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Solution of ordinary differential equations by Lie series - Laplace transformation, Weber parabolic-cylinder functions, Helmholtz equations, and applications in physics
Application of Lie series to various physics problems - rigid body mechanics, electricity, gravity gradient stabilization of artificial satellites, and particle motion in synchrotron
Representation and computation of Mathieu functions by means of Lie series - descriptions and flow diagrams of computer programs used in calculation
Numerical calculation of Weber parabolic cylinder functions - Lie series formalism
Lie series for numerical computation of satellite orbits
Solution of heavy asymmetric gyroscope using properties of Lie operator
Solution to system of n-th order differential equations using Lie series
New Lie series method for numerical integration of ordinary differential equations, and restricted three-body problem application
Euler gyroscope equations solved by means of Lie series making use of recurrence formulas
Exact solutions of Einstein-Maxwell equation of Petrov class N when propagation vector of gravitational field is hypersurface orthogonal
Lie series solution of equations resulting from separation of Helmholtz equation in special coordinate systems
Inhomogeneous second order linear differential equation solution based on Lie formalism, presenting physical applications
A1367 is a puzzling cluster with a large elongation, suggesting a major merger but with an anti-correlation between the luminosity and temperature of the two components of the cluster (NE and SW). The less luminous subconcentration appears hotter and the more luminous portion of the cluster appears cooler in contradiction to the well-established positive correlation of temperature and luminosity for clusters and groups. A1367 lies at the intersection of two large scale filaments in our local Universe - one in the direction of the Coma cluster and a second in the direction of the Virgo cluster. The elongation of the main X-ray structure lies along the Virgo-A1367 filament. With the XMM-Newton observation we have developed a model involving multiple mergers from two directions to explain the observed features of A1367.
The Mars Science Laboratory rover Curiosity has been exploring sedimentary deposits in Gale crater since August, 2012. The rover has traversed up section through approximately 150 m of sedimentary rocks deposited in fluvial, deltaic, and lacustrine environments (Bradbury group and overlying Mount Sharp group). The Murray formation lies at the base of the Mt. Sharp group and has been interpreted to be a finely laminated mudstone likely deposited in a subaqueous lacustrine environment. Four drill samples from several elevations in the Murray fm have been acquired by the rover's sampling system and delivered to the CheMin XRD instrument. The lower section of the Murray fm contains 2:1 phyllosilicate(s), hematite, jarosite, XRD amorphous materials, and primary basaltic minerals. Further up section, the Murray fm contains magnetite, cristobalite, tridymite, abundant Si-rich XRD amorphous materials along with plagioclase and K-feldspars. Murray formation materials appear to have been altered under an open hydrologic system based on the bulk chemistry of these materials measured by the Alpha Particle X-ray Spectrometer (APXS). The 2:1 phyllosilicate only occurs in the lowermost section of the Murray fm and may be detrital or formed during authigenesis of Murray fm materials, similar to the Fe-saponite and magnetite detected in a mudstone in the Yellowknife Bay fm near Curiosity's landing site (stratigraphically at the base of the Bradbury group). The occurrence of jarosite and hematite in the lower section indicates an acidic diagenetic event. These phases may have formed via several acidic alteration mechanisms, including (1) oxidative weathering of mafic igneous rocks containing sulfides; (2) sulfuric acid weathering of Fe-bearing phases; and (3) near-neutral pH subsurface solutions rich in Fe2(+) that were rapidly oxidized to Fe3(+), which produced excess acidity. The transition from abundant hematite in the lowermost Murray fm to magnetite moving up section may indicate changes in lake chemistry, i.e., variable redox conditions, possibly during authigenesis or subsequent diagenetic events. Tridymite, a high temperature mineral, (and possibly cristobalite) is detrital, potentially deposited in a lake from a distal silicic volcanic rock source or from crustal materials present prior to the Gale Crater impact event. Abundant Si-rich XRD amorphous materials in the upper sections of the Murray fm may be detrital or an aqueous alteration product of primary igneous phases and phyllosilicates. Curiosity's science team is still deciphering the authigenesis and diagenetic events that formed the Murray fm. The mineralogy and geochemistry of the formation suggest a complicated history with several (many?) episodes of aqueous alteration under a variety of environmental conditions.
Compact groups of galaxies provide conditions similar to those experienced by galaxies in the earlier universe. Recent work on compact groups has led to the discovery of a dearth of mid-infrared transition galaxies (MIRTGs) in Infrared Array Camera (3.6-8.0 micrometers) color space as well as at intermediate specific star formation rates. However, we find that in compact groups these MIRTGs have already transitioned to the optical ([g−r]) red sequence. We investigate the optical color-magnitude diagram (CMD) of 99 compact groups containing 348 galaxies and compare the optical CMD with mid-infrared (mid-IR) color space for compact group galaxies. Utilizing redshifts available from Sloan Digital Sky Survey, we identified new galaxy members for four groups. By combining optical and mid-IR data, we obtain information on both the dust and the stellar populations in compact group galaxies. We also compare with more isolated galaxies and galaxies in the Coma Cluster, which reveals that, similar to clusters, compact groups are dominated by optically red galaxies. While we find that compact group transition galaxies lie on the optical red sequence, LVL (Local Volume Legacy) + (plus) SINGS (Spitzer Infrared Nearby Galaxies Survey) mid-IR (infrared) transition galaxies span the range of optical colors. The dearth of mid-IR transition galaxies in compact groups may be due to a lack of moderately star-forming low mass galaxies; the relative lack of these galaxies could be due to their relatively small gravitational potential wells. This makes them more susceptible to this dynamic environment, thus causing them to more easily lose gas or be accreted by larger members.
The evolution of galaxies in an intergalactic medium dominated by explosions of star systems is considered analogously to star formation by nonlinearly interacting processes in the interstellar medium. Conditions for the existence of a hydrodynamic instability by which galaxy formation leads to more galaxy formation due to the propagation of the energy released at the death of massive stars are examined, and it is shown that such an explosive amplification is possible at redshifts less than about 5 and stellar system masses between 10 to the 8th and 10 to the 12th solar masses. Explosions before a redshift of about 5 are found to lead primarily to the formation of massive stars rather than galaxies, while those at a redshift close to 5 will result in objects of normal galactic scale. The model also predicts a dusty interstellar medium preventing the detection of objects of redshift greater than 3, numbers and luminosities of protogalaxies comparable to present observations, unvirialized groups of galaxies lying on two-dimensional surfaces, and a significant number of black holes in the mass range 1000-10,000 solar masses.
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
The exceptional imagery and data acquired by the Mars Exploration Rovers since their January 2004 landing have captured the attention of scientists, the public, and students and teachers worldwide. One aspect of particular interest lies with a group of high school teachers and students actively engaged in the Athena Student Interns Program. The Athena Student Interns Program (ASIP) is a joint effort between NASA s Mars Public Engagement Office and the Athena Science Investigation that began in early 1999 as a pilot student-scientist research partnership program associated with the FIDO prototype Mars rover field test . The program is designed to actively engage high school students and their teachers in Mars exploration and scientific inquiry. In ASIP, groups of students and teachers from around the country work with mentors from the mission s Athena Science Team to carry out an aspect of the mission.