The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

核磁共振法测定高聚物的结构—核磁共振二维谱

介绍了核磁共振(NMR)波谱,尤其是核磁共振二维谱(2D NMR)在最近几年内的进展。内容包括怎样用NMR测定高聚物的序列分布、共聚物结构、聚合物的混溶性、聚合物液晶的取向度、分子量、短链度和长链支化度、凝聚态高聚物的多相结构等。     

Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.     

Excess molar heat capacities of ((<Emphasis Type="Italic">R</Emphasis>)-(+)-α-pinene+(<Emphasis Type="Italic">S</Emphasis>)-(-)- α-pinene) at temperatures between 293.15-308.15 K

Summary {\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\f0\fs20 New explanations are given for two types of irregular thermogravimetric (TG) data. A TG relationship between mass and temperature is derived on the basis of migration behavior of bubbles generated in bulk of sample system, and superposed on that derived on the basis of kinetics of the 4\super th\nosupersub order event, which is superposed on the experimental TG data obtained from three reference papers. This suggests that these TG data are reflecting migration of bubbles. A dependence of TG behavior on heating rate, which is contrary to usual that, is shown and is explained in terms of event-rate determination by boiling. \par }     

n型T'-214相超导体的结构和性质

T＇－214相化合物R2-xCexCuO4（R为稀土离子）成为超导体决定于R3+的离子半径大小、Ce4+的取代量和化合物的热处理时的稳定性．从Raman光谱实验结果提出热处理过程中发生电荷转移．Ce4+的取代引起TN（Cu）下降，当TN（Cu）降到0时，超导性出现。不同的稀土离子TN（Cu）不同，稀土离子的反铁磁性（AFM）与超导性（SC）共存。热电势的测量结果可以用双通道模型解释，n型超导体中电子与空穴共存．     

Classical Valence Similarity in Fullerene Derivatives

Summary.  The generalized Pauling bond order was enumerated in the C₆₀ fullerene cage molecule (truncated icosahedral symmetry). This index measures chemical similarity in fullerene derivatives such as dihydrofullerene (C₆₀H₂), anionized monohydrofullerene (C₆₀H⁻), N-substituted monohydrofullerene (C₅₉NH), the fullerene dimer ((C₆₀)₂), and the dianionic fullerene dimer ((C₆₀)₂ ²⁻). It is also useful in judging the chemical stability of isomers. Received October 9, 2001. Accepted November 9, 2001     

Excess heat capacities and orientational order in systems containing hexadecane isomers of different molecular structure

Using the Picker flow microcalorimeter, excess heat capacities have been obtained at 25°C throughout the concentration range for 2,2-dimethylbutane,n-hexane, and cyclohexane each mixed with a series of hexadecane isomers of increasing degrees of orientational order, as determined by depolarized Rayleigh scattering. The isomers are 2,2,4,4,6,8,8-heptamethylnonane, 6-, 4-, and 2-methylpentadecane, andn-hexadecane. Thec _p ^E values are negative, increasing rapidly in magnitude with increase of orientational order, and are not predicted by the Prigogine—Flory theory which neglects order. Values ofc _p ^E are obtained at 10, 25, and 55°C for cyclohexane +6-, 4-, and 2-methylpentadecane which with other literature data lead to the temperature dependence of the thermodynamic excess functions for cyclohexane solutions of the five C₁₆ isomers. The excess enthalpy and entropy vary with the C₁₆ isomer and with temperature, but the corresponding variation of the excess free energy is small, indicating a high degree of enthalpy-entropy compensation. This is consistent with a rapid decrease with temperature of orientational order in the C₁₆ isomers.     

热动力学的研究 X. 一级反应的热谱峰高法

本文根据一级反应的热谱曲线方程、建立了速度常数的一种新算法。这种新方法,只需要热谱曲线在各个特征时刻的峰高,而不需要任何峰面积,即可算得反应体系的无量纲参数和速度常数,称为一级反应的热谱峰高法。     

Infrared dichroism measurements on the alkyl chain packing of an ionic detergent intercalated between silicate layers

 Microcrystals of the metal silicate hydrate ilerite orient macroscopically on the surface of a ATR-crystals and thus, are accessible for infrared linear dichroism measurements. We present first results which indicate that the alkyl chain packing and the orientation of the polar group of dodecyltrimethylammoniumbromide (DTAB) intercalated between silicate layers can be determined in terms of infrared order parameters. The properties of DTAB can be modulated by the relative humidity of the surrounding atmosphere and by temperature. Upon heating DTAB undergoes a phase transition from a paraffin-like solid to a fluid phase. The former is characterized by the orthorhombic perpendicular packing of the frozen alkyl chains with tilted long axes. The interactions between the ionic groups of the surfactant and that of the host matrix stabilize the lamellar arrangement of DTAB in the crystalline and in the fluid phases. Received: 14 January 1998 Accepted: 27 July 1998