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.     

The many proofs of an identity on the norm of oblique projections

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P ²=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.     

Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.     

X波段盘圈加速结构热阴极微波电子枪的研究

介绍了采用盘圈(DAW)加速结构在11.43GHz下研制的热阴极微波电子枪注入器，分析了注入器中DAW加速结构支撑杆对于微波特性的影响以及加速结构中的模式重叠问题. 针对该结构的强腔间耦合以及次临近耦合不能忽略的特点，对其调谐方法进行了分析研究.给出了该长腔链热阴极微波电子枪注入器的物理设计及粒子动力学计算结果，电子能量为5—6MeV，脉冲流强为40mA，电子束发射度为3.4πmm.mrad. 该微波电子枪的加工焊接已经完成，文中给出了其冷测结果.     

Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence

We construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2^δ > δ ⁺ and δ is < 2^δ supercompact. In these models, the structure of the class of supercompact cardinals can be arbitrary, and the size of the power set of κ can essentially be made as large as desired. This extends and generalizes [5, Theorem 2] and [4, Theorem 4]. We also sketch how our techniques can be used to establish a weak indestructibility result. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

聚四氟乙烯材料表面激光改性与刻蚀

利用波长为248 nm的准分子激光束在不同激光能量密度下照射聚四氟乙烯(PTFE)材料的表面,并用扫描电镜(SEM)、X射线光电子能谱(XPS)、拉曼(Raman)光谱等手段对激光处理前后样品的表面形貌、化学成分和结构进行测量和分析,进而对激光与聚四氟乙烯相互作用的机理进行了研究。实验结果表明,激光辐照使聚四氟乙烯表面产生去氟效应,导致表面碳化、分子链的交联以及含氧基团的产生,随着激光能量密度的增加,C=C双键逐渐形成。这些结构的变化可以导致表面硬度和粘结性增强。激光能量密度的大小对照射后样品表面的物理性质和化学结构有着重要的影响,它是聚合物表面激光改性和烧蚀的关键因素。     

水闸闸室结构三维样条边界元分析

用三维样边界元法分析水闸闸室结构。底板，闸墩和载水墙等为其子结构，交通桥，工作桥和胸墙等处理为内部支撑。地基和边载可以是任意的，只要能给定地表位移面力关系。在各种工况下，不论是设置平板门还是弧形门，是平底板是反拱底板，即使在稀疏剖分下也能给出高精度的位移场，应力场和地基反力场。     

Recent studies on phosphorus-bridging carbonyl derivatives: organophosphorus analogs of aldehydes and ketones

Reactions of disodium tetracarbonylferrate, Na₂Fe(CO)₄, with sterically hindered dialkylaminodichlorophosphines, R₂NPCl₂ (R₂N=diisopropylamino, dicyclohexylamino, and 2,2, 6, 6-tetramethylpiperidino) in diethyl ether lead to the air-stable phosphorus-bridging carbonyl derivatives (R₂NP)₂COFe₂(CO)₆ as the major products. The phosphorus-bridging carbonyl group in (i-Pr₂NP)₂COFe₂(CO)₆ has been found to undergo the following types of reactions: 1)Reduction, 2)Acylation, 3)Extrusion of the carbonyl group. The mechanisms of the reactions have been considered.This work was presented at the Workshop «The Modern Problems of Heteroorganic Chemistry» held on the ship «Nikolai Bauman» during the period May 8–13, 1993.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1858–1867, November, 1993.