pinecone/core-2020-05-10-deduplication huggingface dataset:
Historical Remarks on the Surjectivity of the Exponential Function of Lie Groups

AbstractIn 1892, F. Engel and E. Study investigated the exponential map of classical Lie groups for the first time. They showed that the special projective Lie groups over C possess surjective exponential functions. Engel also gave a “proof” for the corresponding claims for the other projective classical groups. However, it is known that the latter claims are wrong. Nevertheless, these “results” are still cited in the literature without comments. In the present paper, the mentioned works of Engel and Study are critically discussed. © 2002 Elsevier Science (USA).Im Jahre 1892 untersuchten F. Engel und E. Study als erste die Exponentialfunktion klassischer Lie-Gruppen. Sie zeigten, daß die speziellen projektiven Lie-Gruppen über C eine surjektive Exponentialfunktion besitzen. Engel formulierte auch einen ,,Beweis“ für die entsprechenden Aussagen über die anderen projektiven klassischen Gruppen. Inzwischen weiß man, daß die letzteren Aussagen jedoch falsch sind. Dennoch werden jene ,,Ergebnisse“ immer noch unkommentiert in der Literatur zitiert. Im vorliegendein in Artikel werden die besagten Arbeiten von Engel und Study kritisch diskutiert. © 2002 Elsevier Science (USA).MSC subject classifications: 22-03; 01A55; 01A60; 22E15
Symbolical Algebra as a Foundation for Calculus: D. F. Gregory's Contribution

AbstractDuncan Farquharson Gregory (1813–1844) was a mathematician and founder of the Cambridge Mathematical Journal. His 1841 Examples of the Processes of the Differential and Integral Calculus was an extensive revision of Peacock's 1820 textbook of a similar title. Among the new material in Gregory's version is an exposition of symbolical algebra, prominently featuring the method of “separation of symbols.” We examine Gregory's career; the mathematicians he influenced; and Servois and Murphy, who influenced him. We consider Gregory's use of separation of symbols in the Examples and consider whether he believed these techniques to be capable of providing an adequate foundation for calculus. © 2002 Elsevier Science (USA).Le mathématicien Duncan Farquharson Gregory (1813–1844) fut également fondateur du Cambridge Mathematical Journal. Son ouvrage publié en 1841, Examples of the Processes of the Differential and Integral Calculus, constitue une révision substantielle du livre de Peacock au titre similaire. L'un des apports du livre de Gregory est un exposé de l'algèbre symbolique, et en particulier de la méthode de ⪡séparation des symboles⪢. Dans cet article nous passons en revue la carrière de Gregory et nous parlons des mathématiciens qu'il a influencés, ainsi que de l'influence que Servois et Murphy ont eu sur ses travaux. Nous considérons son usage de la séparation des symboles dans ses Examples, et nous examinons si Gregory croyait que ses techniques pouvaient constituer un fondement pour le calcul différentiel. © 2002 Elsevier Science (USA).MSC 1991 subject classifications: 01A55, 01A70, 01A50, 26-03, 26A03, 34-03, 34A30
Expectations from a Microlensing Search for Planets

The statistical distribution of the masses of planets about stars between the Sun and the center of the galaxy is constrained to within a factor of three by an intensive search for planets during microlensing events. Projected separations in terms of the lens Einstein ring radius yield a rough estimate of the distribution of planetary semimajor axes with planetary mass. The search consists of following ongoing stellar microlensing events involving sources in the center of the galaxy lensed by intervening stars with high time resolution, 1% photometry in two colors in an attempt to catch any short time scale planetary perturbations of the otherwise smooth light curve. It is assumed that 3000 events are followed over an 8 year period, but with half of the lenses, those that are members of binary systems, devoid of planets. The remaining 1500 lenses have solar-system-like distributions of 4 or 5 planets. The expectations from the microlensing search are extremely assumption dependent with 56, 138, and 81 planets being detected for three sets of assumptions involving how the planetary masses and separations vary with lens mass. The events can be covered from 54% to 62% of the time on average by high time resolution photometry from a system of three or four dedicated two meter telescopes distributed in longitude, so 38% to 46% of the detectable small mass planets (very short perturbations of the light curve) will be missed. But perturbations comparable to a day in length means all of the detectable Jupiters and Saturns will in fact be detected as well as a large fraction of the Uranuses. Although meaningful statistics on planetary masses and separations can be inferred from such an intensive search, they, like the inferred data set, will be dependent on the assumed nature of the systems
The Keplerian map for the restricted three-body problem as a model of
  comet evolution

We examine the evolution of highly eccentric, planet-crossing orbits in the
restricted three-body problem (Sun, planet, comet). We construct a simple
Keplerian map in which the comet energy changes instantaneously at perihelion,
by an amount depending only on the azimuthal angle between the planet and the
comet at the time of perihelion passage. This approximate but very fast mapping
allow us to explore the evolution of large ensembles of long-period comets. We
compare our results on comet evolution with those given by the diffusion
approximation and by direct integration of comet orbits. We find that at long
times the number of surviving comets is determined by resonance sticking rather
than a random walk.Comment: 24 pages, 10 figures, some of figures have been bitmappe
Catastrophic disruptions revisited

We use a smooth particle hydrodynamics method (SPH) to simulate colliding
rocky and icy bodies from cm-scale to hundreds of km in diameter, in an effort
to define self-consistently the threshold for catastrophic disruption. Unlike
previous efforts, this analysis incorporates the combined effects of material
strength (using a brittle fragmentation model) and self-gravitation, thereby
providing results in the ``strength regime'' and the ``gravity regime'', and in
between. In each case, the structural properties of the largest remnant are
examined.Comment: To appear in Icaru
ISO-SWS observations of Jupiter: measurement of the ammonia tropospheric
  profile and of the 15N/14N isotopic ratio

We present the results of the Infrared Space Observatory Short Wavelength
Spectrometer (ISO-SWS) observations of Jupiter related to ammonia. We focus on
two spectral regions; the first one (the 10-micron region), probes atmospheric
levels between 1 and 0.2 bar, while the second one (the 5-micron window),
sounds the atmosphere between 8 and 2 bars. The two spectral windows cannot be
fitted with the same ammonia vertical distribution. From the 10-micron region
we infer an ammonia distribution of about half the saturation profile above the
1-bar level, where the N/H ratio is roughly solar. A totally different picture
is derived from the 5-micron window, where we determine an upper limit of
3.7E-5 at 1 bar and find an increasing NH3 abundance at least down to 4 bar.
This profile is similar to the one measured by the Galileo probe (Folkner et
al. 1998). The discrepancy between the two spectral regions most likely arises
from the spatial heterogeneity of Jupiter, the 5-micron window sounding dry
areas unveiled by a locally thin cloud cover (the 5-micron hot spots), and the
10-micron region probing the mean jovian atmosphere above 1 bar. The 15NH3
mixing ratio is measured around 400 mbar from nu_2 band absorptions in the
10-micron region. We find the atmosphere of Jupiter highly depleted in 15N at
this pressure level (15N/14N)_{Jupiter}=(1.9^{+0.9}_{-1.))E-3, while
(15N/14N)_{earth}=3.68E-3. It is not clear whether this depletion reveals the
global jovian (15N/14N) ratio. Instead an isotopic fractionation process,
taking place during the ammonia cloud condensation, is indicated as a possible
mechanism. A fractionation coefficient alpha higher than 1.08 would explain the
observed isotopic ratio, but the lack of laboratory data does not allow us to
decide unambiguously on the origin of the observed low (15N/14N) ratio.Comment: 57 pages, 2 tables, 15 figures. Accepted for publication in ICARU
Collisional evolution in the Vulcanoid region: Implications for
  present-day population constraints

We explore the effects of collisional evolution on putative Vulcanoid
ensembles in the region between 0.06 and 0.21 AU from the Sun, in order to
constrain the probable population density and population structure of this
region today. Dynamical studies have shown that the Vulcanoid Zone (VZ) could
be populated. However, we find that the frequency and energetics of collisional
evolution this close to the Sun, coupled with the efficient radiation transport
of small debris out of this region, together conspire to create an active and
highly intensive collisional environment which depletes any very significant
population of rocky bodies placed in it, unless the bodies exhibit orbits that
are circular to ~10^-3 or less, or highly lossy mechanical properties that
correspond to a fraction of impact energy significantly less than 10% being
imparted to ejecta. The most favorable locale for residual bodies to survive in
this region is in highly circular orbits near the outer edge of the dynamically
stable Vulcanoid Zone (i.e., near 0.2 AU), where collisional evolution and
radiation transport of small bodies and debris proceed most slowly. If the mean
random orbital eccentricity in this region exceeds ~10^-3, then our work
suggests it is unlikely that more than a few hundred objects with radii larger
than 1 km will be found in the entire VZ; assuming the largest objects have a
radius of 30 km, then the total mass of bodies in the VZ down to 0.1 km radii
is likely to be no more than ~10^-6Mearth, <10^-3 the mass of the asteroid
belt. Despite the dynamical stability of large objects in this region (Evans &
Tabachnik 1999), it is plausible that the entire region is virtually empty of
km-scale and larger objects.Comment: text plus 7 .ps figures, gzipped. Icarus, 2000, in pres
Vapor pressure isotope fractionation effects in planetary atmospheres:
  application to deuterium

The impact of the vapor pressure difference between deuterated and
nondeuterated condensing molecules in planetary atmospheres is quantitatively
assessed. This difference results in a loss of deuterium in the vapor phase
above the condensation level. In Titan, Uranus and Neptune, the effect on CH3D
is too subtle to alter current D/H ratio determinations. In Mars, the effect
can induce a large depletion of HDO, starting about one scale height above the
condensation level. Although the current infrared measurements of the D/H ratio
appear to be almost unaffected, the intensity of disk-averaged millimetric HDO
lines can be modified by about 10%. The effect is much stronger in limb
sounding, and can be easily detected from orbiter observations.Comment: 24 pages, 1 table, 6 figures. Paper accepted for publication in
  ICARU
Chasma Australe, Mars: Structural Framework\ud
for a Catastrophic Outflow Origin

Chasma Australe, 500 km long and up to 80 km wide, is the most\ud
remarkable of the martian south pole erosional reentrants carved in\ud
the polar layered deposits. We have interpreted Chasma Australe\ud
erosional and depositional features as evidence for a flood origin,\ud
which we have reconstructed using a modified Manning equation.\ud
The main characteristics of the flow are a water velocity between\ud
30 and 50 m s¡1 and discharge values between 7 x 10^8 and 3 x 10^9 m3 s-1, very near to MGS data-based estimations for martian\ud
outflow channels (D. E. Smith et al. 1998, Science 279, 1686–1692).\ud
We thus postulate that Chasma Australe originated in a catastrophic\ud
flood.\ud
The tectonic study of an area (roughly 20 million km2 in size)\ud
around Mars’ south pole included the measurement and projection\ud
in rose diagrams of more than 300 lineaments, of which 85 were\ud
wrinkle ridges and the rest straight scarps. The whole set of lineaments\ud
can be explained by a stress field with a d1 N10ºE in strike,\ud
the wrinkle ridges being reverse faults and the other lineaments direct\ud
and strike-slip faults. The straight layout of parts of Chasma\ud
Australe almost 200 km long suggests that the chasma was carved\ud
following a fracture network. The effectiveness of the erosional process\ud
(the canyon is up to 1000 m deep) leads us to suspect that this\ud
carving was preceded by a sapping period. Endogenetic and exogenetic\ud
processes would thus have contributed to the origin of this\ud
landfor
A Search for Resonant Structures in the Zodiacal Cloud with COBE DIRBE:
  The Mars Wake and Jupiter's Trojan Clouds

We searched the COBE DIRBE Sky and Zodi Atlas for a wake of dust trailing
Mars and for Trojan dust near Jupiter's L5 Lagrange point. We compare the DIRBE
images to a model Mars wake based on the empirical model of the Earth's wake as
seen by the DIRBE and place a 3-sigma upper limit on the fractional overdensity
of particles in the Mars wake of 18% of the fractional overdensity trailing the
Earth. We place a 3-sigma upper limit on the effective emitting area of large
(10-100 micron diameter) particles trapped at Jupiter's L5 Lagrange point of 6
x 10^17 cm^2, assuming that these large dust grains are distributed in space
like the Trojan asteroids. We would have detected the Mars wake if the surface
area of dust in the wake scaled simply as the mass of the planet times the
Poynting-Robertson time scale.Comment: Sixteen pages, and figures 1, 2, 3a, 3b, 4, 5, 6, and 7. Accepted for
  publication in Icaru
Collision rates in the present-day Kuiper Belt and Centaur Regions:
  Applications to surface activation and modification on Comets, Kuiper Belt
  Objects, Centaurs, and Pluto-Charon

We extend previous results showing that the surfaces of Edgeworth-Kuiper Belt
objects are not primordial and have been moderately to heavily reworked by
collisions. Objects smaller than about $r = 2.5$ km have collisional disruption
lifetimes less than 3.5 Gyr in the present-day collisional environment and have
been heavily damaged in their interiors by large collisions. In the 30--50 AU
region, impacts of 1 km radius comets onto individual 100 km radius objects
occur on $7\times10^7$--$4\times10^8$ yr timescales, cratering the surfaces of
the larger objects with $\sim$8--54 craters 6 km in diameter over 3.5 Gyr.
Collision time scales for impacts of 4 meter radius projectiles onto 1 km
radius comets range from 3--5 $ \times 10^7$ yr. The cumulative fraction of the
surface area of 1 and 100 km radius objects cratered by projectiles with radii
larger than 4 m ranges from a few to a few tens percent over 3.5 Gyr. The flux
of EKO projectiles onto Pluto and Charon is also calculated and is found to be
$\sim$3--5 times that of previous estimates. Our impact model is also applied
to Centaur objects in the 5--30 AU region. We find the collisional/cratering
histories of Centaurs are dominated by the time spent in the Edgeworth-Kuiper
Belt rather than the time spent on planet-crossing orbits. Hence, the
predominant surface activity of Centaur objects like Chiron is almost certainly
not impact-induced.Comment: 17 pages, 8 figures. Icarus, 2000, in pres
Earth Trojan asteroids: A study in support of observational searches

Observational searches for asteroids orbiting near Earth's triangular
Lagrange points face unique obstacles. A population of such asteroids would
occupy a large projected area on the sky (possibly hundreds of square degrees)
and is not favorably placed with respect to the Sun. Here we examine the
properties of synthetic populations of Earth ``Trojans'' in order to aid in the
optimization of observational searches for them. We find that the highest
on-sky projected number densities are not located at the positions of the L4
and L5 points themselves, but rather a few degrees closer to the Sun. Also,
asteroids on orbits about the L4 and L5 points typically brighten as the
difference between their ecliptic longitude and that of the Sun increases owing
to phase effects, but their number density on the sky concurrently falls
rapidly.Comment: 20 pages, 5 figures and 3 tables. Submitted to Icaru
Snapshot coronagraphy with an interferometer in space

Diluted arrays of many optical apertures will be able to provide h
igh-resolution snapshot images if the beams are combined according to the
densified-pupil scheme. We show that the same principle can also provide
coronagraphic images, for detecting faint sources near a bright unresolved one.
Recent refinements of coronagraphic techniques, i.e. the use of a phase mask,
active apodization and dark-speckle analysis, are also applicable for enhanced
contrast. Implemented in the form of a proposed 50-500m Exo-Earth Discoverer
array in space, the principle can serve to detect Earth-like exo-planets in the
infra-red. It can also provide images of faint nebulosity near stars, active
galactic nuclei and quasars. Calculations indicate that exo-planets are
detectable amidst the zodiacal and exo-zodiacal emission faster than with a
Bracewell array of equivalent area, a consequence of the spatial selectivity in
the image.Comment: 23 pages, 10 figures, to appear in Icaru
Direct N-body Simulations of Rubble Pile Collisions

There is increasing evidence that many km-sized bodies in the Solar System
are piles of rubble bound together by gravity. We present results from a
project to map the parameter space of collisions between km-sized spherical
rubble piles. The results will assist in parameterization of collision outcomes
for Solar System formation models and give insight into fragmentation scaling
laws. We use a direct numerical method to evolve the positions and velocities
of the rubble pile particles under the constraints of gravity and physical
collisions. We test the dependence of the collision outcomes on impact
parameter and speed, impactor spin, mass ratio, and coefficient of restitution.
Speeds are kept low (< 10 m/s, appropriate for dynamically cool systems such as
the primordial disk during early planet formation) so that the maximum strain
on the component material does not exceed the crushing strength. We compare our
results with analytic estimates and hydrocode simulations. Off-axis collisions
can result in fast-spinning elongated remnants or contact binaries while fast
collisions result in smaller fragments overall. Clumping of debris escaping
from the remnant can occur, leading to the formation of smaller rubble piles.
In the cases we tested, less than 2% of the system mass ends up orbiting the
remnant. Initial spin can reduce or enhance collision outcomes, depending on
the relative orientation of the spin and orbital angular momenta. We derive a
relationship between impact speed and angle for critical dispersal of mass in
the system. We find that our rubble piles are relatively easy to disperse, even
at low impact speed, suggesting that greater dissipation is required if rubble
piles are the true progenitors of protoplanets.Comment: 30 pages including 4 tables, 8 figures. Revised version to be
  published in Icarus
N$_2^+$ and CO$^+$ in Comets 122P/1995 S1 (deVico) and C/1995 O1
  (Hale-Bopp)

We observed comets 122P/1995\,S1 (deVico) and C/1995\,O1 (Hale-Bopp) with
high spectral resolving power in order to determine the ratio of N$_2^+$/CO$^+$
in their comae. While we clearly detected the CO$^+$ in both of these comets,
no N$_2^+$ was detected in either comet. From these spectra, we derive
sensitive upper limits for N$_2^+$/CO$^+$. These upper limits are substantially
below other reported detections of N$_2^+$/CO$^+$ in other comets. We discuss
the prior N$_2^+$ detections and compare them with our observations. The
abundance of N$_2$ in comets is important to our understanding of the
condensation of ices in the solar nebula. In addition, N$_2$ is a tracer of Ar
so study of N$_2$ allows an understanding of the role of comets for delivering
volatiles to the terrestrial planets. It appears that many, if not most, comets
are depleted in N$_2$ and it will be necessary to search for a mechanism for
depleting this molecule in order to be consistent with current models of the
solar nebula.Comment: 25 pages, 3 tables, 7 figures, accepted for publication in Icaru
Secular Instability and Planetesimal Formation in the Dust Layer

Late in the gaseous phase of a protostellar disk, centimeter-sized bodies
probably settle into a thin ``dust layer'' at the midplane. A velocity
difference between the dust layer and the gas gives rise to turbulence, which
prevents further settling and direct gravitational instability of the layer.
The associated drag on the surface of the layer causes orbital decay in a few
thousand years---as opposed to a few hundred years for an isolated meter-sized
body. Within this widely-accepted theoretical framework, we show that the
turbulent drag causes radial instabilities even if the selfgravity of the layer
is negligible. We formulate axisymmetric, height-integrated dynamical equations
for the layer that incorporate turbulent diffusion of mass and momentum in
radius and height, vertical settling, selfgravity, and resistance to
compression due to gas entrained within the dust layer. In steady-state, the
equations describe the inward radial drift of a uniform dust layer. In
perturbation, overdense rings form on an orbital timescale with widths
comparable to the dust-layer thickness. Selfgravity is almost irrelevant to the
linear growth rate but will eventually fragment and collapse the rings into
planetesimals larger than a kilometer. We estimate that the drag instability is
most efficient at 1 AU when most of the ``dust'' mass lies in the size range
0.1-10 meters.Comment: 25 pp., 2 figures. Uses aastex version 5.0
The formation of Encke meteoroids and dust trail

We observed comet 2P/Encke with the Infrared Space Observatory ISOCAM on July 14, 1997 from a particularly favorable viewing geometry above the comet's orbital plane and at a distance of 0.25 AU. A structured coma was observed, along with a long, straight dust trail. For the first time, we are able to observe the path of particles as they evolve from the nucleus to the trail. The particles that produce the infrared coma are large, with a radiation to gravitational force ratio beta<0.001 (corresponding to >mm-sized particles). The dust trail follows the orbit of the comet across our image, with a central core that is 20,000 km wide, composed of particles with beta<1e-5 (size $\sim 5$ cm) from previous apparitions. The abundant large particles near the comet pose a significant hazard to spacecraft. There is no evidence of a classical cometary dust tail due to small particles with beta>0.001, in marked contrast to other comets like P/Halley or C/Hale-Bopp. The structure of the coma requires anisotropic emission and that the spin axis of the nucleus to be nearly parallel to the orbital plane, resulting in strong seasonal variations of the particle emission. While most of the infrared coma emission is due to dust produced during the 1997 apparition, the core of the dust trail requires emissions from previous apparitions. The total mass lost during the 1997 apparition is estimated to be 2-6e13 g. Comparing to the gas mass loss from ultraviolet observations, the dust-to-gas mass ratio is 10-30, much higher than has ever been suggested from visual light observations. Using the recently-measured nuclear diameter, we find that Encke can only last 3000-10,000 rhoN yr (where rhoN is the nuclear density in g/cc) at its present mass loss rate