\em ab initio} techniques to obtain the melting curve and volume and entropy
of melting. Comparisons of the calculated melting properties with experimental
measurement and with other recent {\em ab initio} predictions are presented.
Experiment-theory comparisons are also presented for the pressures at which the
solid and liquid Hugoniot curves cross the melting line, and the sound speed
and Gr\"{u}neisen parameter along the Hugoniot. Additional comparisons are made
with a commonly used equation of state for high-pressure/high-temperature Fe
based on experimental data.Comment: 16 pages including 6 figures and 5 table
An exploratory study on the potential of social enterprise to act as the institutional glue of network governance
This study combines two topics of contemporary salience for public administration: social enterprise and governance networks. While operating at different levels, both are institutions which attempt to draw together the three pillars of state, market, and civil society. Nevertheless, the respective literatures focus on particular aspects of the three pillars. We connect the two concepts and suggest that some social enterprises can act as the institutional glue of networks due to their ability to benefit organizations in each of the three sectors. This requires social enterprises to have the managerial capacity to diffuse social know-how, and is facilitated by the trust of other organizations and a supportive policy framework. The links are explicated at the conceptual level before providing evidence from South Korea and the UK. Finally, research propositions are offered, which suggest new avenues for future research
Portion Size: What We Know and What We Need to Know
There is increasing evidence that the portion sizes of many foods have increased and in a laboratory at least this increases the amount eaten. The conclusions are, however, limited by the complexity of the phenomenon. There is a need to consider meals freely chosen over a prolonged period when a range of foods of different energy densities are available. A range of factors will influence the size of the portion size chosen: amongst others packaging, labeling, advertising, and the unit size rather than portion size of the food item. The way portion size interacts with the multitude of factors that determine food intake needs to be established. In particular, the role of portion size on energy intake should be examined as many confounding variables exist and we must be clear that it is portion size that is the major problem. If the approach is to make a practical contribution, then methods of changing portion sizes will need to be developed. This may prove to be a problem in a free market, as it is to be expected that customers will resist the introduction of smaller portion sizes, given that value for money is an important motivator
Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study
A41 Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study
In: Addiction Science & Clinical Practice 2017, 12(Suppl 1): A4
Description of Atmospheric Conditions at the Pierre Auger Observatory using the Global Data Assimilation System (GDAS)
Atmospheric conditions at the site of a cosmic ray observatory must be known
for reconstructing observed extensive air showers. The Global Data Assimilation
System (GDAS) is a global atmospheric model predicated on meteorological
measurements and numerical weather predictions. GDAS provides
altitude-dependent profiles of the main state variables of the atmosphere like
temperature, pressure, and humidity. The original data and their application to
the air shower reconstruction of the Pierre Auger Observatory are described. By
comparisons with radiosonde and weather station measurements obtained on-site
in Malarg\"ue and averaged monthly models, the utility of the GDAS data is
shown
All-sky search for long-duration gravitational wave transients with initial LIGO
We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4Ă10-5 and 9.4Ă10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society
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