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Most read

This page lists the top ten most read articles for this journal based on the number of full text views and downloads recorded on Cambridge Core over the last 30 days. This list is updated on a daily basis.

Contents
  • The determinant of the sum of two matrices
  • Chi-Kwong Li, Roy Mathias
  • Published online by Cambridge University Press: 17 April 2009, pp. 425-429
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    Let A and B be n × n matrices over the real or complex field. Lower and upper bounds for |det(A + B)| are given in terms of the singular values of A and B. Extension of our techniques to estimate |f(A + B)| for other scalar-valued functions f on matrices is also considered.

  • A simple proof of the Erdos-Gallai theorem on graph sequences
  • S.A. Choudum
  • Published online by Cambridge University Press: 17 April 2009, pp. 67-70
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    A central theorem in the theory of graphic sequences is due to P. Erdos and T. Gallai. Here, we give a simple proof of this theorem by induction on the sum of the sequence.

  • THE AVERAGE DISTANCE BETWEEN TWO POINTS
  • BERNHARD BURGSTALLER, FRIEDRICH PILLICHSHAMMER
  • Published online by Cambridge University Press: 02 October 2009, pp. 353-359
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    We provide bounds on the average distance between two points uniformly and independently chosen from a compact convex subset of the s-dimensional Euclidean space.

  • A determinant for rectangular matrices
  • V.N. Joshi
  • Published online by Cambridge University Press: 17 April 2009, pp. 137-146
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    The familiar notion of the determinant is generalised to include rectangular matrices. An expression for a normalised generalised inverse of a matrix is given in terms of its determinant and a possible generalisation of the Schur complement is discussed as a simple application.

  • Elementary observations on 2-categorical limits
  • G.M. Kelly
  • Published online by Cambridge University Press: 17 April 2009, pp. 301-317
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    With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be complete but do admit a wide class of limits. Accordingly, we introduce a variety of particular 2-categorical limits of practical importance, and show that certain of these suffice for the existence of indexed lax- and pseudo-limits. Other important 2-categories fail to admit even pseudo-limits, but do admit the weaker bilimits; we end by discussing these.

  • TRACE INEQUALITIES FOR MATRICES
  • KHALID SHEBRAWI, HUSSIEN ALBADAWI
  • Published online by Cambridge University Press: 02 August 2012, pp. 139-148
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    Trace inequalities for sums and products of matrices are presented. Relations between the given inequalities and earlier results are discussed. Among other inequalities, it is shown that if A and B are positive semidefinite matrices then for any positive integer k.

  • EDITORIAL: A CENTENARY OF THE BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • J. H. LOXTON
  • Published online by Cambridge University Press: 05 July 2019, pp. 1-4
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  • UNIQUENESS OF ENTIRE FUNCTIONS SHARING A VALUE WITH LINEAR DIFFERENTIAL POLYNOMIALS
  • INDRAJIT LAHIRI, RAJIB MUKHERJEE
  • Published online by Cambridge University Press: 30 November 2011, pp. 295-306
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    We study the uniqueness of entire functions sharing a nonzero finite value with linear differential polynomials and improve a result of P. Li.

  • ALGORITHMS TO IDENTIFY ABUNDANT p-SINGULAR ELEMENTS IN FINITE CLASSICAL GROUPS
  • ALICE C. NIEMEYER, TOMASZ POPIEL, CHERYL E. PRAEGER
  • Published online by Cambridge University Press: 06 August 2012, pp. 50-63
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    Let G be a finite d-dimensional classical group and p a prime divisor of ∣G∣ distinct from the characteristic of the natural representation. We consider a subfamily of p-singular elements in G (elements with order divisible by p) that leave invariant a subspace X of the natural G-module of dimension greater than d/2 and either act irreducibly on X or preserve a particular decomposition of X into two equal-dimensional irreducible subspaces. We proved in a recent paper that the proportion in G of these so-called p-abundant elements is at least an absolute constant multiple of the best currently known lower bound for the proportion of all p-singular elements. From a computational point of view, the p-abundant elements generalise another class of p-singular elements which underpin recognition algorithms for finite classical groups, and it is our hope that p-abundant elements might lead to improved versions of these algorithms. As a step towards this, here we present efficient algorithms to test whether a given element is p-abundant, both for a known prime p and for the case where p is not known a priori.

  • On co-FPF modules
  • Le Van Thuyet
  • Published online by Cambridge University Press: 17 April 2009, pp. 257-264
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    A ring R is called right co-FPF if every finitely generated cofaithful right R-module is a generator in mod-R. This definition can be carried over from rings to modules. We say that a finitely generated projective distinguished right R-module P is a co-FPF module (quasi-co-FPF module) if every P-finitely generated module, which finitely cogenerates P, generates σ[P] (P, respectively). We shall prove a result about the relationship between a co-FPF module and its endomorphism ring, and apply it to study some co-FPF rings.