An evaluation of semidefinite programming based approaches for discrete lot-sizing problems

The present work is intended as a first step towards applying semidefinite programming models and tools to discrete lot-sizing problems including sequence-dependent changeover costs and times. Such problems can be formulated as quadratically constrained quadratic binary programs. We investigate several semidefinite relaxations by combining known reformulation techniques recently proposed for generic quadratic binary problems with problem-specific strengthening procedures developed for lot-sizing problems. Our computational results show that the semidefinite relaxations consistently provide lower bounds of significantly improved quality as compared with those provided by the best previously published linear relaxations. In particular, the gap between the semidefinite relaxation and the optimal integer solution value can be closed for a significant proportion of the small-size instances, thus avoiding to resort to a tree search procedure. The reported computation times are significant. However improvements in SDP technology can still be expected in the future, making SDP based approaches to discrete lot-sizing more competitive.     

m次幂等矩阵的等价条件

利用矩阵的秩和齐次线性方程组解空间的维数,给出了m(m≥2)次幂等矩阵的一些等价条件,推广了2,3次幂等矩阵的相应结果.此外,所获结果还给推广到了m次幂等线性变换中.     

可加稳定过程的自相交局部时

本文研究了可加稳定过程的自相交局部时的问题.利用Borel–Canteil引理等方法,得到可加稳定过程的自相交局部时的Hlder上界,推广了文献[5]中的结果.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

采用反应挤出三次加料法合成苯乙烯/异戊二烯/苯乙烯

以同向啮合双螺杆挤出机为反应器,采用苯乙烯和异戊二烯为聚合单体,以正丁基锂为引发剂,采用三次加料法合成苯乙烯/异戊二烯/苯乙烯(SIS)三嵌段热塑性弹性体.氢核磁共振(1H NMR)谱分析结果表明,共聚物中聚异戊二烯嵌段以1,4-结构为主.采用四氧化锇催化双氧水氧化降解聚合物分子链,利用凝胶渗透色谱对氧化降解后的聚苯乙烯碎片进行分析,证明共聚物分子为(聚苯乙烯-聚异戊二烯-聚苯乙烯)(PS-PI-PS)三嵌段结构.动态力学分析(DMA)及透射电子显微镜(TEM)分析结果表明,SIS具有两相分离结构.拉伸试验结果表明,共聚物拉伸强度与苯乙烯含量有关.     

Interpretation of NMR Relaxation as a Tool for Characterising the Adsorption Strength of Liquids inside Porous Materials

Nuclear magnetic resonance (NMR) relaxation times are shown to provide a unique probe of adsorbate–adsorbent interactions in liquid‐saturated porous materials. A short theoretical analysis is presented, which shows that the ratio of the longitudinal to transverse relaxation times (T₁/T₂) is related to an adsorbate–adsorbent interaction energy, and we introduce a quantitative metric e_surf (based on the relaxation time ratio) characterising the strength of this surface interaction. We then consider the interaction of water with a range of oxide surfaces (TiO₂ anatase, TiO₂ rutile, γ‐Al₂O₃, SiO₂, θ‐Al₂O₃ and ZrO₂) and show that e_surf correlates with the strongest adsorption sites present, as determined by temperature programmed desorption (TPD). Thus we demonstrate that NMR relaxation measurements have a direct physical interpretation in terms of the characterisation of activation energy of desorption from the surface. Further, for a series of chemically similar solid materials, in this case a range of oxide materials, for which at least two calibration values are obtainable by TPD, the e_surf parameter yields a direct estimate of the maximum activation energy of desorption from the surface. The results suggest that T₁/T₂ measurements may become a useful addition to the methods available to characterise liquid‐phase adsorption in porous materials. The particular motivation for this work is to characterise adsorbate–surface interactions in liquid‐phase catalysis.     

Shifting of gas chromatographic retention times due to solvent effects — a study using sulfur chemiluminescence detection

Gas chromatrography (GC) with sulfur chemiluminescence detection (SCD) is an outstanding combination for selectively determining trace concentrations of sulfur compounds in hydrocarbon samples. GC peaks can be identified by retention times when reproducible, automated injection techniques are used. However, as described in this work, analysts should be on the look out for retention shifting due to solvent effects from sample components. Three examples of retention shifting are presented: (1) thiophene by benzene; (2) methylthiophenes by toluene; and (3) dibenzothiophene by gas oil. Depending on samples and analysis conditions, retention shifts from a few hundredths to 1.5 min have been observed. Such retention shifts are likely to cause errors in peak identifications. Therefore, when using SCD, simultaneous FID monitoring is recommended as an aid in evaluating chromatograms for possible retention shifting due to solvent effects.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

A Communication Multiplexer Problem: Two Alternating Queues with Dependent Randomly-Timed Gated Regime

Two random traffic streams are competing for the service time of a single server (multiplexer). The streams form two queues, primary (queue 1) and secondary (queue 0). The primary queue is served exhaustively, after which the server switches over to queue 0. The duration of time the server resides in the secondary queue is determined by the dynamic evolution in queue 1. If there is an arrival to queue 1 while the server is still working in queue 0, the latter is immediately gated, and the server completes service there only to the gated jobs, upon which it switches back to the primary queue. We formulate this system as a two-queue polling model with a single alternating server and with randomly-timed gated (RTG) service discipline in queue 0, where the timer there depends on the arrival stream to the primary queue. We derive Laplace–Stieltjes transforms and generating functions for various key variables and calculate numerous performance measures such as mean queue sizes at polling instants and at an arbitrary moment, mean busy period duration and mean cycle time length, expected number of messages transmitted during a busy period and mean waiting times. Finally, we present graphs of numerical results comparing the mean waiting times in the two queues as functions of the relative loads, showing the effect of the RTG regime.