Some remarks on the modulus of continuity of a conformal mapping of the disk onto a Jordan domain

Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))². LetH(x) be an arbitrary primitive of 1/h ^–1(x). Note that the functionH ^–1 x is positive and increasing on (–, +),H ^–1 0 asx– andH ^–1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000.     

Crumpled laminations and manifolds of nonfinite type

Using a group-theoretic construction due to Bestvina and Brady, we build -manifolds which admit partitions into closed, connected -manifolds but which do not have finite homotopy type.

     

Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

The role of additional solvents in transition metal complex catalyzed asymmetric reductions in ionic liquid containing systems

When ionic liquids (ILs) are employed as solvents for transition metal complex (TMC) catalyzed reductions, a second solvent can be added to increase the efficiency of the catalytic cycle and the solubility of the reactant in the IL phase. Two industrially relevant asymmetric hydrogenations, the enantioselective reductions of methyl 2-acetamidoacrylate with Rh-EtDuPHOS and methyl acetoacetate with Ru-BINAP, were performed in different catalytic systems including 1-butyl-3-methylimidazolium hexafluorophosphate/ tetrafluoroborate as ILs. Product separation and TMC recycling was performed by extracting the product from the reaction mixture. This can be accomplished by cooling the system, by adding an excess of the second solvent or by adding a third solvent. A high solubility of the second solvent in the IL catalytic phase favors the reaction activity, but can induce leaching of the IL and TMC.     

Measurements of HO2 uptake coefficient on aqueous (NH4)2SO4 aerosol using aerosol flow tube with LIF system

The γ(HO₂) was elevated with increase of Cu(II) concentrations in aqueous (NH₄)₂SO₄ aerosol. The threshold of Cu(II) concentration was 10^-3 mol/L for the dramatic increase of γ(HO₂) to 0.1, suggesting sensitive γ(HO₂) value to concentration of transition metal ions in aerosol.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

DFT法研究分子筛催化trans-2-丁烯的双键异构

利用一个3T簇模型模拟分子筛催化剂的酸性位, 采用密度泛函理论(DFT)的 B3LYP/6-31G(d, p)方法, 研究了分子筛催化1-丁烯双键异构为trans-2-丁烯的反应机理. 对反应各驻点进行了全优化, 经过零点能校正后, 得到了反应的活化能. 研究表明, 反应分三步进行：物理吸附→化学反应→物理脱附. 分子筛的酸性位OH基团首先吸附1-丁烯的双键形成了π配位复合物, 然后按协同反应机理发生双键异构反应, 生成吸附态的trans-2-丁烯, 最后脱附成产物. 计算得到的表观活化能为57.1 kJ•mol^-1, 与实验结果接近.     

Characterization of individual atmospheric particles by element mapping in electron probe microanalysis

In this paper procedures for the characterization of individual aerosol particles by element mapping in the electron microprobe are presented. The number, size and qualitative chemical composition of particles is derived from a combination of secondary or backscattered electron images and element distribution maps. Accuracy of the size distribution and reliability of the qualitative analysis procedure were checked with silicate samples. In order to obtain a semi-quantitative estimate of the chemical composition of individual particles the count rates taken from element distribution maps are corrected for matrix and geometric effects using particle ZAF procedures.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

PHOTOEMISSION WITHIN AND BEYOND THE ONE-STEP MODEL

Photoemission in the vacuum ultraviolet photon regime has proved to be an effective tool for the investigation of valence band surface electronic structure. The interpretation cannot be exclusively confined to the valence bands but has to consider cross sections with realistic final states consistently designed within the one-step model. Therefore especially in the surface sensitive photoemission, several effects hide the final goal of deducing the energetic and wavefunction structure together with microscopic potential parameters through a convincing agreement of calculated with measured spectra. The final states band structure is much less well understood than the valence band structure under consideration. The optical potential, which controls the surface sensitivity through the underlying damping mechanisms, widely relies on empirical assumptions. Furthermore, the photon field is not only strongly influenced but in the vicinity of the plasma frequency also deteriorated by the electronic response. In view of high resolution spectroscopy the accuracy of the data interpretation is affected, and in fact, band-mapping methods are no longer valid. Examples of recent calculations to account for these effects are reviewed.     

Spin-transition behaviour of transition metal complexes with 2,6-bis-(benzimidazol-2′-yl)-pyridine induced by deprotonation of the complex

Summary 2,6-bis-(Benzimidazol-2-yl)-pyridine (bzimpy = H₂ L) acts as a bidentate ligand when combining with transition metal ions. The complexes [M(bzimpy)₂](ClO₄)₂ (M = Fe²⁺, Mn²⁺, Zn²⁺, Co²⁺, and Ni²⁺) were obtained as solids. The protonation constants (logK) for the ligand and the complexes were evaluated in 30:70 (v/v) H₂O:EtOH at 293 K and at constant ionic strength of 0.12M KCl. Coordination of the ligand to the metal ions leads to an increase of acidity of the imino-hydrogen of the benzimidazole group of the ligand as a function of the complex stability. Deprotonation leads to a spin-state transition (intermediate spin-state low-spin) of the iron(II)-complex, followed by a shift of the metal-to-ligandcharge transfer band (MLCT) to lower energies (_max=563 to 580 nm). The d-d absorption bands are found to shift to higher energies and the low-spin isomer is favoured at room temperature. An opposite shift of theMLCT band (_max=563 to 557 nm) is observed when HClO₄ is added to the complex solution, rendering the high-spin state of the complex more favourable.On leave from the Chemistry Department, Jahangirnagar University, Dhaka, Bangladesh