Classification of torus manifolds with codimension one extended actions

The purpose of this paper is to classify torus manifolds (M ²ⁿ , T ⁿ ) with codimension one extended G-actions (M ²ⁿ , G) up to essential isomorphism, where G is a compact, connected Lie group whose maximal torus is T ⁿ . For technical reasons, we do not assume torus manifolds are orientable. We prove that there are seven types of such manifolds. As a corollary, if a nonsingular toric variety or a quasitoric manifold has a codimension one extended action then such manifold is a complex projective bundle over a product of complex projective spaces.     

基于地对空观测光谱的大气CO2柱浓度反演分析

基于地对空高光谱观测获取大气CO₂柱浓度(大气中CO₂的垂直总含量)数据是验证和改进卫星高光谱观测反演CO₂浓度的重要数据源之一,而目前在中国还没有基于地面光谱观测进行大气CO₂柱浓度反演研究的报告。利用光谱分析仪与太阳跟踪仪等构成的地面观测系统在中国内蒙古锡林郭勒草原进行了地对空高光谱观测,基于高光谱观测数据反演了大气CO₂柱浓度。在基于1.6 μm大气CO₂的光谱吸收特征进行CO₂浓度反演过程中,评价分析了观测光谱的波长漂移和气象参数对大气CO₂柱浓度反演精度的影响。结果显示观测期间平均大气CO₂柱浓度为390.9 μg·mL-1。波长的漂移将会导致反演浓度值整体偏低;波长漂移从-0.012～0.042 nm范围时,将会导致1 μg·mL-1以上的偏差。同时,研究发现光谱透过率在6 357～6 358,6 360～6 361和6 363～6 364 cm-1谱段敏感于气象参数的变化。对比利用与光谱观测同时和非同时观测的气象参数进行的浓度反演结果发现,非同时观测气象参数的利用引起的浓度偏差最小在0.11 μg·mL-1,最大可达4 μg·mL-1;本论文的分析结果对基于光谱反演CO₂柱浓度算法的改进有着一定的参考价值。     

Structural elucidation of a methylenation reagent of esters: synthesis and reactivity of a dinuclear titanium(iii) methylene complex

Transmetallation of a zinc methylene complex [ZnI(tmeda)]₂(μ-CH₂) with a titanium(iii) chloride [TiCl₃(tmeda)(thf)] produced a titanium methylene complex. The X-ray diffraction study displayed a dinuclear methylene structure [TiCl(tmeda)]₂(μ-CH₂)(μ-Cl)₂. Treatment of an ester with the titanium methylene complex resulted in methylenation of the ester carbonyl to form a vinyl ether. The titanium methylene complex also reacted with a terminal olefin, resulting in olefin-metathesis and olefin-homologation. Cyclopropanation by methylene transfer from the titanium methylene proceeded by use of a 1,3-diene. The mechanistic study of the cyclopropanation reaction by the density functional theory calculations was also reported.

Transmetallation of a zinc methylene complex [ZnI(tmeda)]₂(μ-CH₂) with a titanium(iii) chloride [TiCl₃(tmeda)(thf)] produced a titanium methylene complex.     

Incommensurate spin fluctuations in hole-overdoped superconductor KFe2As2

A neutron scattering study of heavily hole-overdoped superconducting KFe2As2 revealed a well-defined low-energy incommensurate spin fluctuation at [π(1 ± 2 δ),0] with δ = 0.16. The incommensurate structure differs from the previously observed commensurate peaks in electron-doped AFe2As2 (A = Ba, Ca, or Sr) at low energies. The direction of the peak splitting is perpendicular to that observed in Fe(Te,Se) or in Ba(Fe,Co)2As2 at high energies. A band structure calculation suggests interband scattering between bands around the Γ and X points as an origin of this incommensurate peak. The perpendicular direction of the peak splitting can be understood within the framework of multiorbital band structure. The results suggest that spin fluctuation is more robust in hole-doped than in electron-doped samples, which can be responsible for the appearance of superconductivity in the heavily hole-doped samples.     

An application of a boundary element method to natural convection

The direct boundary element method is applied to the numerical modelling of thermal fluid flow in a transient state. The Navier-Stokes equations are considered under the Boussinesq approximation and the viscous thermal flow equations are expressed in terms of stream function, vorticity, and temperature in two dimensions. Boundary integral equations are derived using logarithmic potential and time-dependent heat potential as fundamental solutions. Boundary unknowns are discretized by linear boundary elements and flow domains are divided into a series of triangular cells. Charged points are translated upstream in the numerical evaluation of convective terms. Unknown stream function, vorticity, and temperature are staggered in the computational scheme.

Simple iteration is found to converge to the quasi steady-state flow. Boundary solutions for two-dimensional examples at a Reynolds number 100 and Grashoff number 10⁷ are obtained.     

Unconventional pairing originating from disconnected Fermi surfaces in the iron-based superconductor

For the iron-based high T_c superconductor LaFeAsO_1?xF_x, we construct a minimal model, where all of the five Fe d bands turn out to be involved. We then investigate the origin of superconductivity with a five-band random-phase approximation by solving the Eliashberg equation. We conclude that the spin fluctuation modes arising from the nesting between the disconnected Fermi pockets realise, basically, an extended s-wave pairing, where the gap changes sign across the nesting vector.     

Superdrawing of polytetrafluoroethylene nascent powder by solid‐state coextrusion

A film of nascent powder of polytetrafluoroethylene (PTFE), compacted below the ambient melting temperature (T_m, 335 °C), was drawn by two‐stage draw techniques consisting of a first‐stage solid‐state coextrusion followed by a second‐stage solid‐state coextrusion or tensile draw. Although the ductility of extrudates was lost for the second‐stage tensile draw at temperatures above 150 °C due to the rapid decrease in strength, as previously reported, the ductility of extrudates increased with temperature even above 150 °C when the second‐stage draw was made by solid‐state coextrusion, reflecting the different deformation flow fields in a free space for the former and in an extrusion die for the latter. Thus, a powder film initially coextruded to a low extrusion draw ratio (EDR) of 6–20 at 325 °C was further drawn by coextrusion to EDRs up to ～?400 at 325–340 °C, near the T_m. Extremely high chain orientation (f_c = 0.998 ± 0.001), crystallinity (96.5 ± 0.5)%, and tensile modulus (115 ± 5 GPa at 24 °C, corresponding to 73% of the X‐ray crystal modulus) were achieved at high EDRs. Despite such a morphological perfection and a high modulus, the tensile strength of a superdrawn tape, 0.48 ± 0.03 GPa, was significantly low when compared with those (1.4–2.3 GPa) previously reported by tensile drawing above the T_m. Such a low strength of a superdrawn, high‐modulus PTFE tape was ascribed to the low intermolecular interaction of PTFE and the lack of intercrystalline links along the fiber axis, reflecting the initial chain‐extended morphology of the nascent powder combined with the fairly high chain mobility associated with the crystal/crystal transitions at around room temperature. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3369–3377, 2006     

On SL(3, ℝ)-actions on 4-spheres

We construct a natural, continuous SL(3, ℝ)-action on S ⁴ which is an extension of the SO(3)-action ψ of Uchida. The construction is based on the Kuiper theorem asserting that the quotient space of ℂP(2) by complex conjugation is S ⁴. We also give a new proof of the Kuiper theorem. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 99–105, 2005.