Elementary construction of residue currents associated to Cohen–Macaulay ideals

Let n be a positive integer. We give an elementary construction for the nth variation, Vn(f), of a real valued continuous function f and prove an analogue of the classical Jordan decomposition theorem. In fact, let C[0, 1] denote the real valued continuous functions on the closed unit interval, let An denote the semi-algebra of non-negative functions in C[0, 1] whose first n differences are non-negative, and let Sn denote the difference algebra An - An. We show that Sn is precisely that subset of C[0, 1] on which Vn(f)<∞. (Theorem 1).

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An elementary construction of the color wave functions in the quark model

American Journal of Physics ◽

10.1119/1.18459 ◽

1996 ◽

Vol 64 (5) ◽

pp. 589-593

Author(s):

Peter von Brentano ◽

Winfried Frank

Keyword(s):

Quark Model ◽

Wave Functions ◽

Elementary Construction

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Various approaches to products of residue currents

Journal of Functional Analysis ◽

10.1016/j.jfa.2012.10.004 ◽

2013 ◽

Vol 264 (1) ◽

pp. 118-138 ◽

Cited By ~ 3

Author(s):

Richard Lärkäng ◽

Håkan Samuelsson Kalm

Keyword(s):

Residue Currents

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Tetris Tight Frames Construction via Hadamard Matrices

Abstract and Applied Analysis ◽

10.1155/2014/917491 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

A. Abdollahi ◽

M. Monfaredpour

Keyword(s):

Hadamard Matrices ◽

New Method ◽

Tight Frames ◽

Frame Operator ◽

Elementary Construction ◽

Unit Norm

We present a new method to construct unit norm tight frames by applying altered Hadamard matrices. Also we determine an elementary construction which can be used to produce a unit norm frame with prescribed spectrum of frame operator.

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A new construction of the Ree groups of type 2G2

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s001309150800028x ◽

2010 ◽

Vol 53 (2) ◽

pp. 531-542 ◽

Cited By ~ 2

Author(s):

Robert A. Wilson

Keyword(s):

Lie Algebras ◽

Algebraic Groups ◽

Maximal Subgroups ◽

Simple Groups ◽

Finite Simple Groups ◽

New Construction ◽

Elementary Construction

AbstractWe give a new elementary construction of Ree's family of finite simple groups of type 2G2, which avoids the need for the machinery of Lie algebras and algebraic groups. We prove that the groups we construct are simple of order q3(q3 + 1)(q − 1) and act doubly transitively on an explicit set of q3 + 1 points, where q = 32k+1. Moreover, our construction is practical in the sense that generators for the groups and many of their maximal subgroups may easily be obtained.

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