Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Embeddings of partial Steiner triple systems

Any partial Steiner triple system of order u can be embedded in a Steiner triple system of order v if v equivalent to 1, 3 (mod 6) and v greater than or equal to 3u - 2. (C) 2004 Elsevier Inc. All rights reserved.

PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4.

Steiner triple systems with two disjoint subsystems

It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.

Some generalization of Desargues and Veronese configurations

2000 Mathematics Subject Classification: 51E14, 51E30.

Catalytic oxidation of cyclohexene to cyclohexanone by a triple system in acidic aqueous acetonitrile medium

The catalytic oxidation of cyclohexene to cyclohexanone using Pd(OAc)(2)/HQ/FePc was investigated in an acidic aqueous solution of acetonitrile. The role of each component of this system in the oxidation of cyclohexene was explored by means of UV-VIS, IR, XPS spectroscopy and. cyclic voltammetry, respectively. Based on the experimental results, the mechanism of the oxidation of cyclohexene catalyzed by Pd(OAc)(2)/HQ/FePc was elucidated.

WASP-22 b: A Transiting "Hot Jupiter" Planet in a Hierarchical Triple System

We report the discovery of a transiting planet orbiting the star TYC 6446-326-1. The star, WASP-22, is a moderately bright (V = 12.0) solar-type star (Teff = 6000 ± 100 K, [Fe/H] = -0.05 ± 0.08). The light curve of the star obtained with the WASP-South instrument shows periodic transit-like features with a depth of about 1% and a duration of 0.14 days. The presence of a transit-like feature in the light curve is confirmed using z-band photometry obtained with Faulkes Telescope South. High-resolution spectroscopy obtained with the CORALIE and HARPS spectrographs confirms the presence of a planetary mass companion with an orbital period of 3.533 days in a near-circular orbit. From a combined analysis of the spectroscopic and photometric data assuming that the star is a typical main-sequence star we estimate that the planet has a mass M p = 0.56 ± 0.02M Jup and a radius R p = 1.12 ± 0.04R Jup. In addition, there is a linear trend of 40 m s-1 yr-1 in the radial velocities measured over 16 months, from which we infer the presence of a third body with a long-period orbit in this system. The companion may be a low mass M-dwarf, a white dwarf, or a second planet.

WASP-34b: a near-grazing transiting sub-Jupiter-mass exoplanet in a hierarchical triple system

We report the discovery of WASP-34b, a sub-Jupiter-mass exoplanet transiting its 10.4-magnitude solar-type host star (1SWASP J110135.89-235138.4; TYC 6636-540-1) every 4.3177 days in a slightly eccentric orbit (e = 0.038±0.012). We find a planetary mass of 0.59±0.01 MJup and radius of 1.22-0.08+0.11 RJup. There is a linear trend in the radial velocities of 55±4 m s-1 y-1 indicating the presence of a long-period third body in the system with a mass ?0.45 MJup at a distance of ?1.2 AU from the host star. This third-body is either a low-mass star, a white dwarf, or another planet. The transit depth ((RP/Rstar)2 = 0.0126) and high impact parameter (b = 0.90) suggest that this could be the first known transiting exoplanet expected to undergo grazing transits, but with a confidence of only 80%. Radial velocity and photometric data are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/526/A130

Stability regions around the components of the triple system 2001 SN263

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The aster mission: Exploring for the first time a triple system asteroid

2001 SN263 is a triple system asteroid. Although it was discovery in 2001, in 2008 astronomical observation carried out by Arecibo observatory revealed that it is actually a system with three bodies orbiting each other. The main central body is an irregular object with a diameter about 2.8 km, while the other two are small objects with less than 1 km across. This system presents an orbital eccentricity of 0.47, with perihelion of 1.04 and aphelion of 1.99, which means that it can be considered as a Near Earth Object. This interesting system was chosen as the target for the Aster mission - first Brazilian space exploration undertaking. A small spacecraft with 150 kg of total mass, 30 kg of payload with 110 W available for the instruments, is scheduled to be launched in 2015, and in 2018 it will approach and will be put in orbit of the triple system. This spacecraft will use electric propulsion and in its payload it will carry image camera, laser rangefinder, infrared spectrometer, mass spectrometer, and experiments to be performed in its way to the asteroid. This mission represents a great challenge for the Brazilian space program. It is being structured to allow the full engagement of the Brazilian universities and technological companies in all the necessary developments to be carried out. In this paper, we present some aspects of this mission, including the transfer trajectories to be used, and details of buss and payload subsystems that are being developed and will be used. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Stable retrograde orbits around the triple system 2001 SN263

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Oral rehabilitation with implantations: association of fixed partial prosthesis, UCLA system, and EsthetiCone

The objective of modern odontology is to reconstitute to the patient the comfort, the function, the aesthetic form, the phonetic capability, and normal health. However, the more the patient is toothless, the more this objective becomes difficult inside traditional dentistry. As a result of continuous research of materials and techniques, permissible success is now a reality, whitewashing many challenging clinical situations. Thus, the objective of the article was to present a clinical case where association of the universal cast to long abutment pillars and EsthetiCone were used for aesthetic whitewashing. A man presented to the clinic of the Faculty of Dentistry, Universidade Estadual Paulista. After clinical examination and radiographic evaluation evidenced the necessity of substitution of fixed prostheses (15-25), he was presented with disadaptation and a favorable aesthetic solution. Ahead of the evaluated picture and considering the extension of the toothless space made, it was opted more, to the accomplishment of surgery, the setting of 2 implantations in the region and 2 in each edentate side of the posterior portion of the jaw. On 6 implants and 2 teeth, 10 metal ceramic crowns had been confectioned: 4 of them being joined in the region of the 12 to the 22 and the other 6 as unit crowns in the region of the 13, the 14, the 15, the 23, the 24, and the 25. The carried-through treatment was capable to return the aesthetic form, the function, the phonetic capability, the comfort, and the health of the verbal socket.

The magnetically-active, low-mass, triple system WDS 19312+3607 (Research Note)

Aims. We investigated in detail the system WDS 19312+3607, whose primary is an active M4.5Ve star previously inferred to be young (τ ~ 300–500 Ma) based on its high X-ray luminosity. Methods. We collected intermediate- and low-resolution optical spectra taken with 2 m-class telescopes, photometric data from the B to 8 μm bands, and data for eleven astrometric epochs with a time baseline of over 56 years for the two components in the system, G 125–15 and G 125–14. Results. We derived the M4.5V spectral types of both stars, confirmed their common proper motion, estimated their heliocentric distance and projected physical separation, determined their Galactocentric space velocities, and deduced a most-probable age of older than 600 Ma. We discovered that the primary, G 125–15, is an inflated, double-lined, spectroscopic binary with a short period of photometric variability of 1.6 d, which we associated with orbital synchronisation. The observed X-ray and Hα emissions, photometric variability, and abnormal radius and effective temperature of G 125–15 AB are indicative of strong magnetic activity, possibly because of the rapid rotation. In addition, the estimated projected physical separation between G 125–15 AB and G 125–14 of about 1200 AU ensures that WDS 19312+3607 is one of the widest systems with intermediate M-type primaries. Conclusions. G 125–15 AB is a nearby (d ≈ 26 pc), bright (J ≈ 9.6 mag), active spectroscopic binary with a single proper-motion companion of the same spectral type at a wide separation. They are thus ideal targets for specific follow-ups to investigate wide and close multiplicity or stellar expansion and surface cooling because of the lower convective efficiency.

Orbital and Physical Properties of the σ Ori Aa, Ab, B Triple System

We provide a complete characterization of the astrophysical properties of the σ Ori Aa, Ab, B hierarchical triple system and an improved set of orbital parameters for the highly eccentric σ Ori Aa, Ab spectroscopic binary. We compiled a spectroscopic data set comprising 90 high-resolution spectra covering a total time span of 1963 days. We applied the Lehman-Filhés method for a detailed orbital analysis of the radial velocity curves and performed a combined quantitative spectroscopic analysis of the σ Ori Aa, Ab, B system by means of the stellar atmosphere code FASTWIND. We used our own plus other available information on photometry and distance to the system for measuring the radii, luminosities, and spectroscopic masses of the three components. We also inferred evolutionary masses and stellar ages using the Bayesian code BONNSAI. The orbital analysis of the new radial velocity curves led to a very accurate orbital solution of the σ Ori Aa, Ab pair. We provided indirect arguments indicating that σ Ori B is a fast-rotating early B dwarf. The FASTWIND+BONNSAI analysis showed that the Aa, Ab pair contains the hottest and most massive components of the triple system while σ Ori B is a bit cooler and less massive. The derived stellar ages of the inner pair are intriguingly younger than the one widely accepted for the σ Orionis cluster, at 3 ± 1 Ma. The outcome of this study will be of key importance for a precise determination of the distance to the σ Orionis cluster, the interpretation of the strong X-ray emission detected for σ Ori Aa, Ab, B, and the investigation of the formation and evolution of multiple massive stellar systems and substellar objects.

Generalizations of Cole's Systems

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.