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.     

Runge–Kutta Methods for Systems of Differential Equation with Piecewise Continuous Arguments: Convergence and Stability

This work deals with the convergence and stability of Runge–Kutta methods for systems of differential equation with piecewise continuous arguments x^′(t) = Px(t)+Qx([t+1∕2]) under two cases for coe?cient matrix. First, when P and Q are complex matrices, the su?cient condition under which the analytic solution is asymptotically stable is given. It is proven that the Runge–Kutta methods are convergent with order p. Moreover, the su?cient condition under which the analytical stability region is contained in the numerical stability region is obtained. Second, when P and Q are commutable Hermitian matrices, using the theory of characteristic, the necessary and su?cient conditions under which the analytic solution and the numerical solution are asymptotically stable are presented, respectively. Furthermore, whether the Runge–Kutta methods preserve the stability of analytic solution are investigated by the theory of Padé approximation and order star. To demonstrate the theoretical results, some numerical experiments are adopted.     

基于基金项目的“一带一路”研究格局与态势分析

以国家和有关部委的资助项目库为数据来源，检索2014-2016年“一带一路”的相关基金立项，运用文献计量和空间分析的方法从项目的负责人、科研单位、所属地域、学科、研究内容等多个角度进行解析，旨在揭示 “一带一路”研究的格局与态势.结果表明：（1）“一带一路”相关基金立项数目总体呈逐年上升趋势，增速平缓，国家社科基金主体地位明显.（2）项目所属单位、省份在空间上呈现集中分布趋势，体现了一定的区位优势、空间关联与地理邻近效应.（3）单个负责人的立项数目差异不大，分布较为平均.（4）“一带一路”、丝绸之路经济带、21世纪海上丝绸之路为目前学者主要的研究对象和议题.（5）各类基金高频词汇基本保持同步，五类基金研究的热门领域大体趋于一致，包括经济学、国际问题研究、民族问题研究和交叉学科研究等.最后，从研究数据、时间、空间及学科与合作前景上，对未来的研究趋势做了总结和展望.     

空化可压缩流动空穴溃灭激波特性研究

为深入研究空化可压缩流动中空泡/空泡团溃灭过程中激波产生、传播及其与空穴相互作用规律,本文采用数值模拟方法对空化可压缩流动空穴溃灭激波特性展开了研究.数值计算基于OpenFOAM开源程序,综合考虑蒸汽相和液相的压缩性,通过在原无相变两相可压缩求解器的控制方程中耦合模拟空化汽液相间质量交换的源项,实现了对空化流动的非定常可压缩计算.利用上述考虑汽/液相可压缩性的空化流动求解器,对周期性云状空化流动进行了数值模拟,并重点研究了空穴溃灭激波特性.结果表明:上述数值计算方法可以准确捕捉到空穴非定常演化过程及大尺度脱落空泡云团溃灭激波现象,大尺度脱落空泡云团溃灭过程分为3个阶段:(1) U型空泡团形成; (2) U型空泡团头部溃灭; (3) U型空泡团腿部溃灭.在U 型空泡团腿部溃灭瞬间,观察到激波产生,并向上游和下游传播,向上游传播的激波与空穴相互作用,导致水翼吸力面新生的附着型片状空穴回缩,直至完全溃灭.并且空穴溃灭激波存在回弹现象, 抑制了下一周期的空化发展.      

Small data solutions of 2-D quasilinear wave equations under null conditions

2 Abstract For the 2-D quasilinear wave equation(?_t~2-?_x)u+2∑ij=0g~(ij)(?u)?_(ij)u = 0 satisfying i,j=0 null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation(?_t~2-?_x)_u+2∑ij=0g~(ij)(?u)?_(ij)u = 0 satisfying null conditions with small initial data and the coefficients i,j=0 depending simultaneously on u and ?u. Through construction of an approximate solution,combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.     

Naturally occurring antitubercular cyclic peptides

The antibiotic pipeline has failed to keep pace with the rise of multidrug resistant tuberculosis and extensively drug-resistant tuberculosis pathogens. Naturally occurring peptides provide a rich source of lead compounds for developing novel pharmaceuticals with high selectivity and potency. Given the vast number of naturally-occurring bioactive cyclic peptides identified so far, the following digest highlights several cyclic peptides, discovered in the preceding decade, that exhibit promising activity against Mycobacterium tuberculosis.     

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。     

石英砂-聚乙烯二元混合体系的太赫兹光谱特性研究

太赫兹时域光谱技术目前逐渐应用于对岩石的研究中。在制备样品时通常需要将岩石磨碎后与粘合剂混合压片，岩石的含量、粒径等都会对测试结果造成影响。将自然界中常见的石英砂粉末（不同粒径）与聚乙烯（PE）微粒以不同的比例混合，通过压片的手段将其制成适用于太赫兹系统测试的样品，用以探究样品中石英砂的含量以及其粒径对实验结果的影响。首先研究石英砂含量对实验结果造成的影响。在保持样品中石英砂的粒径不变的情况下，发现不同石英砂含量样品的时域光谱图中，时间延迟以及峰值都呈现出非单调的变化趋势。为了探究出现这种现象的原因，对样品的折射率以及吸收系数做了进一步的分析。结果表明样品的折射率会随着样品中石英砂含量的增加而逐渐增大，通过适用于本实验的有效介质理论能够解释这一现象。样品对于太赫兹波段的吸收系数随着石英砂含量的增加呈现出先增大后减小的现象，并且在石英砂质量分数为60%时达到最大值。为了解释这一现象产生的原因，利用扫描电子显微镜对样品的微观形貌进行观察，发现随着石英砂含量的增加，在压制样品时PE颗粒破碎程度加剧，导致PE的粒径变小。根据米氏散射以及瑞利散射的原理，石英砂粒径不变而PE粒径减小，随之降低的散射强度与石英砂的吸收效应发生竞争，从而导致了吸收系数先增大后减小的现象。进一步研究了石英砂粒径对实验结果的影响，对不同粒径的石英砂样品进行测试，发现折射率不随石英砂粒径的变化而改变，但其吸收系数随着石英砂粒径的减小而逐渐减小。根据米氏散射，样品吸收系数的变化是由于散射强度随石英砂粒径的减小而逐渐减小。研究表明，样品中石英砂的含量和粒径都会对实验结果产生影响。石英砂粒径相同时，样品的吸收系数随石英砂含量的增加呈现先增大后减小的趋势，样品的折射率随石英砂含量的增加而逐渐增大；石英砂含量相同时，样品的吸收系数随石英砂粒径的减小而逐渐减小，而样品的折射率基本不变。这一结论对矿物样品的制备以及对混合物的实验结果分析有一定程度的指导意义。