Brunnian links are determined by their complements

If L_1 and L_2 are two Brunnian links with all pairwise linking numbers 0, then we show that L_1 and L_2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three components. If L_1 is a Brunnian link with all pairwise linking numbers 0, and the complement of L_2 is homeomorphic to the complement of L_1, then we show that L_2 may be obtained from L_1 by a sequence of twists around unknotted components. Finally, we show that for any positive integer n, an algorithm for detecting an n-component unlink leads immediately to an algorithm for detecting an unlink of any number of components. This algorithmic generalization is conceptually simple, but probably computationally impractical.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-7.abs.htm

A note on doubles of groups

Recently, Rips produced an example of a double of two free groups which has unsolvable generalized word problem. In this paper, we show that Rips\u27s example fits into a large class of doubles of groups, each member of which contains F2×F2 and therefore has unsolvable generalized word problem and is incoherent. © 2001 Elsevier Science B.V

Ternary Nitride Semiconductors in the Rocksalt Crystal Structure

Inorganic nitrides with wurtzite crystal structures are well-known semiconductors used in optoelectronic devices. In contrast, rocksalt-based nitrides are known for their metallic and refractory properties. Breaking this dichotomy, here we report on ternary nitride semiconductors with rocksalt crystal structures, remarkable optoelectronic properties, and the general chemical formula Mg$_{x}$TM$_{1-x}$N (TM=Ti, Zr, Hf, Nb). These compounds form over a broad metal composition range and our experiments show that Mg-rich compositions are nondegenerate semiconductors with visible-range optical absorption onsets (1.8-2.1 eV). Lattice parameters are compatible with growth on a variety of substrates, and epitaxially grown MgZrN$_{2}$ exhibits remarkable electron mobilities approaching 100 cm$^{2}$V$^{-1}$s$^{-1}$. Ab initio calculations reveal that these compounds have disorder-tunable optical properties, large dielectric constants and low carrier effective masses that are insensitive to disorder. Overall, these experimental and theoretical results highlight Mg$_{G-3}$TMN$_{G-2}$ rocksalts as a new class of semiconductor materials with promising properties for optoelectronic applications

MUSTANG 3.3 Millimeter Continuum Observations of Class 0 Protostars

We present observations of six Class 0 protostars at 3.3 mm (90 GHz) using the 64-pixel MUSTANG bolometer camera on the 100-m Green Bank Telescope. The 3.3 mm photometry is analyzed along with shorter wavelength observations to derive spectral indices (S_nu ~ nu^alpha) of the measured emission. We utilize previously published dust continuum radiative transfer models to estimate the characteristic dust temperature within the central beam of our observations. We present constraints on the millimeter dust opacity index, beta, between 0.862 mm, 1.25 mm, and 3.3 mm. Beta_mm typically ranges from 1.0 to 2.4 for Class 0 sources. The relative contributions from disk emission and envelope emission are estimated at 3.3 mm. L483 is found to have negligible disk emission at 3.3 mm while L1527 is dominated by disk emission within the central beam. The beta_mm^disk <= 0.8 - 1.4 for L1527 indicates that grain growth is likely occurring in the disk. The photometry presented in this paper may be combined with future interferometric observations of Class 0 envelopes and disks.Comment: 19 pages, 3 figures, AJ accepted, in pres

Socially Disorganized Rural Communities

The article talks about the social disorganization of rural communities in the U.S. It is stated that family farming has been on the decline for decades, with the numbers of farmers dropping by 16 million since 1950 and farms decreasing by over 4 million during the past century. It is inferred that a part of a community\u27s history and way of life are being forfeited when local business are closing. According to the author, the theory of social disorganization emphasizes social integration and stability as necessary conditions for community. It offers some of the disadvantages of disorganized communities, such as the lack of collective efficacy

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead