Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

空间雷电探测实时采集定位系统

星载雷电探测定位系统是利用光学探测器探测闪电事件的地理位置和光脉冲波形,系统采用CPLD+DSP的数字图像处理方案,利用了CPLD复杂逻辑可编程特性将系统的部分或全部功能集成在一片CPLD上,减小了系统硬件复杂程度,节省了印制版空间.利用DSP高速数字信号处理特性完成实时处理图像数据的功能.系统用CPLD完成图像信号的采集、编码和存储控制,缩小了星载设备体积,简化了电路结构;用DSP完成大量图像数据处理工作,提高了系统工作的实时性.     

分子逻辑器件研究进展

分子器件具有尺寸小、设计合成可控、存储量大、反应速度快、人工智能等诸多优点,是当今化学、物理和材料等领域研究最为重要的一个交叉领域.综述了近些年来分子逻辑器件领域的研究进展.介绍了各种类型的分子逻辑门、半(加)减法器、分子逻辑线路以及DNA分子和固态分子计算.最后提出了分子器件存在的问题并展望了其应用前景.     

DNA‐Based Adaptive Plasmonic Logic Gates

Self‐assembled plasmonic logic gates that read DNA molecules as input and return plasmonic chiroptical signals as outputs are reported. Such logic gates are achieved on a DNA‐based platform that logically regulate the conformation of a chiral plasmonic nanostructure, upon specific input DNA strands and internal computing units. With systematical designs, a complete set of Boolean logical gates are realized. Intriguingly, the logic gates could be endowed with adaptiveness, so they can autonomously alter their logics when the environment changes. As a demonstration, a logic gate that performs AND function at body temperature while OR function at cold storage temperature is constructed. In addition, the plasmonic chiroptical output has three distinctive states, which makes a three‐state molecular logic gate readily achievable on this platform. Such DNA‐based plasmonic logic gates are envisioned to execute more complex tasks giving these unique characteristics.     

Controlled Logic Gates—Switch Gate and Fredkin Gate Based on Enzyme‐Biocatalyzed Reactions Realized in Flow Cells

Controlled logic gates, where the logic operations on the Data inputs are performed in the way determined by the Control signal, were designed in a chemical fashion. Specifically, the systems where the Data output signals directed to various output channels depending on the logic value of the Control input signal have been designed based on enzyme biocatalyzed reactions performed in a multi‐cell flow system. In the Switch gate one Data signal was directed to one of two possible output channels depending on the logic value of the Control input signal. In the reversible Fredkin gate the routing of two Data signals between two output channels is controlled by the third Control signal. The flow devices were created using a network of flow cells, each modified with one enzyme that biocatalyzed one chemical reaction. The enzymatic cascade was realized by moving the solution from one reacting cell to another which were organized in a specific network. The modular design of the enzyme‐based systems realized in the flow device allowed easy reconfiguration of the logic system, thus allowing simple extension of the logic operation from the 2‐input/3‐output channels in the Switch gate to the 3‐input/3‐output channels in the Fredkin gate. Further increase of the system complexity for realization of various logic processes is feasible with the use of the flow cell modular design.     

相似剩余格及其对应逻辑系统的完备性

引入了相似剩余格的概念,讨论了剩余格上相似算子和等价算子的关系,并得到了真值剩余格和相似剩余格相互转化的方法.其次,研究了相似剩余格上的相似滤子,利用相似滤子刻画了可表示的相似剩余格.最后,引入了相似剩余格对应的逻辑系统,证明了其完备性定理,并得到了其成为半线性逻辑的条件.     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．     

集值向量优化的二阶最优性必要条件

在赋范空间中给出了集值映射的二阶切集的概念,利用二阶切集,定义了集值映射的二阶切导数。然后,获得了集值向量优化问题弱极小元的两个二阶最优性必要条件。     

n-极大子群为C-正规的有限群

首先,利用Hall子群的C－正规性,得到了有限群成为。可解群的一个充分条付,推广了Schur-Zassenhaus定理;其次,考查了 n－极大子群或其 2阶及 4阶循环子群为 C-正规对有限群结构的影响．