Bicompletion and Samuel Bicompactification

It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T ₀-space X is a subspace of the quasi-proximity space induced by the Samuel bicompactification of X. The result is then used to establish that the locally finite covering quasi-uniformity defined on the category Top ₀ of topological T ₀-spaces and continuous maps is not lower K-true (in the sense of Brümmer). It is also shown that a functorial quasi-uniformity F on Top ₀ is upper K-true if and only if FX is bicomplete whenever X is sober.     

Samuel Pierpont Langley and his Contributions to the Empirical Basis of Black-Body Radiation

In this paper I deal with an early phase of the history of research on black-body radiation. In this phase, from 1880-1900, the American astrophysicist Samuel Pierpont Langley (1834-1906) invented and used a key instrument, the bolometer, to measure for the first time radiation curves that displayed the characteristic features of asymmetry and of a shifting of their maxima to shorter wavelengths with increasing temperature. I emphasize the complex development of the construction of the bolometer and the early experiments performed with it. I also discuss how these developments became important for theoretical research on the black-body radiation formula. My aim is to show that the often-neglected experimental part of the history of research on black-body radiation represents an important precondition for the theoretical developments that followed.     

The National Synchrotron Light Source, Part II:The Bakeout

This is the second part of a two-part article about the National Synchrotron Light Source (NSLS), the first facility designed and built specifically for producing and exploiting synchrotron radiation. The NSLS,a $24-million project conceived about 1970 and officially proposed in 1976, had its groundbreaking in 1978. Its construction was a key episode in Brookhaven’s history, in the transition of synchrotron radiation from a novelty to a commodity, and in the transition of synchrotron-radiation scientists from parasitic to autonomous researchers. In this part I cover the construction of the NSLS.The story of its construction illustrates many of the tensions and risks involved in building a large scientific facility in a highly politicized environment: risking a facility’s quality by underfunding it versus asking for more funding and risking not getting it; focusing on meeting time and budget promises that risk compromising machine performance versus focusing on performance and risking cancellation; and the pros and cons of a pragmatic versus an analytic approach to commissioning. Robert P. Crease is a Professor in the Department of Philosophy of Stony Brook University in Stony Brook, New York, and historian at Brookhaven National Laboratory.     

The National Synchrotron Light Source, Part I: Bright Idea

The National Synchrotron Light Source (NSLS) was the first facility designed and built specifically for producing and exploiting synchrotron radiation. It was also the first facility to incorporate the Chasman-Green lattice for maximizing brightness. The NSLS was a $24-million project conceived about 1970. It was officially proposed in 1976, and its groundbreaking took place in 1978. Its construction was a key episode in Brookhaven’s history, in the transition of synchrotron radiation from a novelty to a commodity, and in the transition of synchrotron-radiation scientists from parasitic to autonomous researchers. The way the machine was conceived, designed, promoted, and constructed illustrates much both about the tensions and tradeoffs faced by large scientific projects in the age of big science. In this article, the first of two parts, I cover the conception, design, and planning of the NSLS up to its groundbreaking. Part II, covering its construction, will appear in the next issue. Robert P. Crease is a Professor in the Department of Philosophy of Stony Brook University in Stony Brook, New York, and historian at Brookhaven National Laboratory.     

Approximately Cohen-Macaulay Rings and Samuel Functions

Ａｐｐｒｏｘｉｍａｔｅｌｙ　Ｃｏｈｅｎ－Ｍａｃａｕｌａｙ　Ｒｉｎｇｓ　ａｎｄ　Ｓａｍｕｅｌ　ＦｕｎｃｔｉｏｎｓＷａｎｇＦｕｚｈｅｎｇ（王福正）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｅｉｋｉｎｇＵｎｉｖｅｒｓｉｔｙＢｅｉｊｉｎｇ，１００８...     

半Fredholm算子的一个注记

本文研究了(上,下)半Fredholm算子的结构问题.利用经典的算子理论方法,由闭不变子空间诱导的两个映射,获得了(上,下)半Fredholm算子的多种新的等价刻画,推广了(上,下)半Fredholm算子的已有结果.     

An additive formula for Samuel multiplicities on Hilbert spaces of analytic functions

We establish a short exact sequence to relate the germ model of invariant subspaces of a Hilbert space of vector-valued analytic functions and the sheaf model of the corresponding coinvariant subspaces. As a consequence we obtain an additive formula for Samuel multiplicities. As an application, we give a different proof for a formula relating the fibre dimension and the Samuel multiplicity which is first proved in Fang (2005) [11]. The feature of the new proof is that the analytic arguments in Fang (2005) [11] are now subsumed by algebraic machinery.     

Colength,multiplicity, and ideal closure operations

Abstract

In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then R is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.     

Hilbert and Hilbert—Samuel polynomials and partial differential equations

Systems of linear partial differential equations with constant coefficients are considered. The spaces of formal and analytic solutions of such systems are described by algebraic methods. The Hilbert and Hilbert—Samuel polynomials for systems of partial differential equations are defined.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 141–151.Original Russian Text Copyright © 2005 by A. G. Khovanskii, S. P. Chulkov.This revised version was published online in April 2005 with a corrected issue number.