On measurable multifunctions in countably separated spaces

We use an idea of countable separability of points and sets in topological spaces to prove results on intersection of measurable multifunctions and an implicit function theorem. We generalize or extend in part some well known Himmelberg's theorems.     

The approximation of electron densities

This paper discusses the approximate representation of the electron density produced by an ab initio calculation. A linear combination of Gaussians is fitted to the density by minimizing a functional which is the consequent error in field-energy. The practical implementation of the procedure, following a Gaussian 80 calculation, is described and some of the complications are analysed.     

Novel spectrofluorimetric method for the determination of sulfite with rhodamine B hydrazide in a micellar medium

A novel spectrofluorimetric method for the determination of sulfite using rhodamine B hydrazide as fluorogenic reagent in the presence of polyoxyethylene sorbitan monooleate (Tween 80) surfactant micelles is described. The method is based on the mixture of sulfite with rhodamine B hydrazide, a colorless, non-fluorescent substance in Tween 80 surfactant micelles which gives rhodamine B-like fluorescence emission. The fluorescence intensity increase is linearly related to the concentration of sulfite in the range 5-800 ng ml⁻¹ with a detection limit of 1.4 ng ml⁻¹ (3σ). The optimal conditions for the detection of sulfite are evaluated and the possible detection mechanism is also discussed. The method has been successfully applied to the determination of total sulfite in wines and compares well with the standard iodimetric method.     

Separation and selectivity in micellar electrokinetic chromatography using sodium dodecyl sulfate micelles or Tween 20-modified mixed micelles

The separation and selectivity of eight aromatic compounds ranging from hydrophilic to hydrophobic properties in micellar electrokinetic chromatography (MEKC) using sodium dodecyl sulfate (SDS) micelles or Tween 20-modified mixed micelles were investigated. The effect of different operation conditions such as SDS and Tween 20 modifier surfactant concentration, buffer pH, and applied voltage was studied. The resolution and selectivity of analytes could be markedly affected by changing the SDS micelle concentration or Tween 20 content in the mixed micelles. Applied voltage and pH of running buffers were used mainly to shorten the separation time. Complete separation of eight analytes could be achieved with an appropriate choice of the concentration of SDS micelles or Tween 20-modified mixed micelles. Quicker elution and better precision could be obtained with SDS-Tween 20 mixed micelles than with SDS micelles. The mechanisms that migration order of those analytes was mainly based on their structures and solute-micelle interactions, including hydrophobic, electrostatic, and hydrogen bonding interactions, were discussed.     

AlSiP3, a compound with a novel wurtzite-pyrite intergrowth structure

AlSiP₃ is formed by heating aluminum and silicon powder with red phosphorus and adding small amounts of iodine or AlCl₃. Small, black crystals with metallic lustre grow at 1200°K. The compound crystallizes in the orthorhombic space group Pmnb (No. 62) with a = 987.2 pm, b = 586.1 pm, c = 608.8 pm and four formula units. In the structure isolated P atoms as well as P₂ pairs are present (PP = 218.2 pm). Silicon is tetrahedrally bonded (SiP = 224.2 ? 228.2 pm) whereas aluminum has octahedral coordination (AlP = 244.2 – 260.8 pm). The structure can be described as an intergrowth structure of wurtzite and pyrite type.     

流动注射胶束化学发光法测定曲克芦丁

基于HCl介质中曲克芦丁与KIO4-MnSO4反应产生强的化学发光,且吐温-80的存在能使这一反应的化学发光强度大大增强。结合流动注射技术,建立了流动注射化学发光法测定曲克芦丁的新方法。在优化的实验条件下,曲克芦丁的质量浓度在2.0×10-7~8.0×10-5g/mL范围内与化学发光强度呈良好的线性关系,检出限为7×10-8g/mL。对1.0×10-6g/mL曲克芦丁进行11次平行测定,方法的相对标准偏差为1.8%。用于曲克芦丁片剂和针剂中曲克芦丁的测定。     

An Ω(n 4/3) lower bound on the randomized complexity of graph properties

We improve King's (n ^5/4) lower bound on the randomized decision tree complexity of monotone graph properties to (n ^4/3). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.The paper was written while the author was a graduate student at the University of Chicago and was completed at M.I.T. The work was supported in part by NSF under GRANT number NSF 5-27561, the Air Force under Contract OSR-86-0076 and by DIMACS (Center for Discret Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center-NSF-STC88-09648.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

Depression in the cloud point of Tween in the presence of glycol additives and triblock polymers

Cloud point (C_P) measurements of Tween 20 and Tween 80 were carried out in the presence of various glycol oligomers and triblock polymers (TBP). The cloud points of both Tween 20 and 80 decrease in the presence of both types of additives. Among the glycol oligomeric additives, ethylene glycol monobutyl ether was found to reduce the C_P maximum. An increase in the repeating units of polymeric glycol additives leads to a decrease in C_P. Reduction in the C_P in the presence of TBP depends upon the increase in hydrophobic/hydrophilic ratio among the polypropylene to polyethylene units.