Convergence properties and practical estimation of the probability of rank reversal in pairwise comparisons for multi-criteria decision making problems

In this paper, we address the impact of uncertainty introduced when the experts complete pairwise comparison matrices, in the context of multi-criteria decision making. We first discuss how uncertainty can be quantified and modeled and then show how the probability of rank reversal scales with the number of experts. We consider the impact of various aspects which may affect the estimation of probability of rank reversal in the context of pairwise comparisons, such as the uncertainty level, alternative preference scales and different weight estimation methods. We also consider the case where the comparisons are carried out in a fuzzy manner. It is shown that in most circumstances, augmenting the size of the expert group beyond 15 produces a small change in the probability of rank reversal. We next address the issue of how this probability can be estimated in practice, from information gathered simply from the comparison matrices of a single expert group. We propose and validate a scheme which yields an estimate for the probability of rank reversal and test the applicability of this scheme under various conditions. The framework discussed in the paper can allow decision makers to correctly choose the number of experts participating in a pairwise comparison and obtain an estimate of the credibility of the outcome.     

Recent advances in wavefront shaping techniques for biomedical applications

Due to the highly inhomogeneous distributions of refractive indexes, light propagation in complex media such as biological tissue experiences multiple light scattering events. The suppression and control of multiple light scattering events are investigated because they offer the possibility of optical focusing and imaging through biological tissues, and they may open new avenues for diagnosis and treatment of several human diseases. In order to provide insight into how new optical techniques can address the issues of multiple light scattering in biomedical applications, the recent progress in optical wavefront-shaping techniques is summarized.     

多壁碳纳米管修饰玻碳电极测定铜离子

以多壁碳纳米管(MWCNTs)修饰玻碳电极为工作电极,采用阳极溶出线性扫描法研究了铜离子的电化学测定方法。探讨了MWCNTs修饰层数、富集电位、富集时间、溶液pH、支持电解质对峰电流的影响。实验表明,铜离子浓度在1.0×10-8~1.0×10-5mol·L-1范围内与峰电流呈良好的线性关系,检测限为2.0×10-9mol·L-1,且该电极具有良好的稳定性和抗干扰能力。     

Helical Coordination Polymers Based on Keggin-type POMs and N-donor Ligand

Two new 1D helical coordination polymers based on polyoxometalate were synthesized by self-assembly of Keggin-type POMs and copper salts in the presence of triangular N-heterocyclic derivatives or long-chain N-containing carboxylate ligand, that are, (H₃O)[{Cu(H₂tpim)₂}{SiMo₁₂O₄₀}] · 0.5H₂O [Htpim = 2,4,5-tri(4-pyridyl)-imidazole] ( 1 ) and [Cu₂(Hcpp)₃(cpp)(H₂O)][PMo₁₂O₄₀] · 2H₂O [Hcpp = 1-(4-cyanobenzyl)-3–2-yl)pyrazole] ( 2 ). Their structures were determined by single-crystal X-ray diffraction and further characterized by elemental analyses and TG analyses. Compounds 1 and 2 exhibit (1D→2D) interdigitated architectures assembled from 1D helical chains. In compound 1 , the achiral 2D interdigitated nets containing left- and right-handed helixes are further interdigitated with each other to form a 3D supramolecular framework. In compound 2 , adjacent 2D interdigitated layers with opposite chirality are further extended by supramolecular interactions into a 3D supramolecular network, in which non-coordinating Keggin-type POMs as guests are encapsulated.     

Efficient removal for multiple pollutants via Ag2O/BiOBr heterojunction: A promoted photocatalytic process by valid electron transfer pathway

Multiple pollutants including pathogenic microorganism contaminations and emerging organic contaminations (EOCs) have shown a growing threat to the environment, especially the natural waters. However, the control and removal of pathogenic microorganism contaminations and EOCs have been greatly limited since limited knowledge of their environmental behaviors. Thus, a novel and efficient photocatalyst Ag₂O/BiOBr heterojunction was synthesized and used for removal of multiple pollutants including Escherichia coli (E. coli), Staphylococcus aureus (S. aureus), tetracycline and acetaminophen under visible light. The results showed that there were valid electron transfer pathways between BiOBr and Ag₂O, the main electron transfer direction was the BiOBr to Ag₂O. Photo-generated electrons were stored in Ag₂O and thus separation efficiency between holes and photo-generated electrons was obviously enhanced. Active oxygen species were highly produced and eventually end up with the high efficiency of removal of multiple pollutants. For Ag₂O/BiOBr with Ag₂O content at 3% (the best performance) under visible light, log decrease of E. coli was 7.16 (removal efficiency was 100%) in 120 min, log decrease of S. aureus was 7.23 (removal efficiency was 100%) in 160 min, C/C₀ of tetracycline was 0.06 in 180 min, C/C₀ of acetaminophen was 0.17 in 180 min. This work could provide a promising candidate in the actual contaminated natural waters for cleaning multiple pollutants.     

Discrete element simulation of effects of multicontact loading on single particle crushing

Particle crushing commonly occurs in granular materials and affects their structures and mechanical properties. Unlike idealized particles in experimental single particle crushing tests with two loading points, natural particles are crushed under multicontact loading. To date, the criteria and patterns of particle crushing under multicontact conditions are not fully understood. By using the three-dimensional discrete element method, this report explores the effect of multicontact loading on the crushing criterion of a single particle, the crushing pattern, and the relationship between the particle crushing strength and loading distribution. The particles are modelled as aggregates of glued Voronoi polyhedra. The numerical results indicate that the logarithm of the mean principal stress has a good linear correlation with the coordination number. For a specific coordination number, the number of child particles presents a significant normal distribution. For a specific number of child particles, the volumes of child particles can be statistically described as normal or gamma distribution. Three typical models are proposed to qualitatively analyse the relationship between the loading distribution and crushing strength. The relevant conclusions can be helpful in engineering practice and in further studies on crushable granular materials via the discrete element method.     

Bounds on absorption times of directionally biased random sequences

A sequence of random variables X₀,X₁, … with values in {0, 1, …, n} representing a general finite-state stochastic process with absorbing state 0 is said to be directionally biased towards 0, if, for all j > 0, ϵ_j: = inf_k>0 {j − E[X_k | X_k−1 = j]} > 0. For such sequences, let t be the expected value of the time to absorption at 0. For a fixed set of biases, the least upper bound for this time can be computed with an algorithm requiring O(n²) steps. Simple upper bounds are described. In particular, t ≤ E[b_x0], where b_i = Σ_j≤i 1/¯ϵ_j and ¯ϵ_j = min_l≥j {ϵ_l}. If all ϵ_j ≤ ϵ_{j + 1} (so ¯ϵ_j = ϵ_j) and ϵ_n < 1, this bound for t is the best possible. For certain finite stochastic processes which we term conditionally independent of X₀ = i, b(i) bounds the expected time given X₀ = i. Similar results are given for lower bounds. The results of this paper were designed to be a useful tool for determining rates of convergence of stochastic optimization algorithms. © 1996 John Wiley & Sons, Inc.     

空时超分辨方法在高频地波超视距雷达中的应用

本文研究了一种新的高频地波超视距雷达目标距离以及方位角超分辨问题.在该雷达系统中,各个发射阵元采用不同的发射载频,因此目标回波信号中存在目标距离与方位角的耦合,本文提出利用这种耦合关系,采用MUSIC(Multiple Signal Classification)算法获得目标距离以及方位角的超分辩,从而提高在多目标环境下测距、测角精度.仿真结果验证了该方法的有效性.     

Markov链在教育测量中的应用

将“问题解决”的分析、建模、求解和检验四个阶段作为随机过程的状态得到一Markov链.利用有关随机过程的知识对Markov链进行分类和求解.由此,对学生解决问题的能力进行测量,得到了一些合理结果.