59,280 research outputs found
Stable divisorial gonality is in NP
Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph can be defined with help of a chip firing game on . The stable
divisorial gonality of is the minimum divisorial gonality over all
subdivisions of edges of .
In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with
vertices is bounded by for a polynomial
Air speed and attitude probe
An air speed and attitude probe characterized by a pivot shaft normally projected from a data boom and supported thereby for rotation about an axis of rotation coincident with the longitudinal axis of the shaft is described. The probe is a tubular body supported for angular displacement about the axis of rotation and has a fin mounted on the body for maintaining one end of the body in facing relation with relative wind and has a pair of transducers mounted in the body for providing intelligence indicative of total pressure and static pressure for use in determining air speed. A stack of potentiometers coupled with the shaft to provide intelligence indicative of aircraft attitude, and circuitry connecting the transducers and potentiometers to suitable telemetry circuits are described
CONFINEMENT IN RELATIVISTIC POTENTIAL MODELS
In relativistic potential models of quarkonia based on a Dirac-type of
equation with a local potential there is a sharp distinction between a linear
potential V which is vector-like and one which is scalar-like: There are
normalizable solutions for a scalar-like V but not for a vector-like V. It is
pointed out that if instead one uses an equation of the no-pair type, which is
more natural from the viewpoint of field theory, this somewhat bizarre
difference disappears.Comment: LaTeX, 4 page
Perceptions of healthy eating and physical activity in an ethnically diverse sample of young children and their parents: the DEAL prevention of obesity study
Background: Ethnicity is a consistent correlate of obesity; however, little is known about the perceptions and beliefs that may influence engagement with obesity prevention programmes among ethnic minority children. Barriers to (and facilitators of) healthy lifestyles were examined in the qualitative arm of the London (UK) DiEt and Active Living (DEAL) study.
Methods: Children aged 8â13 years and their parents, from diverse ethnic groups, were recruited through schools and through places of worship. Thirteen focus group sessions were held with 70 children (n = 39 girls) and eight focus groups and five interviews with 43 parents (n = 34 mothers).
Results: Across ethnic groups, dislike of school meals, lack of knowledge of physical activity guidelines for children and negativity towards physical education at school among girls, potentially hindered healthy living. Issues relating to families' wider neighbourhoods (e.g. fast food outlets; lack of safety) illustrated child and parental concerns that environments could thwart intentions for healthy eating and activity. By contrast, there was general awareness of key dietary messages and an emphasis on dietary variety and balance. For ethnic minorities, places of worship were key focal points for social support. Discourse around the retention of traditional practices, family roles and responsibilities, and religion highlighted both potential facilitators (e.g. the importance of family meals) and barriers (reliance on convenience stores for traditional foods). Socio-economic circumstances intersected with key themes, within and between ethnic groups.
Conclusions: Several barriers to (and facilitators of) healthy lifestyles were common across ethnic groups. Diversity of cultural frameworks not only were more nuanced, but also shaped lifestyles for minority children.</p
Coronal mass ejections, magnetic clouds, and relativistic magnetospheric electron events: ISTP
The role of high-speed solar wind streams in driving relativistic electron acceleration within the Earth\u27s magnetosphere during solar activity minimum conditions has been well documented. The rising phase of the new solar activity cycle (cycle 23) commenced in 1996, and there have recently been a number of coronal mass ejections (CMEs) and related âmagnetic cloudsâ at 1 AU. As these CME/cloud systems interact with the Earth\u27s magnetosphere, some events produce substantial enhancements in the magnetospheric energetic particle population while others do not. This paper compares and contrasts relativistic electron signatures observed by the POLAR, SAMPEX, Highly Elliptical Orbit, and geostationary orbit spacecraft during two magnetic cloud events: May 27â29, 1996, and January 10â11, 1997. Sequences were observed in each case in which the interplanetary magnetic field was first strongly southward and then rotated northward. In both cases, there were large solar wind density enhancements toward the end of the cloud passage at 1 AU. Strong energetic electron acceleration was observed in the January event, but not in the May event. The relative geoeffectiveness for these two cases is assessed, and it is concluded that large induced electric fields (âB/ât) caused in situ acceleration of electrons throughout the outer radiation zone during the January 1997 event
Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory
In this paper we express the velocity dependent, spin dependent heavy quark
potential in QCD in terms of a Wilson Loop determined
by pure Yang Mills theory. We use an effective dual theory of long-distance
Yang Mills theory to calculate for large loops; i.e. for loops of
size . ( is the flux tube radius, fixed by the value of the
Higgs (monopole) mass of the dual theory, which is a concrete realization of
the Mandelstam 't Hooft dual superconductor mechanism of confinement).
We replace by , given by a functional integral
over the dual variables, which for can be evaluated by a
semiclassical expansion, since the dual theory is weakly coupled at these
distances. The classical approximation gives the leading contribution to
and yields a velocity dependent heavy quark potential which
for large becomes linear in , and which for small approaches lowest
order perturbative QCD. This latter fact means that these results should remain
applicable down to distances where radiative corrections giving rise to a
running coupling constant become important. The spin dependence of the
potential reflects the vector coupling of the quarks at long range as well as
at short range. The methods developed here should be applicable to any
realization of the dual superconductor mechanism. They give an expression
determining independent of the classical approximation, but
semi classical corrections due to fluctuations of the flux tube are not worked
out in this paper. Taking these into account should lead to an effective string
theory free from the conformal anomaly.Comment: 39 pages, latex2e, 1 figure(fig.eps
The Chemical Evolution of the Universe I: High Column Density Absorbers
We construct a simple, robust model of the chemical evolution of galaxies
from high to low redshift, and apply it to published observations of damped
Lyman-alpha quasar absorption line systems (DLAs). The elementary model assumes
quiescent star formation and isolated galaxies (no interactions, mergers or gas
flows). We consider the influence of dust and chemical gradients in the
galaxies, and hence explore the selection effects in quasar surveys. We fit
individual DLA systems to predict some observable properties of the absorbing
galaxies, and also indicate the expected redshift behaviour of chemical element
ratios involving nucleosynthetic time delays.
Despite its simplicity, our `monolithic collapse' model gives a good account
of the distribution and evolution of the metallicity and column density of
DLAs, and of the evolution of the global star formation rate and gas density
below redshifts z 3. However, from the comparison of DLA observations with our
model, it is clear that star formation rates at higher redshifts (z>3) are
enhanced. Galaxy interactions and mergers, and gas flows very probably play a
major role.Comment: 36 pages, 11 figures; accepted by MNRA
The two-phase approximation for black hole collisions: Is it robust?
Recently Abrahams and Cook devised a method of estimating the total radiated
energy resulting from collisions of distant black holes by applying Newtonian
evolution to the holes up to the point where a common apparent horizon forms
around the two black holes and subsequently applying Schwarzschild perturbation
techniques . Despite the crudeness of their method, their results for the case
of head-on collisions were surprisingly accurate. Here we take advantage of the
simple radiated energy formula devised in the close-slow approximation for
black hole collisions to test how strongly the Abrahams-Cook result depends on
the choice of moment when the method of evolution switches over from Newtonian
to general relativistic evolution. We find that their result is robust, not
depending strongly on this choice.Comment: 4 pages, 3 figures, submitted to Classical and Quantum Gravit
Understanding Confinement From Deconfinement
We use effective magnetic SU(N) pure gauge theory with cutoff M and fixed
gauge coupling g_m to calculate non-perturbative magnetic properties of the
deconfined phase of SU(N) Yang-Mills theory. We obtain the response to an
external closed loop of electric current by reinterpreting and regulating the
calculation of the one loop effective potential in Yang-Mills theory. This
effective potential gives rise to a color magnetic charge density, the
counterpart in the deconfined phase of color magnetic currents introduced in
effective dual superconductor theories of the confined phase via magnetically
charged Higgs fields. The resulting spatial Wilson loop has area law behavior.
Using values of M and g_m determined in the confined phase, we find SU(3)
spatial string tensions compatible with lattice simulations in the temperature
interval 1.5T_c < T < 2.5T_c. Use of the effective theory to analyze
experiments on heavy ion collisions will provide applications and further tests
of these ideas.Comment: 18 pages, 5 figures, v2: fixed archive title (only
Gradual diffusion and punctuated phase space density enhancements of highly relativistic electrons: Van Allen Probes observations
Abstract The dual-spacecraft Van Allen Probes mission has provided a new window into mega electron volt (MeV) particle dynamics in the Earth\u27s radiation belts. Observations (up to E ~10 MeV) show clearly the behavior of the outer electron radiation belt at different timescales: months-long periods of gradual inward radial diffusive transport and weak loss being punctuated by dramatic flux changes driven by strong solar wind transient events. We present analysis of multi-MeV electron flux and phase space density (PSD) changes during March 2013 in the context of the first year of Van Allen Probes operation. This March period demonstrates the classic signatures both of inward radial diffusive energization and abrupt localized acceleration deep within the outer Van Allen zone (L ~4.0 ± 0.5). This reveals graphically that both competing mechanisms of multi-MeV electron energization are at play in the radiation belts, often acting almost concurrently or at least in rapid succession. Key Points Clear observations to higher energy than ever before Precise detection of where and how acceleration takes place Provides new eyes on megaelectron Volt
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