Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.     

Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.     

Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

Impact of demand uncertainty on coordinating supply chain inventories through common replenishment epochs

Prior studies have shown that inventories in a one vendor, multi-buyer supply chain with deterministic demands can be coordinated effectively through the use of common replenishment epochs (CRE). In this paper, we study the impact of demand uncertainty on the effectiveness of coordinating such a supply chain. We develop a model to analyse the coordination mechanism using CRE in a one-vendor, multi-buyer supply chain, when the demand faced by the buyers is stochastic. Our numerical study based on the model found that coordination through CRE may not always be beneficial when the demand variance is high. We also investigate a strategy of advance order processing by the vendor to improve the effectiveness of coordination through CRE.     

‘Doing the right problem’ <Emphasis Type="Italic">versus</Emphasis> ‘doing the problem right’: problem structuring within a Land Force environment

The essential first step of any OR investigation is to ensure that the ‘right problem’ is studied. Our approach is to propose a set of six ‘rights’ or questions whereby achievement against particular aspects of a problem space is made and these provide the basis for scoping the context, understanding the system, and proposing sound options to the decision-maker. This style of problem structuring is an essential element of the Defence problem domain, and especially so for the Land Force, where there exist multiple degrees of freedom for poorly defined problems in an environment of uncertainty and ambiguity. Central to this is performing conceptual rather than analytical modelling, as perturbations then provide a basis for exploring a space, rather than solving a problem.     

二元合金微观偏析的相场法数值模拟

使用耦合溶质场的相场模拟研究了Ni-Cu二元合金枝晶生长过程中固相溶质扩散系数D_s 对枝晶形貌和微观偏析等的影响.计算结果表明，随着D_s的减少，固液界 面前沿溶质扩散层越薄，枝晶生长越有利，枝晶尖端生长的速度越大，侧向分支越发达；D< sub>s越小，固相中溶质成分的波动越强烈，随着D_s的增大，固相中溶质 成分的波动相应减小；溶质微观偏析程度随D_s的增大而减小. 关键词： 相场方法 微观偏析 固相扩散系数 数值模拟     

Smaller Output Beam Divergence in the Slowly Opened Q-Switch Operation

The mechanism of the slowly opened Q-switch operation was investigated thoroughly. Maximum energy extraction from the resonator could be optimized, and the smallest output beam divergence could be achieved. In this article, we present a detailed analysis that has numerically verified the mode-selection mechanism in the slowly opened Q-switch operation, and the degree of the smaller output laser beam divergence that has been achieved. The mechanism of the slowly opened Q-switch operation is the inherent advantage of the passive saturable absorber in this operation. We can use the maximum energy extraction and the smallest output beam divergence results of the slowly opened Q-switch operation to design and optimize various passive saturable absorbers: plastic dye sheets, LiF:F₂⁻ color center crystals, Cr4⁺: YAG crystals, RG1000 color glass filters, and the single crystal semiconductor saturable absorber wafers that are in developed in our microchip laser systems.     

Phenylene vinylene‐based electroluminescent polymers with electron transport block in the main chain

We report a new route for the design of soluble phenylene vinylene (PV) based electroluminescent polymers bearing electron‐deficient oxadizole (OXD) and triazole (TZ) moieties in the main chains with the aryloxy linkage. Both series of the PV‐based polymers were prepared by Wittig reaction. By properly adjusting the OXD and/or TZ content through copolymerization, we can achieve an enhanced balance of hole‐ and electron injections, such that the device efficiency is significantly improved. Light‐emitting diodes fabricated from P1, P2, P3, P4, P5, P6, and P7 with the configuration of Indium–Tin Oxide (ITO)/Poly (styrene sulfonic acid) doped poly (ethylenedioxythiophene) (PEDOT)/polymer/Ca/Al, emit bright green light with the maximum peak around 500 nm. For the device using the optimal polymer (P4) as emitting layer, a maximum brightness of 1300 cd/m² at 20 V and a maximum luminance efficiency of 0.325 cd/A can be obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3469–3478, 2006     

Synthesis and application as polymer electrolyte of hyperbranched polyether made by cationic ring‐opening polymerization of 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxymethyl}‐3′‐methyl‐oxetane

A novel cyclic ether monomer 3‐{2‐[2‐(2‐hydroxyethoxy)ethoxy]ethoxy‐methyl}‐3′‐methyloxetane (HEMO) was prepared from the reaction of 3‐hydroxymethyl‐3′‐methyloxetane tosylate with triethylene glycol. The corresponding hyperbranched polyether (PHEMO) was synthesized using BF₃·Et₂O as initiator through cationic ring‐opening polymerization. The evidence from ¹H and ¹³C NMR analyses revealed that the hyperbranched structure is constructed by the competition between two chain propagation mechanisms, i.e. active chain end and activated monomer mechanism. The terminal structure of PHEMO with a cyclic fragment was definitely detected by MALDI‐TOF measurement. A DSC test implied that the resulting polyether has excellent segment motion performance potentially beneficial for the ion transport of polymer electrolytes. Moreover, a TGA assay showed that this hyperbranched polymer possesses high thermostability as compared to its liquid counterpart. The ion conductivity was measured to reach 5.6 × 10^?5 S/cm at room temperature and 6.3 × 10^?4 S/cm at 80 °C after doped with LiTFSI at a ratio of Li:O = 0.05, presenting the promise to meet the practical requirement of lithium ion batteries for polymer electrolytes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3650–3665, 2006