A new stock loan problem based on the mean-reverting equation in an uncertain environment

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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The motion of a lunar orbiter

Symposium - International Astronomical Union ◽

10.1017/s0074180900105686 ◽

1966 ◽

Vol 25 ◽

pp. 373

Author(s):

Y. Kozai

Keyword(s):

Degrees Of Freedom ◽

Dimensional Space ◽

Artificial Satellite ◽

Equations Of Motion ◽

Triaxial Ellipsoid ◽

The Moon ◽

Secular Motion ◽

The Earth ◽

Close Satellite ◽

The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

Symposium - International Astronomical Union ◽

10.1017/s0074180900105480 ◽

1966 ◽

Vol 25 ◽

pp. 197-222 ◽

Cited By ~ 4

Author(s):

P. J. Message

Keyword(s):

Periodic Solution ◽

Periodic Solutions ◽

Large Amplitude ◽

Restricted Problem ◽

Small Amplitude ◽

Minor Planets ◽

Long Period ◽

Numerical Integrations ◽

Period Variations ◽

The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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the effects of resonance with Jupiter in the system of short-period comets

International Astronomical Union Colloquium ◽

10.1017/s0252921100033959 ◽

1974 ◽

Vol 22 ◽

pp. 193-203

Author(s):

L̆ubor Kresák

Keyword(s):

Structural Effects ◽

Order Resonance ◽

Mean Motion ◽

Short Period ◽

The Mean ◽

Compound Effect ◽

Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

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Contrast of Filament Bright Rims

International Astronomical Union Colloquium ◽

10.1017/s0252921100025628 ◽

1994 ◽

Vol 144 ◽

pp. 365-367

Author(s):

E. V. Kononovich ◽

O. B. Smirnova ◽

P. Heinzel ◽

P. Kotrč

Keyword(s):

High Altitude ◽

Line Profile ◽

Line Center ◽

Magnetic Structures ◽

The Mean

AbstractThe Hα filtergrams obtained at Tjan-Shan High Altitude Observatory near Alma-Ata (Moscow University Station) were measured in order to specify the bright rims contrast at different points along the line profile (0.0; ± 0.25; ± 0.5; ± 0.75 and ± 1.0 Å). The mean contrast value in the line center is about 25 percent. The bright rims interpretation as the bases of magnetic structures supporting the filaments is suggested.

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Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

International Astronomical Union Colloquium ◽

10.1017/s0252921100014718 ◽

1997 ◽

Vol 161 ◽

pp. 197-201 ◽

Cited By ~ 1

Author(s):

Duncan Steel

Keyword(s):

Probability Distributions ◽

Regions Of Interest ◽

Significant Fraction ◽

Organic Chemicals ◽

Impact Speed ◽

The Mean ◽

The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

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Status of “AGK4” Project

International Astronomical Union Colloquium ◽

10.1017/s0252921100074558 ◽

1978 ◽

Vol 48 ◽

pp. 527-533

Author(s):

Chr. de Vegt

Keyword(s):

Northern Hemisphere ◽

Proper Motion ◽

The Mean ◽

Spectral Bandpass

The present accuracy limit for the majority of fainter stars on the northern hemisphere is set by the AGK2/3-catalogue, recently completely finished, but it should be noted that its epoch is much earlier (1960). Furtheron the AGK3-catalogue is a direct repetition of the AGK2, the plates have been taken with the same astrograph in a broad blue spectral bandpass and measured visually with the same equipment, therefore virtually an instrumental standard of 1930 is realized again. Figure 1 shows the mean errors of the AGK2/3 catalogue positions as a function of magnitude. The best accuracy for the AGK2/3 data is obtained for the stars of about ninth magnitude: 017 (AGK2) and 020 (AGK3) but decreases for the faint stars with mpg11 to 019 (AGK2) and Pg 027 (AGK3). Here the AGK3 data are even less accurate. With increasing distance to the catalogue epochs, the accuracy of positions decreases due to the proper motion errors. In the upper part of figure 2 the dependence of the AGK2/3 catalogue accuracy on time is shown for the faint stars separately and an averaged value.

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The Bordeaux Automatic Meridian Circle

International Astronomical Union Colloquium ◽

10.1017/s0252921100074170 ◽

1978 ◽

Vol 48 ◽

pp. 227-228

Author(s):

Y. Requième

Keyword(s):

Mean Square Error ◽

Mean Square ◽

Meridian Circle ◽

The Mean ◽

Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

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