Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

A procedure for measuring the flexibility of single wood-pulp fibres

A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t. It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be used to establish the appropriate refiner energy necessary for the production of a specific grade of paper. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

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.     

One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

超高真空中银表面垂直谐波电流的实验测量

在超高真空的条件下,测量了清洁、自由银表面产生的光学二次谐波随基波电矢量与入射面之间夹角(?)的变化,从而通过理论公式,求得由Rudnick和Stern引入的,用于衡量垂直面电流密度的唯象参数a的值,在入射基频光波长为1.064μm时,被测定为-4.0±0.8.     

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。