@article {Jedrzejak2005,
author="Tomasz Jedrzejak",
title="{Height estimates on cubic twists of the Fermat elliptic curve}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="177--186",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="10th January, 2005",
classmath="11G05, 11G50, 11G07, 11G35",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183401",
ZBLID="02246382",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5007-Jedrzejak/index.shtml",
acknowledgement={},
abstract={We give bounds for the canonical height of rational and integral points on cubic twists of the Fermat elliptic curve. As a corollary we prove that there is no integral arithmetic progression on certain curves in this family. }
}
@article {Lasheras2005,
author="Francisco F. Lasheras",
title="{Ascending HNN-extensions and properly 3-realisable groups}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="187--196",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="28th February, 2005",
classmath="57M07, 57M10, 57M20",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183402",
ZBLID="02246383",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5066-Lasheras/index.shtml",
acknowledgement={This work was partially supported by the project MTM 2004-01865.},
abstract={ In this paper, we show that any ascending HNN-extension of a finitely presented group is properly 3-realisable. We recall that a finitely presented group $G$ is said to be properly 3-realisable if there exists a compact 2-polyhedron $K$ with $\pi _1(K) \cong G$ and whose universal cover $\widetilde {K}$ has the proper homotopy type of a (PL) 3-manifold (with boundary). }
}
@article {ChKaKaVa2005,
author="A. Chigogidze and A. Karasev and K. Kawamura and V. Valov",
title="{On {$C^*$}-algebras with the approximate $n$-th root property}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="197--212",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="3rd March, 2005",
classmath="46L85, 54C40",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183403",
ZBLID="02246384",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5072-ChKaKaVa/index.shtml",
acknowledgement={ The second author was partially supported by his NSERC Grant 257231-04. The paper was started during the third author's visit to Nipissing University in July 2004. The last author was partially supported by his NSERC Grant 261914-03.},
abstract={ We say that a $C^*$-algebra $X$ has the approximate $n$-th root property ($n\geq 2$) if for every $a\in X$ with $\|a\|\leq 1$ and every $\varepsilon >0$ there exists $b\in X$ such that $\|b\|\leq 1$ and $\|a-b^n\|<\varepsilon $. Some properties of commutative and non-commutative $C^*$-algebras having the approximate $n$-th root property are investigated. In particular, it is shown that there exists a non-commutative (respectively, commutative) separable unital \break $C^*$-algebra $X$ such that any other (commutative) separable unital $C^*$-algebra is a quotient of $X$. Also we illustrate a commutative $C^*$-algebra, each element of which has a square root such that its maximal ideal space has infinitely generated first {\v C}ech cohomology. }
}
@article {Steinke2005,
author="G{\"u}nter F. Steinke",
title="{Flat Laguerre planes of Kleinewillingh{\"o}fer type E obtained by cut and paste}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="213--223",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="14th March, 2005",
classmath="51H15, 51B15",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183404",
ZBLID="02246385",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5079-Steinke/index.shtml",
acknowledgement={},
abstract={We provide examples of flat Laguerre planes of Kleinewillingh\"ofer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, \textsl {Results Maths.} (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, \textit {Canad. Math. Bull.} (1995) but no examples were given there. \par }
}
@article {CrSm2005,
author="Thomas C. Craven and Tara L. Smith",
title="{Abstract theory of semiorderings}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="225--250",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="31st March, 2005",
classmath=" 12D15, 12F10, 11E81",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183405",
ZBLID="02246386",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5102-CrSm/index.shtml",
acknowledgement={},
abstract={Marshall's abstract theory of spaces of orderings is a powerful tool in the algebraic theory of quadratic forms. We develop an abstract theory for semiorderings, developing a notion of a space of semiorderings which is a prespace of orderings. It is shown how to construct all finitely generated spaces of semiorderings. The morphisms between such spaces are studied, generalising the extension of valuations for fields into this context. An important invariant for studying Witt rings is the covering number of a preordering. Covering numbers are defined for abstract preorderings and related to other invariants of the Witt ring. }
}
@article {FrPoSh2005,
author="John B. Friedlander and Carl Pomerance and Igor E. Shparlinski",
title="{Finding the group structure of elliptic curves over finite fields}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="251--263",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="13th April, 2005",
classmath="11Y16",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183406",
ZBLID="02246387",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5116-FrPoSh/index.shtml",
acknowledgement={During the preparation of this paper, the first author was supported in part by NSERC grant A5123 and by a Killam Research Fellowship. The second author was supported in part by NSF grant DMS-0401422 and the third author was supported in part by ARC grant DP0211459.},
abstract={We show that an algorithm of V.~Miller to compute the group structure of an elliptic curve over a prime finite field runs in probabilistic polynomial time for almost all curves over the field. Important to our proof are estimates for some divisor sums. }
}
@article {YaZh2005,
author="Xin Min Yang and Ping Zhang",
title="{On second-order converse duality for a nondifferentiable programming problem}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="265--270",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="3rd May, 2005",
classmath="49N15, 49J52, 90C30",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183407",
ZBLID="02246388",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5129-YaZh/index.shtml",
acknowledgement={This research was partially supported by the National Natural Science Foundation of China (Grant 10471159), NCET and the Natural Science Foundation of Chongqing.},
abstract={Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29--44). Appropriate modifications are suggested.}
}
@article {ChGao2005,
author="Yujuan Chen and Hongjun Gao",
title="{Existence of positive solutions for nonlocal and nonvariational elliptic systems}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="271--281",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="3rd May, 2005",
classmath="35J20, 35J10, 35A15",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183408",
ZBLID="02246389",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5132-ChGao/index.shtml",
acknowledgement={This project was supported by the NSF of Jiangsu Education Office of PRC 03KJD1101690.},
abstract={In the paper we prove a result on the existence of positive solutions for a class of nonvariational elliptic system with nonlocal source by Galerkin methods and a fixed point theorem in finite dimensions. We establish another existence result by the super and subsolution method and a monotone iteration. }
}
@article {Colonna2005,
author="Flavia Colonna",
title="{Characterisation of the isometric composition operators on the Bloch space}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="283--290",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="3rd May, 2005",
classmath="30D45, 47B33, 47A30",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183409",
ZBLID="02246390",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5133-Colonna/index.shtml",
acknowledgement={I wish to dedicate this article to Professor Maurice Heins for his ninetieth birthday. I owe him a debt of gratitude for his great lectures which deeply stimulated my passion for complex analysis. As a thesis advisor, he was always very patient and generous with his time.},
abstract={ In this paper, we characterise the analytic functions $\f $ mapping the open unit disk $\D $ into itself whose induced composition operator $C_\f : f\mapsto f\circ \f $ is an isometry on the Bloch space. We show that such functions are either rotations of the identity function or have a factorisation $\f =gB$ where $g$ is a non-vanishing analytic function from $\D $ into the closure of $\D $, and $B$ is an infinite Blaschke product whose zeros form a sequence $\{z_n\}$ containing 0 and a subsequence $\{z_{n_{j}}\}$ satisfying the conditions $\bigl |g(z_{n_{j}})\bigr |\to 1$, and $$\lim _{j\to \infty }\prod _{k\ne n_j}\Bigl |\frac {z_{n_j}-z_k}{1-\overline {z_{n_j}}z_k}\Bigr |=1.$$ }
}
@article {HwLiKim2005,
author="Hong Taek Hwang and Longlu Li and Hunnam Kim",
title="{Bounded vector measures on effect algebras}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="291--298",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="4th May, 2005",
classmath=" 28B10, 03G12, 46L51, 81P10",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183410",
ZBLID="02246391",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5136-HwLiKim/index.shtml",
acknowledgement={This paper was supported by Kumoh National Institute of Technology},
abstract={ Let $(L, \bot , \oplus , 0, 1)$ be an effect algebra and $X$ a locally convex space with dual $X^{\prime }$. A function $\mu : L \rightarrow X$ is called a measure if $\mu (a \oplus b) = \mu (a) + \mu (b)$ whenever $a \bot b$ in $L$ and it is bounded if $\bigl \{\mu (a_n) \bigr \}_{n=1}^{\infty }$ is bounded for each orthogonal sequence $\{a_n \}$ in $L$. We establish five useful conditions that are equivalent to boundedness for vector measures on effect algebras. }
}
@article {CaTrTr2005,
author="D. Caponetti and A. Trombetta and G. Trombetta",
title="{Proper $1$-ball contractive retractions in Banach spaces of measurable functions}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="299--315",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="5th May, 2005",
classmath=" 47H09, 46E30",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183411",
ZBLID="02246392",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5138-CaTrTr/index.shtml",
acknowledgement={},
abstract={ In this paper we consider the Wo\'sko problem of evaluating, in an infinite-dimensional Banach space $X$, the infimum of all $k \ge 1$ for which there exists a $k$-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value $1$ is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct. }
}
@article {Dolzan2005,
author="David Dol\v{z}an",
title="{Complementation of the Jacobson group in a matrix ring}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="317--324",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="4th July, 2005",
classmath="16N20, 16U60",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183412",
ZBLID="02246393",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5197-Dolzan/index.shtml",
acknowledgement={},
abstract={ The Jacobson group of a ring $R$ (denoted by $\cJ =\cJ (R)$) is the normal subgroup of the group of units of $R$ (denoted by $G(R)$) obtained by adding 1 to the Jacobson radical of $R$ $\bigl (J(R)\bigr )$. Coleman and Easdown in 2000 showed that the Jacobson group is complemented in the group of units of any finite commutative ring and also in the group of units of a $n\times n$ matrix ring over integers modulo $p^s$, when $n=2$ and $p=2,3$, but it is not complemented when $p\ge 5$. In 2004 Wilcox showed that the answer is positive also for $n=3$ and $p=2$, and negative in all the remaining cases. In this paper we offer a different proof for Wilcox's results and also generalise the results to a matrix ring over an arbitrary finite commutative ring. We show this by studying the generators and relations that define a matrix ring over a field. We then proceed to examine the complementation of the Jacobson group in the matrix rings over graded rings and prove that complementation depends only on the 0-th grade. }
}
@article {Tuck2005,
author="E.O. Tuck",
title="{Riemann--Siegel sums via stationary phase}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="325--328",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="27th July, 2005",
classmath="33E20, 41A60",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183413",
ZBLID="02246394",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5212-Tuck/index.shtml",
acknowledgement={I thank Jim Hill for discussions of this topic.},
abstract={ A new representation is obtained for the Riemann $\xi $ function, in the form of a series of integrals, multiplied by an exponential factor capturing the correct decay rate for large imaginary argument. Each term in this series then has a simple stationary-phase asymptote, the total agreeing with the Riemann--Siegel sum. }
}
@article {Antony2005,
author="Noelle Antony",
title="{On singular Artin monoids}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="329--330",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="2nd August, 2005",
classmath="20M05, 20F36, 20M30",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183414",
ZBLID="02246395",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5221-Antony/index.shtml",
note={Thesis submitted to The University of Sydney, November 2004. Degree approved, May 2005. Supervisor: Dr. David Easdown. Associate Supervisor: Dr. Andrew Mathas.},
abstract={The abstract goes here}
}
@article {Bleile2005,
author="Beatrice Bleile",
title="{Poincar\'e duality pairs of dimension three}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="331--334",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="22nd August, 2005",
classmath="57P10, 55M05, 57M99",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183415",
ZBLID="02246396",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5232-Bleile/index.shtml",
note={Thesis submitted to the University of Sydney, November 2004. Degree approved, February 2005. Supervisor: Dr Jonathan A. Hillman.},
abstract={The abstract goes here}
}
@article {Kemp2005,
author="Michael Kemp",
title="{Geometric Seifert 4-manifolds with hyperbolic bases}",
journal="Bull. Austral. Math. Soc.",
fjournal={Bulletin of the Australian Mathematical Society},
volume="72",
year="2005",
number="2",
pages="335--336",
issn="0004-9727",
coden="ALNBAB",
language="English",
date="20th August, 2005",
classmath=" 57N16, 57N13",
publisher={AMPAI, Australian Mathematical Society},
MRID="MR2183416",
ZBLID="02246397",
url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5239-Kemp/index.shtml",
note={Thesis submitted to The University of Sydney, September 2004. Degree approved, August 2005. Supervisor: Dr. Jonathan Hillman.},
abstract={The abstract goes here}
}