An experiment with arithmetic precision in linear algebra computations

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation. Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.     

剩余格与FI代数的可嵌入性

给出剩余格可嵌入于全序剩余格的乘积的充要条件。还给出定义在格上的FI代数可嵌入于全序FI代数的乘积的充要条件。     

置换群关于变换后基的强生成集的算法

本文给出置换群关于变换后的基的强生成集的一种算法及其理论证明,并讨论了既约强生成集和最小强生成集的问题。     

玻恩和沃尔夫合著的《光学原理》一书写作过程

《光学原理》(Principles of Optics)一书是玻恩与沃尔夫合著的、倍受好评的光学经典名著。回顾、梳理与品味这一名著的撰写过程,会得到诸多感悟。教书育人、著书立说的物理教育家以及物理学家,都可以从中得到一把尺子,用以衡量自己的工作。这有利于中国物理学的发展。     

<Emphasis Type="Italic">N</Emphasis>=2 de Sitter Super-symmetry Algebra

It was shown that N=1 super-symmetry algebra can be constructed in de Sitter space (Pahlavan et al. in Phys Lett. B 627:217–223, 2005), through calculation of charge conjugation in the ambient space notation (Moradi et al. in Phys. Lett. B 613:74, 2005; Phys. Lett. B 658:284, 2008). Calculation of N=2 super-symmetry algebra constitutes the main frame of this paper. N=2 super-symmetry algebra was presented in Pilch et al. (Commun. Math. Phys. 98:105, 1985). In this paper, we obtain an alternative N=2 super-symmetry algebra.     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

John Bell and the Identical Twins

I present a biographical profile of John S. Bell based upon extensive interviews I had with him. I present Bell‘s views on the quantum theory along with a simple explanation of his identity. Jeremy Bernstein is Professor Emeritus of Physics at the Stevens Institute of Technology and a former staff writer for The New Yorker.     

The Politics of Memory: Otto Hahn and the Third Reich

As President of the Kaiser Wilhelm Society and its successor, the Max Planck Society, from 1946 until 1960, Otto Hahn (1879–1968) sought to portray science under the Third Reich as a purely intellectual endeavor untainted by National Socialism. I outline Hahn’s activities from 1933 into the postwar years, focusing on the contrast between his personal stance during the National Socialist period, when he distinguished himself as an upright non-Nazi, and his postwar attitude, which was characterized by suppression and denial of Germany’s recent past. Particular examples include Hahn’s efforts to help Jewish friends; his testimony for colleagues involved in denazification and on trial in Nuremberg; his postwar relationships with émigré colleagues, including Lise Meitner; and his misrepresentation of his wartime work in the Kaiser Wilhelm Institute for Chemistry.     

N(2,2,0)代数的(∈,∈Vq_(λ,μ))-模糊关联理想若干性质

对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想若干性质进行了详细的研究.首先,运用点态化的方法证明了(∈,∈∨q_((λ,μ)))-模糊关联理想的同态像与同态原像的基本性质;其次,研究了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积;最后,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积的投影子集.     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.