Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

基于线性规划的高温超导磁体线圈设计方法

电子真空回旋器件是一种对磁场精度要求较高的微波源装置, 一般采用超导磁体提供磁场环境. 超导磁体的应用中, 磁场分布的实现是超导磁体设计的核心问题. 提供回旋器件磁场的高温超导磁体包含较复杂的磁体绕组, 为了解决此类设计计算问题, 本文提出了一种包含设计区域约束的线性优化方法进行回旋器件高温超导绕组的设计优化, 通过分步的约束和线性优化计算, 可得到同时满足设计要求和绕组可实现的设计磁场电流分布设计. 计算实例的结果给出了一个提供磁场强度1 .3 Tesla, 长度285 mm 的均匀磁场区域, 同时满足多位置的磁场要求, 设计结果与要求一致度较好, 精度满足应用需求. 该计算方法是一种可适用于较复杂磁场要求和超导绕组结构的设计优化方法.     

Surface passivation in n-type silicon and its application in silicon drift detector

Based on the surface passivation of n-type silicon in a silicon drift detector(SDD), we propose a new passivation structure of SiO2/Al2O3/SiO2 passivation stacks. Since the SiO2 formed by the nitric-acid-oxidation-of-silicon(NAOS)method has good compactness and simple process, the first layer film is formed by the NAOS method. The Al2O3 film is also introduced into the passivation stacks owing to exceptional advantages such as good interface characteristic and simple process. In addition, for requirements of thickness and deposition temperature, the third layer of the SiO2 film is deposited by plasma enhanced chemical vapor deposition(PECVD). The deposition of the SiO2 film by PECVD is a low-temperature process and has a high deposition rate, which causes little damage to the device and makes the SiO2 film very suitable for serving as the third passivation layer. The passivation approach of stacks can saturate dangling bonds at the interface between stacks and the silicon substrate, and provide positive charge to optimize the field passivation of the n-type substrate.The passivation method ultimately achieves a good combination of chemical and field passivations. Experimental results show that with the passivation structure of SiO2/Al2O3/SiO2, the final minority carrier lifetime reaches 5223 μs at injection of 5×10¹⁵ cm^-3. When it is applied to the passivation of SDD, the leakage current is reduced to the order of nA.