On the abstract theory of additive and multiplicative Schwarz algorithms

Summary. In recent years, it has been shown that many modern iterative algorithms (multigrid schemes, multilevel preconditioners, domain decomposition methods etc.) for solving problems resulting from the discretization of PDEs can be interpreted as additive (Jacobi-like) or multiplicative (Gauss-Seidel-like) subspace correction methods. The key to their analysis is the study of certain metric properties of the underlying splitting of the discretization space into a sum of subspaces and the splitting of the variational problem on into auxiliary problems on these subspaces. In this paper, we propose a modification of the abstract convergence theory of the additive and multiplicative Schwarz methods, that makes the relation to traditional iteration methods more explicit. The analysis of the additive and multiplicative Schwarz iterations can be carried out in almost the same spirit as in the traditional block-matrix situation, making convergence proofs of multilevel and domain decomposition methods clearer, or, at least, more classical. In addition, we present a new bound for the convergence rate of the appropriately scaled multiplicative Schwarz method directly in terms of the condition number of the corresponding additive Schwarz operator. These results may be viewed as an appendix to the recent surveys [X], [Ys]. Received February 1, 1994 / Revised version received August 1, 1994     

Some remarks on lengths of propositional proofs

We survey the best known lower bounds on symbols and lines in Frege and extended Frege proofs. We prove that in minimum length sequent calculus proofs, no formula is generated twice or used twice on any single branch of the proof. We prove that the number of distinct subformulas in a minimum length Frege proof is linearly bounded by the number of lines. Depthd Frege proofs ofm lines can be transformed into depthd proofs ofO(m ^d+1) symbols. We show that renaming Frege proof systems are p-equivalent to extended Frege systems. Some open problems in propositional proof length and in logical flow graphs are discussed. Supported in part by NSF grant DMS-9205181     

The Dold-Lashof-Fuchs construction revisited

Sia dato uno spazio topologicoE con azione di un monoide topologicoH e siaE→B una funzione continue che, su ogni apertoU di una partizione dell'unità diB, sia, a meno di omotopia, la proiezioneU×H→U (ovvero una fibrazione numerabile). Un classico risultato di A. Dold e R. Lashof (1959) permette di costruire, a partire daE→B, una funzione continuaE _∞→B_∞, conE _∞ debolmente contraibile e munito di azione diH: laH-fibrazione universale associata daH. Tale funzione, in generale, non è purtroppo numerabile e quindi non si presta alla classificazione delleH-fibrazioni numerabili. Successivamente (1971), M. Fuchs ha trovato un modo di modificare la costruzione di Dold-Lashof per recuperare la numerabilità. La costruzione di Dold-Lashof-Fuchs è, da allora, uno dei principali strumenti nella teoria degli spazi classificanti di monoidi topologici, anche se vi è un uso di topologie alquanto complesse e quindi poco maneggevoli. In questo lavoro ci proponiamo di mostrare come, lavorando nella categoria conveniente deik-spazi, sia possibile descrivere la costruzione di Dold-Lashof-Fuchs in modo estremamente semplificato ed adattarla anche alla classificazione delleF-fibrazioni numerabili.

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Conferenza tenuta da R. Piccinini il 15 maggio 1995     

Divergence preservation in the ADI algorithms for electromagnetics

The recent advances in alternating direct implicit (ADI) methods promise important new capability for time domain plasma simulations, namely the elimination of numerical stability limits on the time step. But the utility of these methods in simulations with charge and current sources, such as in electromagnetic particle-in-cell (EMPIC) computations, has been uncertain, as the methods introduced so far do not have the property of divergence preservation. This property is related to charge conservation and self-consistency, and is critical for accurate and robust EMPIC simulation. This paper contains a complete study of these ADI methods in the presence of charge and current sources. It is shown that there are four significantly distinct cases, with four more related by duality. Of those, only one preserves divergence and, thus, is guaranteed to be stable in the presence of moving charged particles. Computational verification of this property is accomplished by implementation in existing 3D-EMPIC simulation software. Of the other three cases, two are verified unstable, as expected, and one remains stable, despite the lack of divergence preservation. This other stable algorithm is shown to be related to the divergence preserving case by a similarity transformation, effectively providing the complement of the divergence preserving field in the finite-difference energy quantity.     

基于法布里-珀罗腔反射光相位特性设计的梳状滤波器

提出了一种用于设计密集波分复用全光网络中梳状滤波器的方法，该器件利用法布里-珀罗腔反射光相位的非线性性质，结合光的相位在一定光程差下随频率呈线性周期变化的特点，通过使这样两束相位匹配的光发生干涉，得到所需滤波特性。运用江膜特征矩阵对模型进行了模拟计算，并分析了计算结果，论证了这种结构的可行性。     

交通事故现场防入侵设备设计

为了提高交通事故现场防护水平和预防二次事故,利用C8051F020单片机以及MMA7260,MicroMag2等传感器设计了一种设备,对车辆入侵进行检测,迅速有效地判断车辆是否侵入防护现场,根据检测结果实现报警。     

基于MSP430F169的水声遥控发射系统设计

随着水声通信技术的快速发展,水声遥控系统也已投入使用,它在水下通信、遥测及水下航行器的控制等方面有着广阔的应用前景.该设计基于微功耗单片机MSP430F169作为处理器设计路以便实现不同频率信号的产生、选择及显示,并选用D类功放对所产生的信号进行功率放大.系统软件根据所设计的电路进行移频编程,根据MFSK调制的基本原理,通过采用添加保护时间抵抗码间干扰的编码方案,完成不同遥控信号的产生、控制及显示.     

Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

金属络合物分子间交换反应的核磁共振研究Ⅲ.噻吩甲酰三氟丙酮铝与苯甲酰丙酮铝体系分子间配体交换的19F NMR研究

用¹⁹F NMR研究了噻吩甲酰三氟丙酮铝与苯甲酰丙酮铝体系分子间的团体交换反应,求得了交换反应的平衡常数及自由能,结果表明交换反应有利于混合配体络合物生成,平衡时混和溶液中各组分分布偏离统计分布。