Excess Molar Volume and Viscosity of Isobutyric Acid + Water Binary Mixtures Near and Far Away from the Critical Temperature

The excess molar volume V^E, shear viscosity deviation Δη and excess Gibbs energy of activation ΔG^∗E of viscous flow have been investigated by using density (ρ) and shear viscosity (η) measurements for isobutyric acid + water (IBA+W) mixtures over the entire range of mole fractions at five different temperatures, both near and close to the critical temperature (2.055K ≤ (T−T_c)≤ 13.055K). The results were also fitted with the Redlich–Kister equation. This system exhibited very large negative values of V^E and very large positive values of Δη due to increased hydrogen bonding interactions and correlation length between unlike molecules in the critical region and to very large differences between the molar volumes of the pure components at low temperatures. The activation parameters ΔH^∗ and ΔS^∗ have been also calculated and show that the critical region has an important effect on the volumetric properties.     

Properties of a Ring Critical Pointas Measures of Intramolecular H-Bond Strength

Summary.  The topological parameters derived from the Bader theory such as the electron density and its Laplacian at the ring critical point (RCP) are analysed here as possible measures of the H-bond stength for intramolecular H-bonds. The parameters of RCP correlate well with the other properties of intramolecular H-bonds which are known as good measures of the H-bond strength. The calculations were performed on two samples of compounds with intramolecular H-bonds: the derivatives of malonaldehyde and the derivatives of o-hydroxybenzaldehyde. MP2 and HF calculations were carried out using a 6-311++G^** basis set. E-mail: slagra@krysia.uni.lodz.pl Received February 18, 2002; accepted (revised) May 27, 2002     

氰乙基纤维素溶致性液晶的研究

氰乙基纤维素在二甲基甲酰胺、二甲基乙酰胺、二甲基亚砜、乙腈以及丙酮等溶剂中可以形成溶致性液晶。随浓度增加,溶液从各向同性状态经两相共存态转变成为完全的液晶态。升高温度到T_c,液晶相消失;降低温度到T′_c,液晶相再生成。T_c总大于T′_c。而且,浓度越高,过冷温度△T=T_c—T′_c越小。在各向同性,两相共存或完全的液晶状态,溶液平均折射率和消光度均与浓度呈线性关系。但在两相间相互转变时,即在C_1~*和C_2~*处,n-C和 A-C 曲线上出现转折点。高聚物与溶剂的相互作用参数X_(12)愈小,临界浓度C_1~*愈小。把描述大分子链柔顺性的参数f与X_(12)联系起来,可用 1956年 Flory的理论定性地解释溶剂对高聚物溶致性液晶形成的影响。     

Concentrated electrolyte solutions at high temperatures and pressures

A survey is given of recent experimental results obtained from high-temperature, high-pressure investigations with water, aqueous solutions, and ionic fluids. Data on the static dielectric constant of water to 550°C and 5 kbar are given and discussed with respect to their relation to water structure. Infrared and Raman spectra of HDO in pure water have been obtained to 400°C and 4 kbar, which give information on hydrogen bonding. Xe–H₂O and CO₂–H₂O mixtures were investigated in the infrared. Ni(II) and Cu(II) complexes were investigated by absorption spectroscopy in aqueous solutions of high chloride content to 350°C and 2–6 kbar. The gas-liquid critical point of ammonium chloride was found at 880°C and 1635 bars. This fluid appears to be predominantly ionic even in the critical region. The possibility of converting pure polar fluids such as ammonia and water into concentrated ionic solutions by self-ionization at very high pressures is mentioned.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.     

支化高分子在溶液中的交叠与缠结

溶液中高分子的交叠和缠结与其链结构密切相关。支化聚苯乙烯的临界交叠浓度C和临界缠结浓度C_E比分子量相同的线型聚苯乙烯的大,说明交叠和缠结同分子在溶液中线团的体积有直接关系。     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.     

The density and minimal gap of visible points in some planar quasicrystals

It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.     

Upper bound of Kähler angles on the β-symplectic critical surfaces

Let (M,g) be a Kähler surface and \mathrm{\Sigma } be a \beta-symplectic critical surface in M. If L_q\left(\mathrm{\Sigma }\right) is bounded for some q>3, then we give a uniform upper bound for the Kähler angle on \mathrm{\Sigma }. This bound only depends on M,q,\beta and the L_q functional of \mathrm{\Sigma }. For q>4, this estimate is known and we extend the scope of q.     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.