Existence of maximal points with respect to ordered bipreference relations

The maximality of a point with respect to an ordered pair of arbitrary preference relations is introduced. Necessary and sufficient conditions for the existence of maximal points are given.The authors are grateful for the referee's comments which led to an improved presentation of the paper.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

Effect of viscosity on stationary phase stability in capillary column gas chromatography

With recent advances in column technology it is now possible to prepare highly efficient, very inert, and thermally stable capillary columns coated with nonpolar polysiloxane stationary phases. Unfortunately, the same degree of success has not been achieved for some of the more polar polysiloxane phases. A parameter that has been studied little in the past in relation to stationary phase film stability is the viscosity of the stationary phase. In this paper the efficiency and stability of coated columns are correlated to the viscosity of the phase. Due to their structure, the viscosity of the phenyl-containing polysiloxanes change rapidly with temperature and hence, thin-film coatings are not stable at elevated temperatures. By using high viscosity phenyl-containing methylphenylpolysiloxanes which were recently synthesized, efficient and stable columns have been prepared.     

Preparation and characterization of spherical polymer packings from polybutadiene for size-exclusion chromatography

Porous polymer spherical particles for column packings in nonaqueous size-exclusion chromatography (SEC) were prepared from 1,2-syndiotactic polybutadiene by suspension and evaporation method. The polymer microbeads obtained were crosslinked by radical reaction between 2-vinyl groups in polybutadiene with ultraviolet radiation, to render them insoluble. These microbeads have wider chromatographic separation width than polystyrene column packings. In addition, the polybutadiene microbeads did not show the excessive retention observed with commercial polystyrene columns for polycyclic aromatic compounds. Therefore, a close correlation between the elution volume and M, for polycyclic aromatic compounds was observed with polybutadiene microbeads columns.     

Relative retention of the fibroblast growth factors FGF-1 and FGF-2 on strong cation-exchange sorbents

The isocratic retention of two heparin-binding fibroblast growth factors, FGF-1 (acidic FGF) and FGF-2 (basic FGF), was compared on a set of six preparative strong cation-exchange adsorbents. The FGFs comprise a solute pair that are structurally equivalent, yet differ in protein parameters of potential importance in cation-exchange chromatography, such as isoelectric point, net charge, and the number and distribution of basic amino acids. The cation-exchange adsorbents comprise a diverse set of materials in common use for protein purification, with physical and chemical properties that have been characterized and described previously. Isocratic k' values for the two proteins obtained on each adsorbent at several different [NaCl] are compared with one another and with corresponding data for hen egg lysozyme, which is also strongly retained on cation-exchangers. Of the six adsorbents examined, three showed strong retention of both FGFs, with equivalent k' values for FGF-1 and FGF-2. Three others, which showed weaker overall retention for the FGF pair, showed much larger retention differences between FGF-1 and FGF-2. The trends in retention order among the stationary phases are very similar to those seen previously with other unrelated proteins. However, retention differences between the two FGFs, and between the FGFs and lysozyme, do not correlate well with simple charge properties such as net charge, indicating, as in some previous studies, the importance of local regions on the protein surface in determining retention. These observations are interpreted in terms of the structural features of the proteins and the physicochemical properties of the adsorbents.     

Critical Points in a Crystal and Procrystal

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, –1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.     

Effect of solvent composition on free release static coating of capillary columns

Summary Three aspects with respect to the selection of solvents for static coating of capillary columns, i.e. coating speed, occurrence of bumping and solubility of stationary phases are discussed. Hypotheses are proposed in an attempt to explain the observed facts that mixed solvents result in much higher coating speeds than those obtained from pure solvents, that a proper choice of solvents together with a good and uniform deactivitation of the column inner wall is needed to prevent bumping. Stationary phase solubility vs. solvent composition is also briefly discussed.     

Surfactants having polyfluoroalkyl chains. II. Syntheses of anionic surfactants having two polyfluoroalkyl chains including a trifluoromethyl group at each tail and their flocculation-redispersion ability for dispersed magnetite particles in water

Anionic surfactants having two polyfluoroalkyl chains per molecule, i.e. the sodium salt of bis(1H, 1H, 2H,2H-heptadeca-fluorodecyl)-2-sulfosuccinate, CF₃(CF₂)₇(CH₂)₂OCOCH₂CH(SO₃Na)COO(CH₂)₂(CF₂)₇CF₃, the sodium salt of bis(1H, 1H, 2H, 2H-tridecafluoro-octyl)-2-sulfosuccinate, CF₃(CF₂)₅(CH₂)₂OCOCH₂CH(SO₃Na)COO(CH₂)₂(CF₂)₅CF₃, and the sodium salt of bis(1H, 1H, 2H, 2H-nonafluorohexyl)-2-sulfosuccinate, CF₃(CF₂)₃(CH₂)₂OCOCH₂CH(SO₃Na)COO(CH₂)₂(CF₂)₃CF₃, have been prepared from maleic anhydride, the corresponding alcohols possessing a polyfluoroalkyl chain and sodium hydrogen sulfite. The flocculation and redispersion abilities of these surfactants for dispersed magnetic particles in water have been examined to investigate the effect of the chain length. It was found that this ability was enhanced by an increase in the chain length. The contact angles for water for pelleted surface-modified magnetite have been measured. In order to compare this ability and the contact angles, data for other fluorinated surfactant have been obtained. The Kraff point, the surface tension and the pNa of the aqueous surfactant solutions have also been measured.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.     

共边排样件激光切割路径的规划

排样软件的应用使材料利用率得到了很大提高，然而后续切割软件若不能保证有效地切割零件、保证零件质量及提高生产率，则排样软件在材料利用率上获得的收益将丧失。基于图论学理论，建立了规则与非规则零件共边排样时激光切割路径规划的数学模型，给出了在充分考虑加工质量、加工效率、制造成本情况下的激光切割路径优化目标：打孔点最少以及切割中割嘴空行程最短。提出了满足激光切割工艺要求的三个切割路径优化算法：用于求解理想情况下共边切割路径优化问题的一个新的欧拉回路算法；基于奇度顶点完全图最小权最大匹配算法来求解一般情况下共边切割路径优化问题的算法；利用废料区域进一步减少打孔点的处理策略与求解算法。给出了各种算法的运行实例，验证了所提出的算法的有效性。