Generation of finite subgroups of the mapping class group of genus 2 surface by Dehn twists

In this note we give presentations, up to conjugacy, of all finite subgroups of the mapping class group of a closed surface of genus 2, using the Humphries generators. An application to homology representations is given.     

Long-wavelength luminescence from GaSb quantum dots grown on GaAs substrates

Self-assembled GaSb quantum dots (QDs) with a photoluminescence wavelength longer than 1.3 μm were successfully grown by suppressing the replacement of As and Sb on the surface of the GaSb QDs. This result means that GaSb can thus join InAs or GaInAs as a suitable material for QD lasers for optical communications.     

Nonasodium decatungstodysprosate pentatriacontahydrate

In the crystal structure of the title compound, Na₉[Dy(W₅O₁₈)₂]·35H₂O, the complex anion has approximate D_4d symmetry, with Dy—O and W—O distances in the ranges 2.355 (6)–2.405 (6) and 1.715 (7)–2.369 (5) Å, respectively.     

Laplace transform impedance analysis in the two-phase coexistence reaction of spinel Li1 + x Mn2O4 positive electrode

Journal of Solid State Electrochemistry - We demonstrate the Laplace transform (LT) impedance technique for measuring electrochemical lithiation and delithiation in the two-phase system of spinel...     

Mg isotope fractionation in biogenic carbonates of deep-sea coral, benthic foraminifera, and hermatypic coral

High-precision Mg isotope measurements by multiple collector inductively coupled plasma mass spectrometry were applied for determinations of magnesium isotopic fractionation of biogenic calcium carbonates from seawater with a rapid Mg purification technique. The mean δ²⁶Mg values of scleractinian corals, giant clam, benthic foraminifera, and calcite deep-sea corals were −0.87‰, −2.57‰, −2.34‰, and −2.43‰, suggesting preferential precipitation of light Mg isotopes to produce carbonate skeleton in biomineralization. Mg isotope fractionation in deep-sea coral, which has high Mg calcite skeleton, showed a clear temperature (T) dependence from 2.5 °C to 19.5 °C: 1,000 × ln(α) = −2.63 (±0.076) + 0.0138 (±0.0051) × T(R ² = 0.82, p < 0.01). The δ²⁶Mg values of large benthic foraminifera, which are also composed of a high-Mg calcite skeleton, can be plotted on the same regression line as that for deep-sea coral. Since the precipitation rates of deep-sea coral and benthic foraminifera are several orders of magnitude different, the results suggest that kinetic isotope fractionation may not be a major controlling factor for high-Mg calcite. The Mg isotope fractionation factors and the slope of temperature dependence from deep-sea corals and benthic foraminifera are similar to that for an inorganically precipitated calcite speleothem. Taking into account element partitioning and the calcification rate of biogenic CaCO₃, the similarity among inorganic minerals, deep-sea corals, and benthic foraminiferas may indicate a strong mineralogical control on Mg isotope fractionation for high-Mg calcite. On the other hand, δ²⁶Mg in hermatypic corals composed of aragonite has been comparable with previous data on biogenic aragonite of coral, sclerosponges, and scaphopad, regardless of species differences of samples.     

A divergent synthesis of dihydropyridazinones,N‐substituted dihydropyrazoles,and O‐substituted pyrazoles

Dihydropyridazinones 4a , 4b , N‐substituted dihydropyrazoles 5b , 5c , 5d , and O‐substituted pyrazoles 6a , 6b , 6c , 6d have been synthesized starting from spirocyclopropanepyrazole derivative 2 . Treatment of 2 with α‐chloro esters, e.g., methyl chloroacetate, ethyl chloroacetate, isopropyl chloroacetate, and tert‐butyl chloroacetate, in potassium carbonate/sodium iodide system caused ring opening and subsequent C‐ or N‐attack nucleophilic substitution to give the corresponding dihydropyridazinones 4a , 4b and N‐substituted dihydropyrazoles 5b , 5c , 5d . On the other hand, in the absence of sodium iodide, O‐substituted pyrazoles 6a , 6b , 6c , 6d were obtained from 2 via an O‐attack nucleophilic substitution. J. Heterocyclic Chem., 2011.     

On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities

Journal of Theoretical Probability - We consider symmetric stable-type processes with degenerate/singular Lévy densities via Dirichlet form theory. We give conditions of some global path...