Gradients of inner functions in strictly pseudoconvex domains

We investigate the unbalanced ordinary partition relations of the form λ → (λ, α)² for various values of the cardinal λ and the ordinal α. For example, we show that for every infinite cardinal κ, the existence of a κ+-Suslin tree implies κ⁺ ? (κ⁺, log _κ (κ⁺) + 2)². The consistency of the positive partition relation b → (b, α)2 for all α < ω₁ for the bounding number b is also established from large cardinals.     

磁场、多孔性和各向异性动脉壁有多处狭窄段时对血液流动的影响

建立一个血液流动的数学模型:多孔介质在磁场作用下,血液流过一段有多处狭窄段的弹性动脉;用一个各向异性的弹性圆柱形管道模拟动脉,用粘性不可压缩的导电流体表示血液,动脉有轻微的局部性狭窄,形成一段内腔局部变窄的动脉,并完成该模型的数学分析．详细阐述了血管壁参数对血液流动的影响,参数包括纵向和圆周向的粘弹性应力分量Tt和Tθ、血管壁的各向异性度γ、血管及其周边结缔组织的总质量M、完全栓管中粘性约束的贡献C和弹性约束的贡献K,并用图形表示壁面剪切应力的分布、径向和轴向的速度等．还研究了狭窄形状参数m、渗透率常数κ、Hartmann数Ha和血管狭窄区的最大高度δ,对血液流动特征的影响．研究表明,流动受到周边结缔组织（动脉壁运动）的影响式微,血管壁的各向异性度,是确定动脉材料的一个重要指标．进一步发现壁剪切力分布,随着Tt和γ的增加而增加,随着Tθ,M,C和K的增加而减少．壁面剪切应力分布的传播,以及壁面处阻力阻抗的传播,栓管与自由管相比要低得多;狭窄段咽喉处的剪切应力分布特性,完全栓管和自由管正相反．靠近中心线的俘获区大小,随着渗透率κ的增加而增大;随着Hartmann数Ha的增加而减小．最后,狭窄段非对称时,逐渐形成俘获区;狭窄段对称时,不出现俘获区,各向同性自由管（无初始应力）中俘获区的大小,比完全栓管中的小得多．     

Description of Simple Exceptional Sets in the Unit Ball

For z B ⁿ, the boundary of the unit ball in . If the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if Eis a G and F subset of the projective (n– 1)-dimensional space then there exists a holomorphic function fin the unit ball B ⁿso that E(f) = E.     

Reactions of azoles with tetrachloro-1,2-difluoroethane and 1,2-dichlorodifluoroethylene

Tetrachloro-1,2-difluoroethane reacted with pyrazole and imidazole sodium salts to give mixtures of the corresponding N-(1,2,2-trichloro-1,2-difluoroethyl) derivatives and (E)-1,2-difluoro-1,2-dihetarylethenes. (E)-1,2-Difluoro-1,2-di(3,5-dimethyl-1H-pyrazol-1yl)ethene was also obtained as a result of replacement of chlorine atoms in 1,2-dichloro-1,2-difluoroethene. Analogous reaction with more nucleophilic imidazole involved replacement of not only chlorine but also fluorine atoms in 1,2-dichloro-1,2-difluoroethene, yielding tetraimidazolyl-substituted ethylene.     

Pyrylium sulfonate based ionic liquids

Pyrylium salts represent a new group of ionic liquids (ILs) containing a positive charge on the oxygen atom. The novel ILs were obtained starting with 4-pyrones from petroleum feedstock and renewable resources and sulfonic acids. The use of carboxylic acids instead of salts resulted in the formation of cocrystals. The synthesized pyrylium ionic liquids were stable in air and in contact with water and common organic solvents. The permanganate indices which are characteristic for prepared sulfonates were also investigated. The pyrylium ionic liquids were useful as immobilizers and dissolving agents in hydrosilylation reactions.     

On the problem of reactor graphite lifetime

Fine-grained dense graphites of different manufacturers were tested and studied for the purpose of predicting their lifetimes at high (∼2000°C) temperatures. The tests consisted in sample heating by electric current to a destruction temperature. The study included a set of electron microscopy, X-ray diffraction, and electrical methods. X-ray diffraction data for initial samples were compared with data for domestic MPG graphite. Scanning electron microscopy was applied to both initial and heated samples. The lifetime prediction was based on the Zhurkov classical formula. It was shown that CGD, Carbone Lorraine, and MPG graphite composites can differ appreciably in both structural characteristics and high-temperature lifetimes.     

Indane Based Molecular Motors: UV-Switching Increases Number of Isomers

We describe azophenylindane based molecular motors (aphin-switches) which have two different rotamers of trans-configuration and four different rotamers of cis-configuration. The behaviors of these motors were investigated both experimentally and computationally. The conversion of aphin-switch does not yield single isomer but a mixture of these. Although the trans to cis conversion leads to the increase of the system entropy some of the cis-rotamers can directly convert to each other while others should convert via trans-configuration. The motion of aphin-switches resembles the work of a mixing machine with indane group serving as a base and phenol group serving as a beater. The aphin-switches presented herein may provide a basis for promising applications in advanced biological systems or particularly in cases where on demand disordering of molecular packing has value, such as lipid bilayers.