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。     

再生核希尔伯特空间连续线性泛函的范数及其应用北大核心

考虑了再生核希尔伯特空间连续线性泛函范数的表示,得到了用其范数平方等于该线性泛函连续两次作于再生核的简明表示.对于常见的Sobolev-Hibert空间而言,其再生核则可用截幂函数来表示,从而得到Sobolev-Hibert空间上连续线性泛函范数的简洁表示,以新视角解释和简化了文献中的现有结果.     

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.     

My Twenty Years in Microwave Chemistry: From Kitchen Ovens to Microwaves that aren't Microwaves

This Personal Account describes the author's involvement in the field of microwave‐assisted organic synthesis (MAOS) from the late 1990’s starting out with kitchen microwave ovens right through to the development of a reactor in 2016 that – although not using microwave technology – in many ways mimics the performance of a modern laboratory microwave. The reader is taken along a journey that has spanned two decades of intense research on various aspects of microwave chemistry, and, at the same time, was intimately linked to key innovations regarding equipment design and development. A “behind the scenes” approach is taken in this article to share – from a very personal point of view – how specific projects and research ideas were conceived and developed in my research group, and how in general the field of microwave chemistry has progressed in the last two decades.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.