Local torus actions modeled on the standard representation

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove that local torus actions are classified topologically by them. As a corollary, we obtain a topological classification of locally standard torus actions, which includes the topological classifications of quasi-toric manifolds by Davis and Januszkiewicz and of effective T²-actions on four-dimensional manifolds without nontrivial finite stabilizers by Orlik and Raymond. We discuss locally toric Lagrangian fibrations from the viewpoint of local torus actions. We also investigate the topology of a manifold equipped with a local torus action when the Euler class of the orbit map vanishes.     

Structure comparison between Th2Zn17-type and TbCu7-type Sm–Fe intermetallic compounds and their nitrides by means of 57Fe-Mössbauer spectroscopy

Samarium–iron intermetallic compounds were prepared by a melt spinning method with low and high wheel speeds, which resulted in a Th₂Zn₁₇-type and a TbCu₇-type structure, respectively. Structure comparison between these types was investigated for Sm–Fe intermetallic compounds and their nitrides by ⁵⁷Fe-Mössbauer spectroscopy.     

Synthesis of macrocycles having tröger base skeletons “[2.2]cyclic tröger base”

[2.2]Cyclic Tröger base2 was synthesized by the condensation of 1,2-bis (4-aminopheyl) ethane with paraformaldehyde under acidic condition in 43.8% yield. [2.2]Cyclic Tröger base2 was separated into meso form and racemate by fractional crystallization or using HPLC. Resolution of the racemate into its optical antipodes by passing the racemate through an activated D-(+)-lactose column was partially succeeded.Presented at the 15th Symposium on Structural Organic Chemistry, Kyoto, October, 1982.The trivial name [2.2]cyclic Tröger base is used because of the cumbersome nomenclature.10,12,25,32-Tetraazanonacyclo[19.7.7.1^4,8.1^14,18.1^25,32.0^7,12.0^7,12.0^10,15.-0^24,34.0^27,31] octatriaconta-1(29),4,6,8(36),14,16,18(37),21,23,27,-30,34-dodecaene.     

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.     

A facile synthesis of [3ncyclophanes,in which aromatic rings are connected with -CH2CO-CH2- bridges

The title compounds, I, were synthesized by the dialkylation of TosMIC, II, with appropriate bis (halomethyl) compounds, III, under phase-transfer condition, followed by acid hydrolysis.     

CFD-PBM approach for the gas-liquid flow in a nanobubble generator with honeycomb structure

In recent years, nanobubble technologies have drawn great attention due to their wide applications in many fields of science and technology. From previous studies, a kind of honeycomb structure for high efficiency nanobubble generation has been proposed. In this paper, the numerical simulations of bubbly flow in the honeycomb structure were performed by using a computational fluid dynamics–population balance model (CFD-PBM) coupled model. The numerical model was based on the Eulerian multiphase model and the population balance model (PBM) was used to calculate the bubble size distribution. The bubble size distributions in the honeycomb structure under different work conditions were predicted. Two different drag force models (Schiller-Naumann model and Tomiyama model) and two different aggregation models (Luo model and turbulent aggregation model) were investigated. Both two drag models gave similar prediction of bubble number density distribution at the outlet. The results obtained from Luo model had better reflection of the trend of number density distribution. The turbulence dissipation rate ε can be used to evaluate the nanobubble generating ability. The water tank was not included in the CFD model in this work. The bubbles in the water tank should be studied in the future.     

Discrete π Stack of a Tweezer-Shaped Naphthalenediimide–Anthracene Conjugate

The design and synthesis of a tweezer-shaped naphthalenediimide (NDI)–anthracene conjugate ( 2NDI ) are reported. In the structure of the closed form (π_NDI ⋅⋅⋅ π_NDI stack) of 2NDI , which was elucidated by single-crystal XRD, the existence of C−H ⋅⋅⋅ O hydrogen bonding involving the nearest carbonyl oxygen atom of an NDI unit was suggested. The tunability of π_NDI ⋅⋅⋅ π_NDI interactions was studied by means of UV/Vis absorption, fluorescence and NMR spectroscopy and molecular modelling. This revealed that the π_NDI ⋅⋅⋅ π_NDI interactions in 2NDI affect the absorption and emission properties depending on the temperature. Furthermore, in polar solvents, 2NDI prefers the stronger π_NDI ⋅⋅⋅ π_NDI stack, whereas the π_NDI ⋅⋅⋅ π_NDI interaction is diminished in nonpolar solvents. Importantly, the conformational variations of 2NDI can be reversibly switched by variation in temperature, and this suggests potential application for fluorogenic molecular switches upon temperature changes.