Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

REVIEW ON OPTIMIZATION OF ASTEROID CAPTURE ORBITS

小行星捕获对研究行星起源、地球生命来源、防御小行星撞击地球和开采行星矿产资源具有重要的意义。由于现有的推进器能力不足,小行星捕获任务中优化小行星捕获所需要的速度增量是任务成败的关键。本文分别从利用引力辅助轨道优化、连续小推力轨迹优化、小行星捕获任务轨道优化设计及小行星临时捕获等4 个方向介绍小行星捕获轨道优化方面国内外研究进展及现状。基于对上述研究现状的分析,尝试展望小行星捕获轨道优化研究的未来发展趋势。     

Study of nano‐Cu/SiO2 catalysts for highly selective hydrogenation of acetophenone

Hydrogenation of acetophenone over nano‐Cu/SiO₂ catalysts was investigated. The catalysts, prepared by a liquid precipitation method using various precipitating agents, were characterized using low‐temperature nitrogen adsorption, X‐ray diffraction, temperature‐programmed desorption of ammonia, hydrogen temperature‐programmed reduction, transmission electron microscopy and X‐ray photoelectron spectroscopy. It was found that the catalysts prepared by a homogeneous precipitation method had better activity and stability than those prepared by a co‐precipitation method. The catalyst prepared using urea as precipitating agent had well‐dispersed copper species, high surface area and abundant pore structure. The catalytic performance and mechanism of the Cu/SiO₂ catalysts were further studied. It was found that the activity and stability of the catalysts could be improved by adjusting the proportion of Cu⁺/(Cu⁺ + Cu⁰). The sample prepared using urea as precipitating agent presented higher activity and selectivity. Also, the catalyst prepared using urea maintained a high catalytic performance while being continuously used for 150 h under the optimal reaction conditions.     

Tuning the phase behavior of semicrystalline hydrogenated polynorbornene via epimerization

Hydrogenated polynorbornene (hPN) synthesized by ring‐opening metathesis polymerization (ROMP) exhibits a thermoreversible change in crystal polymorph at a temperature T _cc below its melting point, T _m. The polymorphic transition corresponds to a sharp increase in rotational disorder around the chain axis as the temperature is increased above T _cc. Saturation of ROMP polynorbornene (PN) to hPN can be achieved through both catalytic and noncatalytic approaches. Here, three different hydrogenation routes were employed on the same precursor polymer: catalytic routes over either supported Pd⁰ or a Ni/Al complex, and noncatalytic saturation with diimide. The different hydrogenation routes result in hPNs with varying degrees of epimerization of the cyclopentylene ring (from cis to trans); these epimerized units are included in the hPN crystals. The crystal structure of the rotationally ordered hPN polymorph, observed below T _cc, changes sharply at low levels of epimerization and then is weakly influenced by further increases in trans content. The stability of the rotationally ordered hPN polymorph decreases with increasing epimerization, as reflected in a reduction of T _cc from 134 °C to 92 °C at 22% epimerization. T _cc is less affected by epimerization than by the inclusion of a similar content of 5‐methylnorbornene units, reflecting the smaller size of the trans defect. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1188–1195     

Synergistic Effects of Pseudocolor Imaging,Differentiation, and Square and Logarithmic Conversion on Accuracy of Quantification of Chemical Characteristics Using Test Strips and Similar Products

Test strips and similar products are highly feasible tools for the rapid and approximate determination of chemical characteristics. Although the application of both the quantitative observation of coloration and regression modeling has recently enabled these products to become quantitative tools, their precision and accuracy may be further improved. In this study, the pseudocolor imaging of the coloration image, derivative spectrophotometry-like differentiation of the coloration values, and logarithmic conversion of the raw and derivative values were compared in terms of the precision and accuracy of the quantitative determination of corrosiveness, glucose, nitrate, and pH using the products. The best regression models for the determination were provided by the combination of pseudocolor imaging and differentiation (nitrate and pH); pseudocolor imaging, differentiation, and square-conversion (corrosiveness); or all of the techniques (glucose). When compared to the use of the original 10 raw coloration variables of red-green-blue, cyan-magenta-yellow-key black, and L*a*b* color models only, the above combinations improved the normalized mean absolute error from 14.8% to 3.09% (corrosiveness), 6.33% to 3.15% (glucose), 7.46% to 4.56% (nitrate), and 3.22% to 0.94% (pH). These achievements were largely attributed to the combination of multiple variables that have non-linear and nonmonotonic relationships with the chemical characteristics.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.