The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

Coxeter Transformation and Quasiquivers

Mathematical Notes -     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

Mutual solubilities of hydrocarbons and water with the CPA EoS

The knowledge of hydrocarbon/water phase equilibria is important in the design and operation of equipment for petroleum transport and refining and petrochemical plants. The presence of water in a hydrocarbon mixture can affect the product quality and damage the operation equipment due to corrosion and formation of gas hydrates. Tracing the concentration of hydrocarbons in aqueous media is also important for technical purposes like preventing oil spills and for ecological concerns such as predicting the fate of these organic pollutants in the environment.     

Structural properties of charged diblock copolymer solutions

Aqueous micellar solutions of ionic/neutral block copolymers have been studied by light scattering, small angle neutron scattering and small angle X-ray scattering. We made use of a polymer comprised of a short hydrophobic block (polyethylene-propylene) PEP and of a long polyelectrolytic block (polystyrene-sulfonate) PSSNa which has been shown previously to micellize in water. The apparent polydispersity of these micelles is studied in detail, showing the existence of a few large aggregates coexisting with the population of micelles. Solutions of micelles are found to order above some threshold in polymer concentration. The order is liquid-like, as demonstrated by the evolution with concentration of the peak observed in the structure factor (), and the degree of order is found to be identical over a large range of concentrations (up to 20 wt%). Consistent values of the aggregation number of the micelles are found by independent methods. The effect of salt addition on the order is found to be weak. Received: 19 June 1997 / Received in final form: 4 September 1997 / Accepted: 9 October 1997     

On concepts of directional differentiability

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of -directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.     

溶剂浮选-间接光度法测定抗坏血酸

于pH 7.0的磷酸盐缓冲介质中,CTMAB＋及I3-离子间借静电引力形成离子缔合物,可将其浮选入5.0 mL苯中,此缔合物在溶剂中,于365 nm处有吸收峰,较简单的I3^-离子在相同条件下的吸收峰（350 nm）红移了15 nm。在此溶液体系中存在抗坏血酸时使离子缔合物产生褪色反应,且在抗坏血酸浓度在25μg/50 mL以内时与吸光度的降低值（ΔA）间呈线性关系。在抗坏血酸浓度为6.0μg/50 mL时连续测定6次,所得结果的RSD为1.2%,回收率在96%-101%之间。     

Thermodynamics of molecular interactions in ethyl iodide+toluene mixtures

The excess Gibb's free energy of mixing, G^E, for ethyl iodide+toluene at 25°C have been obtained from the measured vapor pressuure data. The H^E and G^E values for ethyl iodide+toluene are positive throughout the ethyl iodide concentration range and G^E>H^E. The results have been analyzed in terms of Flory and ideal associated model theory of nonelectrolyte solutions. It has been observed that the ideal associated model approach which assumes the presence of AN and A₂B molecular species describes well (within±10 J-mol^–1 in the worst case) the general dependence of H^E on X_A (mole fraction of ethyl iodide) over the whole composition range for ethyl iodide+toluene mixtures. The equilibrium constants for A+A AB and 2A+BA₂B reactions along with the enthalpies of formation of AB and A₂B molecular species have been calculated.     

Effect of cooperativity on the O-H stretching force constant in associated water species

CNDO/force calculations have been employed to calculate the O-H stretching force constants for various structures of associated water species such as water-dimethylether, water-acetonitrile, water-lithium fluoride, linear and cyclic water polymers. The variation in the O-H stretching force constant in A_m… O-H… D_n species where A_m and D_n represent, respectively,m number of electron-acceptor andn number of electron-donor molecules, is explained on the basis of the cooperativity effect. With increasing electron-acceptor power of A and electron-donor power of D, the hydrogen-bonded O-H stretching force constant is significantly reduced. The results obtained in these studies are in general agreement with experimental observations reported earlier.     

Synthesis of tumor-associated glycopeptide antigens for the development of tumor-selective vaccines

In contrast to normal cells, the glycoprotein profile on epithelial tumor cells is distinctly altered. Due to an incomplete formation of the glycan side-chains resulting from a premature sialylation, additional peptide epitopes become accessible to the immune system in mucin-type glycoproteins on tumor cells. These tumor-associated structure alterations constitute the basis for a selective immunological attack on cancer cells. For the construction of immunostimulating antigens, glycopeptide partial structures from the mucins MUC1 and MUC4 carrying the tumor-associated sialyl-T(N), alpha2,6-sialyl-T and alpha2,3-sialyl-T antigens have been synthesized. Employing different linkers such as the allylic HYCRON or the fluoride-sensitive PTMSEL anchor, the antigenic glycopeptide structures were constructed on the solid phase utilizing pre-assembled glycosyl amino acid building blocks prepared in solution by convergent chemical or chemoenzymatic strategies. The proliferation of cytotoxic T cells has been induced applying a construct composed of a sialyl-T(N) MUC1-glycopeptide conjugated with a tetanus toxin T cell peptide epitope.