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.     

Crystal planes and reciprocal space in Clifford geometric algebra

This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ?^{n+ 1}. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(?^{n+ 1}) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(?^{n+ 1, 1}). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd.     

由从属关系定义的亚纯多叶函数的子类的某些性质

In the present paper, we introduce some new subclasses of meromorphic starlike,convex, close-to-convex and quasi-convex functions of β-reciprocal in terms of the linear operator using subordination. We obtain the coefficient estimates, convolution properties, integral preserving properties and inclusion relationships of the classes. The results presented here include several results as their special cases.     

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.