Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg     

PERI-INTERACTIONS IN NAPHTHALENES, 21. SUBSTITUENT EFFECTS IN (8-DIMETHYLAMINO-NAPHTH-1-YL)- AND [2-DIMETHYLAMINO-METHYL)PHENYL] - PHOSPHINES ON THE 31P-NMR SIGNAL POSITIONS

Abstract

Contrary to claims in the literature, the ³¹P NMR signal positions of ortho-dimethylaminomethyl-substituted triarylphosphines do not provide evidence for hypercoordination at phosphorus; the observed highfield shifts relative to triphenylphosphine are rather due to the ortho-effect. In (8-dimethylamino-naphth-1-yl)phosphines, the signal positions similar to that of triphenylphosphine are the result of the highfield ortho-effect and a lowfield peri-substituent effect of about the same magnitude whose nature remains to be explored.     

Non‐symmetric bent‐core mesogens with one terminal vinyl group

Two series of non‐symmetric banana‐shaped compounds, both with one alkyl and one alkenyl terminal tail, have been synthesized and studied. Both series were compared with the corresponding series with two saturated terminal alkyl tails. All the compounds have a bent central 1,3‐phenylene bis(4‐benzoyloxy)benzoate core; their mesophases were characterized by polarizing optical microscopy, differential scanning calorimetry, X‐ray diffraction and switching current response experiments. In all four series one of the terminal tails is varied from OC₈H₁₇ to OC₁₆H₃₃. The other terminal tails are OC₁₁H₂₃, O(CH₂)₉CH?=?CH₂, OC₁₀H₂₁ and O(CH₂)₈CH?=?CH₂. The short‐tailed compounds show monotropic or enantiotropic B₁ phases and the long‐tailed compounds the B₂ phase. The introduction of one terminal vinyl group slightly lowers the transition temperatures. The introduction of a second terminal vinyl group further suppresses the liquid crystalline properties. All compounds with B₂ phases have layer spacings that suggest a tilt of ～45° of the bent molecules in the layers, and their switching behaviour is antiferroelectric.     

甲硫醇在Cu(111)表面的解离吸附: 密度泛函理论研究

采用基于密度泛函理论的第一性原理方法和平板模型研究了CH₃SH分子在Cu(111)表面的吸附反应.系统地计算了S原子在不同位置以不同方式吸附的一系列构型, 第一次得到未解离的CH₃SH分子在Cu(111)表面顶位上的稳定吸附构型,该构型吸附属于弱的化学吸附, 吸附能为0.39 eV. 计算同时发现在热力学上解离结构比未解离结构更加稳定. 解离的CH₃S吸附在桥位和中空位之间, 吸附能为0.75-0.77 eV. 计算分析了未解离吸附到解离吸附的两条反应路径, 最小能量路径的能垒为0.57 eV. 计算结果还表明S―H键断裂后的H原子并不是以H₂分子的形式从表面解吸附而是以与表面成键的形式存在. 通过比较S原子在独立的CH₃SH分子和吸附状态下的局域态密度, 发现S―H键断裂后S原子和表面的键合强于未断裂时S原子和表面的键合.     

Noncommutative geometry and conformal geometry. III. Vafa–Witten inequality and Poincaré duality

This paper is the third part of a series of papers whose aim is to use the framework of twisted spectral triples to study conformal geometry from a noncommutative geometric viewpoint. In this paper we reformulate the inequality of Vafa–Witten [42] in the setting of twisted spectral triples. This involves a notion of Poincaré duality for twisted spectral triples. Our main results have various consequences. In particular, we obtain a version in conformal geometry of the original inequality of Vafa–Witten, in the sense of an explicit control of the Vafa–Witten bound under conformal changes of metrics. This result has several noncommutative manifestations for conformal deformations of ordinary spectral triples, spectral triples associated with conformal weights on noncommutative tori, and spectral triples associated with duals of torsion-free discrete cocompact subgroups satisfying the Baum–Connes conjecture.     

Left and right centers in quasi-Poisson geometry of moduli spaces

We introduce left central and right central functions and left and right leaves in quasi-Poisson geometry, generalizing central (or Casimir) functions and symplectic leaves from Poisson geometry. They lead to a new type of (quasi-)Poisson reduction, which is both simpler and more general than known quasi-Hamiltonian reductions. We study these notions in detail for moduli spaces of flat connections on surfaces, where the quasi-Poisson structure is given by an intersection pairing on homology.     

Measure of segments which intersect a convex body from rotational formulae

Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in R³. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume.