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.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

DETERMINATION OF DEGREE OF CRYSTALLINITY OF NYLON 1212 BY WIDE-ANGLE X-RAY DIFFRACTION

Based on the X-ray scattering intensity theory and using the approximate expression for the atomic scattering factor, the correction factors for three crystalline peaks and an amorphous peak of Nylon 1212 were calculated and the formula of degree of crystallinity of Nylon 1212 was derived by a graphic multipeak resolution method. The degree of crystallinity calculated from the WAXD method is compatible with those obtained by density and calorimetry methods.     

基质辅助激光解吸附飞行时间质谱分析缩合单宁的阳离子化问题

以单价金属离子Cs 和Na 作为离子化试剂,对3种缩合单宁进行基质辅助激光解吸附飞行时间(MALD I-TOF)质谱分析。加入Na 作为阳离子化试剂,能得到较高质量的质谱图。但由于实验通道中几乎不可能完全去除的K 的干扰而会高估棓儿茶酚/表棓儿茶酚单元的组成比例,从而影响对棓儿茶酚/表棓儿茶酚单元存在与否的判断;选择Cs 作为阳离子化试剂可以避免此问题,但在复杂的缩合单宁分析中,同样因为杂质离子Na 和K 的干扰而使得质谱图变得更复杂;未去离子处理直接对缩合单宁进行MALD I-TOF质谱分析与去离子并加入Cs 的处理比去离子并加入Na 能检测到更高聚合度的高聚物,检测到离子峰强度最高的聚合物随离子不同而不同。     

A temperature study on critical micellization concentration (CMC), solubility, and degree of counterion binding of α-sulfonatomyristic acid methyl ester in water by electroconductivity measurements

 For a sodium salt of α-sulfonatomyristic acid methyl ester (14SFNa), one of the α-SFMe series surfactants, critical micellization concentration (CMC), solubility and degree of counterion binding (β) were determined by means of electrocon-ductivity measurements at different temperatures (at every 5 °C) ranging from 15 to 50 °C. The phase diagram of 14SFNa in pure water was constructed from the CMC- and solubility-temperature data, in which the Krafft temperature (critical solution temperature) was found around 0 °C. The changes in the Gibbs energy, ΔG ⁰ _m, enthalpy, ΔH ⁰ _m, and entropy, ΔS ⁰ _m, upon micelle formation as a function of temperature were evaluated taking βvalues into calculation. Received: 28 August 1996 Accepted: 5 November 1996     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Methylation of Chitosan with Iodomethane: Effect of Reaction Conditions on Chemoselectivity and Degree of Substitution

N,N,N‐trimethylchitosan (TMC) was prepared by reacting purified chitosan with iodomethane, in the presence of sodium hydroxide, water and sodium iodide, at room temperature. The reaction medium was N‐methyl‐2‐pyrrolidone. Different samples of TMC were obtained by adding to the reaction medium a fixed volume (5.5 mL) of aqueous NaOH solutions at different concentrations (15, 20, 30 and 40 wt.‐%) and carrying out the reactions for 9 or 24 h. The features observed in the ¹H and ¹³C NMR spectra of these chitosan derivatives, in respect of the chemical shift, number and relative intensity of the signals, depended strongly on the excess of NaOH and H₃CI added to the reaction medium, but when the lowest excess was employed, the characteristics of the derivative were not affected by the reaction time to the same extent. The average degree of quaternization of these N‐methylated derivatives of chitosan ranged from 10.5% to 44.8%, according to the reaction conditions. Increasing the excess of NaOH, in reactions carried out for 9 h, resulted in TMC samples with progressively higher content of trimethylated sites however, the reaction yields were correspondingly lower and O‐alkylation was favored in these cases.

¹H NMR spectrum of sample [A_X]^24h dissolved in D₂O (C_p = 10 g/L).     

An investigation of heparinase immobilization

A systematic investigation of the parameters that affect the efficiency of immobilizing heparinase onto cyanogen bromide activated crosslinked 8% agarose beads was conducted. Two experimental measures, the “fraction bound” and the “fraction retained,” were used to monitor the coupling efficiency. The fraction bound is the portion of the total initial enzyme that is bound to the agarose gel. The fraction retained is the fraction of bound enzyme that is active. The product of the two measures indicates the coupling efficiency. The activity of the immobilized heparinase was measured under conditions free of both internal and external mass transfer limitations, and thus, the fraction retained represents the true immobilized enzyme activity. Increasing the degree of activation of the beads results in an increase in the fraction bound, the fraction retained, and consequently, the coupling efficiency. As the ratio of enzyme solution to gel volume increases from 1.5 to 2.2, the fraction bound remains constant but the fraction retained decreases (heparinase concentration; 0.15 mg/mL and degree of activation; 9.5 μmol of cyanate esters/g of gel). At volume ratios greater than 2.2, both the fraction bound and the fraction retained decline continuously. Changing the heparinase concentration in the coupling solution changes the coupling efficiency in a manner similar to that of the volume ratio change. When heparin is added during the coupling process, the fraction bound declines as the heparin concentration increases, whereas the fraction retained increases up to a heparin concentration of 12 mg/mL and decreases thereafter. When arginine, lysine, and glycine are used to block the unreacted cyanate ester groups after the coupling process, the immobilized heparinase shows different pH optima of 6.5, 6.9, and 7.2, respectively. Based upon these findings, a protocol to optimize heparinase immobilization is developed.     

CTMAB胶束体系中反离子缔合度的测定

对十六烷基三甲基淡化按（CTMAB）水胶束体系，不同方法测得其反离子缔合度产值不同【‘－＼且很高于由股团电化学理论所得q值0．67问．本文以离子选择性电极法测定CTMAB水胶束体系中反离子缩合度（仁0．65），并研究了外加盐和乙醇的影响·1实验部分1．工试剂和仪器十六烷基三甲基漠化技（CP）在无水乙醇中重结晶两次，纯化物经帕环法测其表面张力在CMC附近无最低声、·淡化钾（AR），水为。次蒸馏水，PXJIC型离子计，302型PB，电极（响应范围为PB，＝1．6～3．3，响应时间为5分钟）222型甘汞电极·1．2实验方法在CMCV／de的稀…