A systematic derivation of a consistent set of “Boussinesq equations”

The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ?, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit $\varepsilon\rightarrow0The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ɛ, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit e?0\varepsilon\rightarrow0 and Ec? 0{Ec}\rightarrow 0 with Ec/e = const.{Ec}/\varepsilon =const. The equations are compared to “Boussinesq equations” of other studies and used to calculate Nusselt numbers in laminar and turbulent flows in infinite vertical channels as an example and for the justification of the asymptotic approach.     

Antioxidant Grain Passivation for Air‐Stable Tin‐Based Perovskite Solar Cells

Tin‐based perovskites with excellent optoelectronic properties and suitable band gaps are promising candidates for the preparation of efficient lead‐free perovskite solar cells (PSCs). However, it is challenging to prepare highly stable and efficient tin‐based PSCs because Sn²⁺ in perovskites can be easily oxidized to Sn⁴⁺ upon air exposure. Here we report the fabrication of air‐stable FASnI₃ solar cells by introducing hydroxybenzene sulfonic acid or its salt as an antioxidant additive into the perovskite precursor solution along with excess SnCl₂. The interaction between the sulfonate group and the Sn²⁺ ion enables the in situ encapsulation of the perovskite grains with a SnCl₂–additive complex layer, which results in greatly enhanced oxidation stability of the perovskite film. The corresponding PSCs are able to maintain 80 % of the efficiency over 500 h upon air exposure without encapsulation, which is over ten times longer than the best result reported previously. Our results suggest a possible strategy for the future design of efficient and stable tin‐based PSCs.     

Ferroelectrically Switching Helical Columnar Assembly Comprising Cisoid Conformers of a 1,2,3‐Triazole‐based Liquid Crystal

The 1,2,3‐triazole molecule, which is a product of click chemistry, possesses a high dipole moment and can be a useful polar motif for ferroelectric columnar liquid crystal (LC) materials—though it has not been used to date. Herein, we report the helical assembly and ferroelectric switching properties of a columnar liquid crystal comprising a naphthalene core and 1,2,3‐triazolyl linkages. The molecule assembles into a double‐stranded helical columnar LC structure (Col_hel). The X‐ray simulations of cisoid and transoid columnar models suggest that the helical assembly comprises cisoid conformers with a non‐zero dipole moment. The helical columns in the Col_hel phase are aligned homeotropically under an electric field. The ferroelectric switching of the axial polarization can be observed in the temperature range of 105–115 °C in the Col_hel phase, wherein the triazolyl hydrogen bonding along the column axis is weakened. The ferroelectric switching event is attributed to the rotation of the polar triazolyl units in response to the electric field.     

Copper catalyzed/mediated direct B–H alkenylation/alkynylation in carboranes

Base metal catalyzed regioselective cage B–H functionalization has been achieved. Under the assistance of a bidentate directing group, Cu-catalyzed [4+2] annulation of carboranyl amides with internal alkynes affords unprecedented C,B-substituted carborane-fused-pyridone derivatives, whereas the use of terminal alkynes leads to B–H/C(sp)–H dehydrocoupling products. The isolation and structural identification of a notably stable Cu(Ⅰ) intermediate shed light on the reaction mechanism, which is proposed to involve a Cu(Ⅲ) intermediate.     

Complete and non-compact conformally flat manifolds with constant scalar curvature

Non-compact conformally flat manifolds with constant scalar curvature and non-compact Kaehler manifolds with vanishing Bochner curvature are studied and classified.Partially supported by TGRC-KOSEF, 1990.     

AUTOINDUCTION AND ALDEHYDE CHAIN-LENGTH EFFECTS ON THE BIOLUMINESCENT EMISSION FROM THE YELLOW PROTEIN ASSOCIATED WITH LUCIFERASE IN Vibrio fischeri STRAIN Y-1b

Abstract— A new strain of the yellow-light emitting bacterium Vibrio fischeri Y-lb, possessing a higher fraction of its emission in the yellow, was isolated and characterized. The in vivo yellow to blue ratio (Y/B) increases during growth in parallel with the autoinduction of luciferase, reaching a value above 5 at 17°C. This Y/B increase is attributed to concomitant increases in the intracellular levels of both luciferase and the specific protein associated with yellow emission, the yellow fluorescent protein (YFP), and to the association of the two proteins at higher concentrations. The yellow emission is rapidly but reversibly lost by brief exposures to a temperature of 27°C (5 s), and irreversibly so at 40°C, attributed to dissociation of the two proteins. A concentrated crude extract emits almost exclusively yellow light in the in vitro reaction, and theY/B ratio decreases with dilution. The Y/B ratio in vitro is also dependent on the aldehyde chain length; experiments with aldehyde analogs suggest that the aldehyde binding site of luciferase must be occupied for YFP to stimulate light emission.     

Fiber-optic extrinsic Fabry-Perot dc magnetic field sensor

We demonstrate a compact extrinsic Fabry-Perot interferometer-based fiber-optic sensor that uses magnetostrictive amorphous metallic wire Unitika AF-10 (Fe77.5B15Si7.5) as a sensor gauge for measuring dc magnetic fields. We present a theoretical model based on a Gaussian electric field distribution to analyze the sensor operation as a function of longitudinal air-gap separation. The model shows good agreement with the experimental results. A resolution of 50 nT over a range of 50-40,000 nT with a simple passive temperature-compensation method is obtained.     

Special domains and nonmanipulability

We investigate domains on which a nonmanipulable, nondictatorial social choice function exists, having at least three distinct values. We do not make the assumptions of Kalai and Muller (1977). We classify all such 2-person functions on the domain which is the cyclic group Z_m. We show that for any domain containing Z_m, existence for 2 voters and existence for some n > 2 voters are equivalent. We show that for an n-person, onto, nonmanipulable social choice function F on Z_m, F(P₁, P₂,…, P_n) {x₁, x₂,…, x_n} always, x_i being the most preferred alternative under preference P_i. We show that no domain containing the dihedral group admits such a social choice function. We show that there exists a domain on which all k-tuples are free for arbitrarily large k, for which such a social choice function does exist.     

On a Conjecture of Phadke and Thakare

We prove the connectedness of the set of all nonzero bounded linear operators on a complex Hilbert space having a generalized inverse.