New Zealand Journal

Mathematics

Volume 35, Number 1

Published by the New Zealand Mathematical Society

andDepartment of Mathematics The University of Auckland

ISSN 1171-6096

New Zealand Journal of MathematicsPublisherA Joint Committee of the New Zealand Mathematical Society and the Department of Mathematics, The University of Auckland.Contact address: New Zealand Journal of Mathematics, Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, NEW ZEALAND.Electronic mail address: nzjmath@math.auckland.ac.nz WWW" location: http://www.math.auckland.ac.nz/NZJM/

Subscriptions RatesInstitutions: $NZ 90.00 SUS 50.00 $A 80.00 Individuals: $NZ 40.00 SUS 20.00 $A 36.00Members of the New Zealand Mathematical Society receive the Journal at a dis­counted rate. Back issues for both New Zealand Journal of Mathematics and the Mathematical Chronicle are available and inquiries should be sent to the Treasurer at the address above'.

ExchangeThe New Zealand Journal of Mathematics welcomes exchange agreements. . Proposals for exchange should be sent to Mr D.P. Alcorn at the address above.Publication dates of recent issuesVolume 27 Number 1 April 1998Volume 27 Number 2 October 1998Volume 28 Number 1 April 1999Volume 28 Number 2 October 1999Volume 29 Number 1 April 2000Volume 29 Number 2 October 2000Volume 30 Number 1 April 2001Volume 30 Number 2 October 2001Volume 31 Number 1 April 2002Volume 31 Number 2 October 2002Volume 32 Number 1 April 2003Volume 32 Number 2 October 2003Volume 33 Number 1 April 2004Volume 33 Number 2 October 2004Volume 34 Number 1 April 2005Volume 34 Number 2 October 2005

Editorial and Production StaffThe Editor of the New Zealand Journal of Mathematics is Professor G.J. Martin, and he is supported by Associates Dr J. An, Ms B. Fong and Ms Patricia Rood.AcknowledgementThis Journal is produced with LM^X (LM^X 2 )̂ and ^VftS-TgX, the T^X macro package of the American Mathematical Society. The assistance of Blue Sky Re­search, makers of Textures, is gratefully acknowledged.

New Zealand Journal

Mathematics

Folume 35, Number 1 April 2006

Published by the New Zealand Mathematical Society

andDepartment of Mathematics The University of Auckland

ISSN 1171-6096

New Zealand Journal of MathematicsPublisherA Joint Committee of the New Zealand Mathematical Society and the Department of Mathematics, The University of Auckland.Contact address: New Zealand Journal of Mathematics, Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, NEW ZEALAND.Electronic mail address: nzjmath@math.auckland.ac.nz W WW location: http://www.math.auckland.ac.nz/NZJM/

Subscriptions RatesInstitutions: $NZ 90.00 SUS 50.00 $A 80.00 Individuals: $NZ 40.00 SUS 20.00 $A 36.00Members of the New Zealand Mathematical Society receive the Journal at a dis­counted rate. Back issues for both New Zealand Journal of Mathematics and the Mathematical Chronicle are available and inquiries should be sent to the Treasurer at the address above.

ExchangeThe New Zealand Journal of Mathematics welcomes exchange agreements. Proposals for exchange should be sent to Mr D.P. Alcorn at the address above.Publicationi dates of recent issuesVolume 27 Number 1 April 1998Volume 27 Number 2 October 1998Volume 28 Number 1 April 1999Volume 28 Number 2 October 1999Volume 29 Number 1 April 2000Volume 29 Number 2 October 2000Volume 30 Number 1 April 2001Volume 30 Number 2 October 2001Volume 31 Number 1 April 2002Volume 31 Number 2 October 2002Volume 32 Number 1 April 2003Volume 32 Number 2 October 2003Volume 33 Number 1 April 2004Volume 33 Number 2 October 2004Volume 34 Number 1 April 2005Volume 34 Number 2 October 2005

Editorial and Production StaffThe Editor of the New Zealand Journal of Mathematics is Professor G.J. Martin, and he is supported by Associates Dr J. An, Ms B. Fong and Ms Patricia Rood.AcknowledgementThis Journal is produced with I^T^X (LT^X 2 )̂ and *4a/(<S-T^X, the T^X macro package of the American Mathematical Society. The assistance of Blue Sky Re­search, makers of Textures, is gratefully acknowledged.

New Zealand Journal of Mathematics

VOLUME 35, Number 1 April 2006

Titchmarsh-Weyl theory for complex Dirac systemAdnan Alhomaidan ....................................................................................... 1

Invertibility of multiplication modules Majid M. A l i ....................................................................................................... 17

Neumann near-rings and Neumann centersHoward E. Bell and Abraham A. Klein ....................................................... 31

Maximal symmetry groups of hyperbolic 3-manifolds Marston Conder, Gaven Martin and Anna Torstensson ............................ 37

0 -supplemented modules relative to a torsion theory M. Tamer Ko§an and Abdullah H a rm a n c i................................................... 63

Apartness and formal topologyErik Palmgren and Peter Schuster ............................................................... 77

Remarks on the hyperbolic geometry of product Teichmuller spacesIoannis D. P l a t i s ............................................................................................... 85

A fixed point theorem in the Menger probabilistic metric space Abdolrahman R a z a n i.......................................................................................109

A criterion of Bloch functions and little Bloch functions PengchengWu ...............................................................................................115