Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.     

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.     

纳米碳酸锌的制备和热分解动力学参数的测定

Nanosized zinc carbonate was prepared in the droplet of nano-reactor based on microemusion. The influences of the concentration of the surfactant and reactant on the diameter of nanoparticles were studied and the kinetic pa-rameters of thermal decomposition reaction were determined. It can be shown from experimental results， the di-ameter of the droplet in the microemulsion which have dissolved reactant zinc nitrate and sal volatile is between 4.9nm and 7.7nm， 6.2nm and 12.4nm， respectively. Nanosized zinc carbonate prepared by the method of mi-croemusion has shown good dispersion， narrow distribution and light agglomeration. The particle size of nanosized zinc carbonate is between 5nm and 40nm， and its kinetic parameters of thermal decomposition reaction-activation energy E and reaction order n are 110kJ·mol^-1 and 0.9， respectively.     

减压渣油供氢剂减黏裂化研究

减黏裂化作为一种不生成焦炭的热加工方法主要涉及两类化学反应，裂解反应和缩合反应。裂解反应使减压渣油的平均分子量及其胶团直径变小，改善渣油的倾点和黏度；缩合反应使减压渣油及其中间产物中的芳烃、烯烃等缩合成大分子量产物，产生新的胶核，甚至生成焦炭。常规减黏裂化过程中，这两类化学反应主要与反应温度和反应时间有关。在热作用下渣油中的大分子裂解为H／C原子比相对较高的饱和烃自由基和H／C原子比相对较低的芳香性自由基。后者还可失去自身的环烷氢而使其H／C原子比进一步降低。如果体系中有足量的氢化芳烃存在，那么氢化芳烃分子上的活泼氢就可能转移到芳香性自由基的单电子位，将自由基封闭，从而阻止芳香性自由基之间的相互缩合，抑制使分子长大的缩合反应。如果体系中的氢化芳烃含量不足。则热反应体系中就没有足够的活泼氢将芳香性自由基封闭，芳香性自由基缩合反应的几率较高，造成过早地生焦。这种来自渣油分子自身的活泼氢的化学行为与渣油热反应生焦诱导期有一定关系。     

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。     

Mn位掺杂钙钛矿结构化合物LaSr2Mn2-xNixO7的磁性和电性的研究

The effect of Ni substitution for Mn on magnetic and transport properties has been investigated for layered manganese oxides LaSr₂Mn_2-xNi_xO₇. Nickel doping hampered the canted antiferromagnetic (AFM) exchange at low temperature and their Neel temperature (T_N) decreased from 138 K (x=0) to 102 K (x=0.3). Meanwhile, spin glass, charge ordering and metal-insulator transition are suppressed by Ni addition. The resistivity increases obviously with increasing x due to double exchange interaction channel broken by Ni²⁺ addition. The resistivity of all samples in low temperature range fits to the Mott′s variable rang hopping (VRH) model, while it fits to nearest neighbor hopping of small polarons model in high temperature range.     

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 }     

Second Dissociation Constants of 4-[N-morpholino]butanesulfonic Acid and N-[2-hydroxyethyl]piperazine-N′-4-butanesulfonic Acid from 5 to 55°C

The values of the second dissociation constant, pK ₂, for the dissociation of the NH⁺ charge center of the zwitterionic buffer compounds 4-(N-morpholino)butanesulfonic acid (MOBS), and N-(2-hydroxyethyl)piperazine-N-4-butanesulfonic acid (HEPBS) have been determined from 5 to 55°C, including, 37°C at intervals of 5°C. The electromotive-force (emf) measurements have been made utilizing hydrogen electrodes and silver–silver chloride electrodes. The value of pK ₂ for MOBS was found to be 7.702 ± 0.0005, and 8.284 ± 0.0004 for HEPBS, at 25°C, respectively. The related thermodynamic quantities, G ^o, H ^o, S ^o, and C _p ^o for the dissociation processes of MOBS and HEPBS have been derived from the temperature coefficients of pK ₂. Both the MOBS and HEPBS buffer materials are useful as primary pH standards for the control of pH 7.3 to 8.6 in the region close to that of physiological fluids.