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.     

基于异质预期的量子伯川德博弈复杂动力机制分析

针对伯川德双寡头垄断博弈经济系统中出现的混沌现象,利用量子博弈论,构建了基于有限理性与天真预期行为的量子伯川德动态博弈模型,分析了量子纠缠度对纳什均衡点稳定性及复杂动力行为的影响。结果表明:量子纠缠度能增强该系统的稳定性,企业价格调整速度达到某一程度时会导致该系统的复杂混沌特性,纠缠度可以有效控制混沌状态。最后利用数值模拟从分岔、最大李雅普诺夫指数、奇怪吸引子、初始条件敏感性及分数维数方面验证了理论准确性。     

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.     

拟合粘度曲线法研究高聚物的长链支化

本文介绍了用计算机试误法拟合粘度曲线,讨论支化参数的方法,本法可以同时确定支化临界分子量和支化程度,在此基础上可以同时得到支化参数及平均分子量、分子量分布.以聚乙烯标准参考物:SRM 1475(线型)、1476(支化物)及镍催化顺式聚丁二烯为对象介绍了上述方法.     

碳氟醇与阴离子表面活性剂的相互作用

测定了不同比例的C_(10)_H_(21)SO_4Na-C_3F_7CH_2OH、C_7F_(15)COONa-C_3H_7CH_2OH混合水溶液的表面张力,加入C_3F_7CH_2OH可增加阴离子表面活性剂的表面活性;在表面层中,C_3F_7CH_2OH与C_(10)H_(21)SO_4Na间分子相互作用比C_3F_7CH_2OH-C_7F_(15)COONa体系弱;这是由于CF链与CH链间“互疏”作用的结果;随着C_3F_7CH_2OH浓度增加,对C_(10)H_(21)SO_4Na胶团反离子结合度也随之增加。     

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).