Sequential star formation at the periphery of the HII regions Sh 217 and Sh 219

The HII regions Sh 217 and Sh 219 are textbook examples of a Stromgren sphere surrounded by an annular photodissociation region (PDR). The annular PDR is observed in both the 21 cm atomic hydrogen emission and the dust (PAH) emission near 8 micron (MSX Survey). An ultracompact radio continuum source is observed in the direction of the annular PDR, in both Sh 217 and Sh 219. JHKobservations show the presence of highly reddened stellar clusters (AV ~ 20 mag) in the directions of these radio sources. These clusters are also IRAS sources, of luminosities 22700 Lo for Sh 217 and 5900 Lo for Sh 219. Each cluster contains at least one luminous star with an IR colour excess; the one in the Sh 219 cluster shows H-alpha emission. The cluster associated with Sh 217 is almost spherical and contains luminous objects at its centre. The cluster associated with Sh 219 is elongated along the ionization front of this HII region. We argue that these are `second-generation clusters', which means that the physical conditions present in the PDRs, close to the ionization fronts, have favoured the formation of clusters containing massive objects. We discuss the physical mechanisms which may be at the origin of the observed triggered star formation.Comment: 12 pages, Late

Enhancement of second harmonic generation in a doubly resonant metamaterial

We investigate second harmonic (SH) generation in a doubly resonant metamaterial. We show that SH generation can be enhanced when the resonant condition is satisfied for the SH frequency as well as for the fundamental frequency. A unit cell of the doubly resonant metamaterial consists of two coupled resonators, one of which resonates at the fundamental frequency, whereas the other resonates around the SH frequency. We observe that the SH generation in the doubly resonant metamaterial is 4.6 times as large as that in a singly resonant metamaterial.Comment: 4 pages, 4 figure

The Shapovalov determinant for the Poisson superalgebras

Among simple Z-graded Lie superalgebras of polynomial growth, there are several which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields on the (1|6)-dimensional supercircle preserving the contact form, and the series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov described irreducible finite dimensional representations of po(0|n) and sh(0|n); we generalize his result for Verma modules: give criteria for irreducibility of the Verma modules over po(0|2k) and sh(0|2k)

Abnormal Action Potentials Associated with the Shaker Complex Locus of Drosophila

Intracellular recordings of action potentials were made from the cervical giant axon in Shaker (Sh) mutants and normal Drosophila. The mutants showed abnormally long delays in repolarization. The defect is not due to abnormal Ca2+ channels, because it persists in the presence of Co2+, a Ca2+-channel blocker. On the other hand, the K+-channel blocker 4-aminopyridine causes a similar effect in normal animals, suggesting that the Sh mutant may have abnormal K+ conductance. Gene-dosage analysis of Sh shows that the defect is not due to underproduction of an otherwise normal molecule; it may be due to an abnormal molecule produced by the mutated gene. Gel electrophoresis failed to detect an abnormal protein, suggesting that, if Sh codes for a nervous system protein, it is rare. Genetic analysis of the Sh locus indicates three regions. Mutations or chromosome breaks in the two flanking regions cause Sh mutant physiology; the central region shows a "haplolethal effect"--i.e., heterozygous females are lethal

Grothendieck quantaloids for allegories of enriched categories

For any small involutive quantaloid Q we define, in terms of symmetric quantaloid-enriched categories, an involutive quantaloid Rel(Q) of Q-sheaves and relations, and a category Sh(Q) of Q-sheaves and functions; the latter is equivalent to the category of symmetric maps in the former. We prove that Rel(Q) is the category of relations in a topos if and only if Q is a modular, locally localic and weakly semi-simple quantaloid; in this case we call Q a Grothendieck quantaloid. It follows that Sh(Q) is a Grothendieck topos whenever Q is a Grothendieck quantaloid. Any locale L is a Grothendieck quantale, and Sh(L) is the topos of sheaves on L. Any small quantaloid of closed cribles is a Grothendieck quantaloid, and if Q is the quantaloid of closed cribles in a Grothendieck site (C,J) then Sh(Q) is equivalent to the topos Sh(C,J). Any inverse quantal frame is a Grothendieck quantale, and if O(G) is the inverse quantal frame naturally associated with an \'etale groupoid G then Sh(O(G)) is the classifying topos of G.Comment: 28 pages, final versio

An omnidirectional shear horizontal wave transducer based on ring array of face-shear (d24) piezoelectric ceramics

The non-dispersive fundamental shear horizontal (SH0) wave in plate-like structures is of practical importance in non-destructive testing (NDT) and structural health monitoring (SHM). Theoretically, an omnidirectional SH0 transducer phased array system can be used to inspect defects in a large plate in the similar manner to the phased array transducers used in medical B-scan ultrasonics. However, very few omnidirectional SH transducers have been proposed so far. In this work, an omnidirectional SH wave piezoelectric transducer (OSH-PT) was proposed which consists of a ring array of twelve face-shear (d24) trapezoidal PZT elements. Each PZT element can produce face-shear deformation under applied voltage, resulting in circumferential shear deformation in the OSH-PT and omnidirectional SH waves in the hosting plate. Both finite element simulations and experiments were conducted to examine the performance of the proposed OSH-PT. Experimental testing shows that the OSH-PT exhibits good omnidirectional properties, on matter it is used as a SH wave transmitter or a SH wave receiver. This work may greatly promote the applications of SH waves in NDT and SHM.Comment: 15 pages, 8 figure