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1.
Dinatural transformations, which generalise the ubiquitous natural transformations to the case where the domain and codomain functors are of mixed variance, fail to compose in general; this has been known since they were discovered by Dubuc and Street in 1970. Many ad hoc solutions to this remarkable shortcoming have been found, but a general theory of compositionality was missing until Petri?, in 2003, introduced the concept of g-dinatural transformations, that is, dinatural transformations together with an appropriate graph: he showed how acyclicity of the composite graph of two arbitrary dinatural transformations is a sufficient and essentially necessary condition for the composite transformation to be in turn dinatural. Here we propose an alternative, semantic rather than syntactic, proof of Petri?'s theorem, which the authors independently rediscovered with no knowledge of its prior existence; we then use it to define a generalised functor category, whose objects are functors of mixed variance in many variables, and whose morphisms are transformations that happen to be dinatural only in some of their variables.We also define a notion of horizontal composition for dinatural transformations, extending the well-known version for natural transformations, and prove it is associative and unitary. Horizontal composition embodies substitution of functors into transformations and vice-versa, and is intuitively reflected from the string-diagram point of view by substitution of graphs into graphs.This work represents the first, fundamental steps towards a substitution calculus for dinatural transformations as sought originally by Kelly, with the intention then to apply it to describe coherence problems abstractly. There are still fundamental difficulties that are yet to be overcome in order to achieve such a calculus, and these will be the subject of future work; however, our contribution places us well in track on the path traced by Kelly towards a calculus of substitution for dinatural transformations.  相似文献   
2.
At each time nN,letY¯(n)(ξ)=(y1(n)(ξ),y2(n)(ξ),) be a random sequence of non-negative numbers that are ultimately zero in a random environmentξ=ξnnN. The existence and uniqueness of the nonnegative fixed points of the associated smoothing transformation in random environment are considered. These fixed points are solutions to the distributional equation for a.e.ξ,Z(ξ)=di+yi(0)(ξ)Zi(1)(ξ),where Zi(1):i+ are random variables in random environment which satisfy that for any environmentξ; under Pξ; Zi(1):i+are independent of each other and Y(0)(ξ), and have the same conditional distribution Pξ(Zi(1)(ξ))=PTξ(Z(Tξ)) where T is the shift operator. This extends the classical results of J. D. Biggins [J. Appl. Probab., 1977, 14: 25-37] to the random environment case. As an application, the martingale convergence of the branching random walk in random environment is given as well.  相似文献   
3.
基于半刚性的配体3'',5''-di (1H-1,2,4-triazol-1-yl)-(1,1''-biphenyl)-3,5-dicarboxylic acid (H2DTBDA)和硝酸钴制备了一个柔性超微孔的金属有机骨架{[Co (DTBDA)]·4H2O}n(FJI-H35),并对该材料的结构进行了系统的表征。FJI-H35活化以后可以发生自适应的结构转变,使得孔径从0.43 nm收缩到0.37 nm。气体吸附测试表明FJI-H35可以从氮气和甲烷中选择性捕获二氧化碳,具有很高的吸附选择性和相对低的吸附焓。突破实验进一步证实FJI-H35可以从二氧化碳/氮气(15∶85,V/V)和二氧化碳/甲烷(50∶50,V/V)混合气中高效选择性捕获二氧化碳。  相似文献   
4.
对3种不同残奥(RA)含量的马氏体高强钢进行干滑动摩擦磨损试验, 研究RA含量对其磨损性能的影响. 利用扫描电镜、透射电镜、X射线衍射仪等对试验后的磨损表面及横截面显微组织进行表征. 结果表明, RA含量越高, 磨损表面越光滑, 摩擦系数和磨损率越小, 也即马氏体高强钢的耐磨性越好. 磨损引起的大应变使RA发生应变诱导马氏体相变, 导致硬度和硬化层厚度显著增大. RA含量最高的HT3试样的硬度提高了18.3%, 硬化层厚度达70μm. 相比RA含量低的试样, HT3试样表现出很好的耐磨性. 这是因为马氏体相变使硬度逐步增加, 抗裂纹萌生能力提高; 同时由于亚表面良好的韧性, 可延缓和阻止裂纹扩展, 使得点蚀和剥落不易形成. 因此, 要提高马氏体高强钢的耐磨性, 除了硬度要求外, 还需要考虑其亚表面韧性.  相似文献   
5.
黄刚  许燕红 《化学教育》2022,43(7):31-37
在化学课堂中开展社会性科学议题的教学能够发展学生的社会参与意识,结合微项目学习模式,从课堂教学角度出发,构建选定项目、启动项目、实施项目、交流成果等4个教学流程,确立实施教学的核心问题,设计了鲁科版高一化学“物质的性质与转化单元复习课”,进行了基于社会性科学议题的化学微项目学习的实践教学,结合实践的基本情况提出4点反思。  相似文献   
6.
氮气分子具有高的化学惰性, 氮气的活化与转化充满挑战. 含氮有机物在国民经济发展中具有广泛且重要的价值, 实现温和条件下由氮气直接转化为含氮有机物在科学和经济上均具有重要意义. 目前对氮气的活化与转化的研究主要集中在主族与过渡金属配合物, 稀土和锕系元素由于具有特殊的电子结构, 在氮气的活化与转化领域展现出了区别于主族和过渡金属的特殊反应活性. 我国作为稀土和钍资源大国, 开展稀土及锕系元素的固氮转化研究具有重要的战略意义. 本综述归纳和总结了过去五年内稀土和锕系金属氮气配合物的合成, 以及由稀土和锕系配合物促进的以氮气为原料生成含氮有机物的研究.  相似文献   
7.
As a representative of traditionally fermented Chinese medicine, Massa Medicata Fermentata (MMF) shows the functions of invigorating the spleen and stomach and promoting digestion, which plays an important role in the treatment of gastrointestinal diseases. The fermentation mechanism and the key factors that affect the quality of MMF have not been revealed yet, which has become an urgent issue that limits its clinical application. This article aims to systematically and comprehensively reveal the transformation of physical properties and the dynamic trend of chemical components including substrate components, volatile components, and lactic acid as anaerobic fermentation product during MMF fermentation. Along with obvious hyphae growth observed for MMF, the weight of MMF decreased, and the moisture and temperature increased. Through the quantified 14 components from substrate, ferulic acid increased from 45.53 ± 6.94 to 141.89 ± 78.40 μg/g, while glycosides and phenolic acids declined except caffeic acid. Also, within the 66 volatile components analyzed, alcohols and acids increased, while aldehydes and ketones decreased. Lactic acid was not detected in the fermentation substrate, but an apparent increase in lactic acid content was observed along with the increased fermentation days, resulting in 2.54 ± 0.15 mg/g on day 8. Based on the tested components, the fermentation process of MMF was discriminated into three distinct stages by principal component analysis, and an optimal fermentation time of four days was proposed. The results of this study will be of great significance to clarify the characteristics of fermentation and conduce to improving quality standards of MMF.  相似文献   
8.
In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2Nm)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.  相似文献   
9.
共振隧穿二极管(RTD)可编程逻辑门是一种由单双稳态转换逻辑单元(MOBILE)及正、负输入分支组成的阈值逻辑电路。基于二进制神经元模型中的三层网络结构,提出了基于RTD可编程逻辑门的n变量函数实现算法。按照汉明距离由大到小的顺序,搜索最优输入向量,用定理1或定理2方法产生隐层函数,通过变换次数,确定输入向量的真假及隐层函数的权重。由于定义了最优输入向量及变换次数,提高了算法的准确性;又由于采用了定理2方法,令设计的电路更简单。  相似文献   
10.
《中国物理 B》2021,30(5):56101-056101
The mechanical property and deformation mechanism of twinned gold nanowire with non-uniform distribution of twinned boundaries(TBs) are studied by the molecular dynamics(MD) method. It is found that the twin boundary spacing(TBS) has a great effect on the strength and plasticity of the nanowires with uniform distribution of TBs. And the strength enhances with the decrease of TBS, while its plasticity declines. For the nanowires with non-uniform distribution of TBs, the differences in distribution among different TBSs have little effect on the Young's modulus or strength, and the compromise in strength appears. But the differences have a remarkable effect on the plasticity of twinned gold nanowire. The twinned gold nanowire with higher local symmetry ratio has better plasticity. The initial dislocations always form in the largest TBS and the fracture always appears at or near the twin boundaries adjacent to the smallest TBS. Some simulation results are consistent with the experimental results.  相似文献   
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