On indecomposable modules over the Virasoro algebra

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains the trivial module as one of its composition factors.Comment: 5 pages, Latex, to appear in Science in China

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

Common Warm Dust Temperatures Around Main-sequence Stars

We compare the properties of warm dust emission from a sample of main-sequence A-type stars (B8-A7) to those of dust around solar-type stars (F5-K0) with similar Spitzer Space Telescope Infrared Spectrograph/MIPS data and similar ages. Both samples include stars with sources with infrared spectral energy distributions that show evidence of multiple components. Over the range of stellar types considered, we obtain nearly the same characteristic dust temperatures (~190 K and ~60 K for the inner and outer dust components, respectively)—slightly above the ice evaporation temperature for the inner belts. The warm inner dust temperature is readily explained if populations of small grains are being released by sublimation of ice from icy planetesimals. Evaporation of low-eccentricity icy bodies at ~150 K can deposit particles into an inner/warm belt, where the small grains are heated to T_(dust)~ 190 K. Alternatively, enhanced collisional processing of an asteroid belt-like system of parent planetesimals just interior to the snow line may account for the observed uniformity in dust temperature. The similarity in temperature of the warmer dust across our B8-K0 stellar sample strongly suggests that dust-producing planetesimals are not found at similar radial locations around all stars, but that dust production is favored at a characteristic temperature horizon

Intergovernmental Relationships in Costal Land Management

In order to decrease the degradation rate of magnesium (Mg) alloys for the potential orthopedic applications, manganese-calcium phosphate coatings were prepared on an Mg-Ca-Zn alloy in calcium phosphating solutions with different addition of Mn2+. Influence of Mn content on degradation behaviors of phosphate coatings in the simulated body fluid was investigated to obtain the optimum coating. With the increasing Mn addition, the corrosion resistance of the manganese-calcium phosphate coatings was gradually improved. The optimum coating prepared in solution containing 0.05 mol/L Mn2+ had a uniform and compact microstructure and was composed of MnHPO4 center dot 3H(2)O, CaHPO4 center dot 2H(2)O, and Ca-3 (PO4)(2). The electrochemical corrosion test in simulated body fluid revealed that polarization resistance of the optimum coating is 36273 Omega cm(2), which is about 11 times higher than that of phosphate coating without Mn addition. The optimum coating also showed the most stable surface structure and lowest hydrogen release in the immersion test in simulated body fluid

The Decay of Debris Disks around Solar-Type Stars

We present a Spitzer MIPS study of the decay of debris disk excesses at 24 and 70 $\mu$m for 255 stars of types F4 - K2. We have used multiple tests, including consistency between chromospheric and X-ray activity and placement on the HR diagram, to assign accurate stellar ages. Within this spectral type range, at 24 $\mu$m, $13.6 \pm 2.8 \%$ of the stars younger than 5 Gyr have excesses at the 3$\sigma$ level or more, while none of the older stars do, confirming previous work. At 70 $\mu$m, $22.5 \pm 3.6\%$ of the younger stars have excesses at $\ge$ 3 $\sigma$ significance, while only $4.7^{+3.7}_{-2.2}$% of the older stars do. To characterize the far infrared behavior of debris disks more robustly, we double the sample by including stars from the DEBRIS and DUNES surveys. For the F4 - K4 stars in this combined sample, there is only a weak (statistically not significant) trend in the incidence of far infrared excess with spectral type (detected fractions of 21.9$^{+4.8}_{-4.3}\%$, late F; 16.5$^{+3.9}_{-3.3}\%$, G; and 16.9$^{+6.3}_{-5.0}\%$, early K). Taking this spectral type range together, there is a significant decline between 3 and 4.5 Gyr in the incidence of excesses with fractional luminosities just under $10^{-5}$. There is an indication that the timescale for decay of infrared excesses varies roughly inversely with the fractional luminosity. This behavior is consistent with theoretical expectations for passive evolution. However, more excesses are detected around the oldest stars than is expected from passive evolution, suggesting that there is late-phase dynamical activity around these stars.Comment: 46 pages. 7 figures. Accepted to Ap

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page