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.     

On invexity-type nonlinear programming problems

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments.     

Cluster description of water-in-oil microemulsions near the critical and percolation points

The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40 degrees centigrades and 10% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to high volume fraction side at progressively lower temperatures. In this paper we review the evidence that allows to interpret the phase behavior of our system in terms of interacting spherical droplets. We also investigate the dynamics of droplets, below and approaching the critical point by dynamic light scattering. The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation is also reviewed and interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent complex dielectric constant of this system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Conjugate points in

An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnold.

     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

套索冠醚毛细管色谱柱的研制

用套索冠醚N,N′-双(2-甲基吡啶)-二氮杂-18-冠-6作为固定相,涂渍在弹性石英毛细管内,测其柱效、惰性、热稳定性、平均极性及选择性等性质.其结构由元素分析、红外光谱、核磁共振及质谱分析的试验数据所证实.试验表明,它具有良好的色谱性能、中等极性,适用于对醇、卤代烃、芳香烃等各类异构体的分离,并用分子结构观点探讨了保留机理.     

Synthesis of siloxane stationary phases for capillary gas chromatography and supercritical fluid chromatography

A comparison is made between dichlorosilanes and cyclic siloxanes as starting materials in the synthesis of stationary phases for capillary gas chromatography (CGC) and supercritical fluid chromatography (SFC). Siloxanes containing one or more of the side groups methyl, vinyl, phenyl, and cyanoethyl in various ratios were synthesized and compared. These phases were characterized by chromatographic (gel permeation, GPC), spectroscopic (IR, ¹H NMR, ²⁹Si NMR), and thermal (DSC) methods. Coated fused silica columns were evaluated with respect to polarity, crosslinkability with several free-radical initiators, and thermal stability. A new liquid phase, 7% cyanoethyl, 7% phenyl, 1% vinyl methyl polysiloxane is shown to be more polar than OV-1701, more temperature stable, easily crosslinked and suitable for use in supercritical fluid chromatography.     

Elution order in gas chromatography

The retention behavior of a heterogeneous group of solutes has been examined on seven different stationary phases under isothermal and temperature-programmed conditions. Both ΔH_v (enthalpy of solute vaporization from the stationary phase) and ΔS_v (entropy of solute vaporization from the stationary phase) values were determined for each solute – stationary phase combination under isothermal conditions. Both program rate and carrier gas velocity were shown to affect solute elution order. Unless these and other experimental factors discussed are controlled, column equivalency studies based on solute elution order have dubious value.     

Deactivation of silica surfaces with a silanol-terminated polysiloxane; structural sharacterization by inverse gas chromatography and solid-state NMR

Retention gape deactivated with Silicone OV-1701-OH show good chromatographic performance and remarkable stability against water induced stationary phase degradrdation. In an attempt to better understand the findamentals off the deactivation process using silanol terminated polysiloxanes, a fumed silica was deactivated with Silicon OV-1701-OH. In contrast to fused silic capillaries, fumed silica (Aerosil A-200) can be studied by ²⁹Si cross-polarization magic-angle-spinning (CPMAS) NMR, thus serving as a model substrate for fused silica. Retention data from inverse gas chromatography at infinite dilurion and ²⁹Si CP MAS NMR data of five Aerosil phases, differing in residual silanol surface concentration, are correlated with the aim of validating this approach for stationary phase characterization. A comparatively detailed model of the deactivating polymer layer that explains the observed absorption activities is deduced. Surface silanols are shown to play a key role in the polymer layer, the structure of which is of primary importance for the absorption behavior after deactivation. Contrary to common belief, the absolute silanol surface concentration after deativation is only of secondary importance for the overall absorption activity. High silanol surface concentrations enhance degradation of the polysiloxane chains into small cyclic fragments as well as subsequent absorption and immobolization to the silica substrate surface. The mobility of linear polysiloxane chains in the kHz regime (as determined bby NMR cross-polarization dynamics) appears to determine the extent which the residual silanols are accessible for analytes. It is therefore anticipated that there is an optimum silanol surface concentration of fused silica surfaces to be deactivated with silanol terminated polysiloxanes; it should be lazrge enough to adsord polymer fragments, but not large to avoid excessive residual silanol activity.