Stochastic preference analysis in numerical preference relations

Numerical preference relations (NPRs) consisting of numerical judgments can be considered as a general form of the existing preference relations, such as multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), interval MPRs (IV-MPRs) and interval FPRs (IV-FPRs). On the basis of NPRs, we develop a stochastic preference analysis (SPA) method to aid the decision makers (DMs) in decision making. The numerical judgments in NPRs can also be characterized by different probability distributions in accordance with practice. By exploring the judgment space of NPRs, SPA produces several outcomes including the rank acceptability index, the expected priority vector, the expected rank and the confidence factor. The outcomes are obtained by Monte Carlo simulation with at least 95% confidence degree. Based on the outcomes, the DMs can choose some of them which they find most useful to make reliable decisions.     

Effect of the structure of titanium–magnesium catalysts on the morphology of polyethylene produced

The structure and formation of polyethylene (PE) particles on supported titanium–magnesium catalysts having different structural characteristics (sizes of microcrystallites, mesopores, and subparticles) were studied for the first time. Scanning electron microscopy was used to identify structural elements of the polymer particles formed over such catalysts and to reveal morphological changes in the growing polymer particles when the yield was increased from approximately 0.2 g PE/g catalyst to approximately 13 kg PE/g catalyst. A relationship was found between structural characteristics of the porous catalyst particles, morphology of the nascent polymer particles, and bulk density of the polymer powder. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2298–2308     

Linear wave dispersion relation of a magnetized relativistic rectilinear electron beam-dielectric system

A general dispersion relation is derived for a relativistic rectilinear electron beam of arbitrary momentum distributions interacting with a dielectric in a guide magnetic field, on the basis of Maxwell equations and the relativistic Vlasov equation. The instability occurs when the beam velocity exceeds the wave phase velocity in the medium. The linear wave dispersion relation, growth rate, spatial growth rate are studied analytically for delta and Lorentzian distributions of beam momentums in detail. The results are of importance for a new kind of high-power microwave generation or amplification devices based on anomalous Doppler effect.     

带凹性生产成本运输问题的新随机规划模型及其求解

提出了一种新的能反映决策者满意度的随机变量序关系,并据此研究了随机不等式的确定性等价类,方法被称为满意度方法.最后将其应用于带凹性生产成本运输问题的求解中,并将方法与常用的机会约束方法进行比较,说明满意度法不仅合理可行,而且当决策者对约束条件的要求越高时,它所得最优值越优于机会约束法所得最优值.     

Quantum topology phase diagrams for molecules,clusters, and solids

The need to make more quantitative use of the total electronic charge density distribution is demonstrated in this short perspective. This is framed in the perspective of the ground breaking early work of Bader and coworkers, along with mathematicians who captured the essential nature of a molecule in a suitably compact form in real space. We see that this simple form is the Poincaré–Hopf relation for molecules and clusters and the Euler–Hopf relation in solids. Thom's theory of elementary catastrophes combined with the Poincaré–Hopf relation provides the inspiration for the new quantum topology. An alternative use of the Poincaré–Hopf relation, molecular recognition, is discussed. Quantum topology is then used to create a topology phase diagram for both molecules and solids. The author adds their perspectives of the huge potential of the quantum topology approach by demonstrating the ease with which new theoretical ideas can be generated. © 2013 Wiley Periodicals, Inc.     

Synthesis and comparative study of the heterocyclic rings on liquid crystalline properties of 2,5-aryl-1,3,4-oxa(thia)diazole derivatives containing furan and thiophene units

A series of heterocyclic liquid crystalline compounds containing 1,3,4-oxadiazole/thiadiazole, furan and thiophene units were synthesised and characterised by means of electrospray ionisation-mass spectrometry (ESI-MS), high-resolution mass spectroscopy (HRMS), ¹H nuclear magnetic resonance (NMR) and ¹³C NMR. The thermal behaviours were investigated by differential scanning calorimetry (DSC) and polarised optical microscopy (POM). The effect of the 1,3,4-oxadiazole, 1,3,4-thiadiazole, furan, thiophene and benzene rings on the liquid crystalline properties was discussed briefly in context with the geometrical and electronic factors. The results showed that the tendency to form mesophases follows the sequence: 1,4-disustituted benzene >2,5-disubstituted thiophene >2,5-disustituted furan and 1,3,4-thiadiazole >1,3,4-oxadiazole.     

Gap formulas for closed linear relations

A classical formula for the gap between two densely defined closed operators in a Hilbert space is extended to the case of linear relations. Copyright © 2014 John Wiley & Sons, Ltd.     

4类图完美匹配数目的递推求法

本文研究了4类特殊图完美匹配数目的显式表达式.利用划分,求和,再递推的方法分别给出了图3-n Z4,2-n(2-C6),2-n(2-K4)和3-n(C4-C6)的完美匹配数目的计算公式.     

Micro-CT参数对骨质疏松性椎体压缩性骨折术后复发的预测价值

本研究探讨Micro-CT参数对骨质疏松性椎体压缩性骨折(OVCF)患者术后复发的预测价值。选取OVCF患者127例,根据术后6个月骨折复发情况分为复发组(n=41)与未复发组(n=86)。患者均接受Micro-CT检查,对比两组Micro-CT参数,即骨体积分数(BV/TV)、骨小梁厚度(Tb.Th)、骨小梁间隙(Tb.Sp)、结构模型指数(SMI),以及骨密度(BMD)、骨矿含量(BMC),分析各参数与BMD、BMC及术后复发相关性,并评价各参数对术后复发的预测价值。结果显示,复发组骨体积分数(BV/TV)、骨小梁厚度(Tb.Th)低于未复发组,骨小梁间隙(Tb.Sp)、结构模型指数(SMI)高于未复发组(P<0.05);BV/TV、Tb.Th与骨密度(BMD)、骨矿含量(BMC)呈正相关,Tb.Sp、SMI与BMD、BMC呈负相关(P<0.05);将年龄、BMD、BMC等其他因素控制后,BV/TV、Tb.Sp、Tb.Th、SMI与OVCF术后骨折复发显著相关(P<0.05);BV/TV、Tb.Sp、Tb.Th、SMI联合预测OVCF术后骨折复发的曲线下面积(AUC)最大,为0.888(P<0.05)。提示Micro-CT参数在OVCF患者中呈异常表达,采用Micro-CT检查可为临床预测OVCF术后骨折复发提供科学指导。