New Zealand Journal of Mathematics

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1 New Zealand Journal of Mathematics Volume 32, 1 April 2003 Published by the New Zealand Mathematical Society and Departm ent of Mathematics The University of Auckland ISSN

2 Publisher A 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: / Subscriptions Rates Institutions: $NZ $US $A Individuals: $NZ $US $A Members 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. Exchange The 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 issues 25 1 April October April October April October April October April October April October April October 2002 Editorial and Production Staff The Editor of the New Zealand Journal of Mathematics is Professor G.J. Martin, and he is supported by the Executive Editor Dr J.L. Schiff and Associates Dr J. An, Ms B. Fong and Miss Min-Young Lee. Acknowledgement This Journal is produced with I^T^X (LM^X 2g) and ^Vf»S-T^X, the T jx macro package of the American Mathematical Society. The assistance of Blue Sky Research, makers of Textures, is gratefully acknowledged.

3 New Zealand Journal of Mathematics Volume 32, 1 April 2003 Published by the New Zealand Mathematical Society and D epartm ent of Mathematics The University of Auckland ISSN

4 Publisher A 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: / Subscriptions Rates Institutions: $NZ SUS $A Individuals: $NZ SUS $A Members 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. Exchange The New Zealand Journal of Mathematics welcomes exchange agreements. Proposals for exchange should be sent to Mr D.P. Alcorn at the address above. dates of Publication Volume 25 Volume 25 Volume 26 Volume 26 Volume 27 Volume 27 Volume 28 Volume 28 Volume 29 Volume 29 Volume 30 Volume 30 Volume 31 Volume 31 recent issues April 1996 October 1996 April 1997 October 1997 April 1998 October 1998 April 1999 October 1999 April 2000 October 2000 April 2001 October 2001 April 2002 October 2002 Editorial and Production Staff The Editor of the New Zealand Journal of Mathematics is Professor G.J. Martin, and he is supported by the Executive Editor Dr J.L. Schiff and Associates Dr J. An, Ms B. Fong and Miss Min-Young Lee. Acknowledgement This Journal is produced with (I^TgX 2 ) and X ^S-T^X, the TgX macro package of the American Mathematical Society. The assistance of Blue Sky Research, makers of Textures, is gratefully acknowledged.

5 VOLUME 32, 1 April 2003 On properties of matrix / ( _1) of sine methods Iyad T. Abu-Jeib and Thomas S. S h o r e s On semiregular rings H uanyin Chen and Miaosen Chen On the derivation of discrete conjugate boundary value problem for an optimal control parabolic problem M.H. Farag Solving a Neumann nonlinear boundary value problem F. Gorunescu and M. G o r u n e s c u Rigidity in commuting squares M. Khoshkam and B. Mashood The method of averaging and differential systems with two time scales M ustapha L a k r ib A note on developability and metrizability Abdul M. M ohamad Absolute Euler summability of differentiated Fourier series and some other associated series B.K. Ray and G.D. D ik s h it Zalcman functions and rational dynamics Norbert S te in m e tz...91

New Zealand Journal M athematics

New Zealand Journal M athematics Volume 33, Number 1 Published by the New Zealand Mathematical Society and Department of Mathematics ISSN 1171-6096 New Zealand Journal of Mathematics Publisher A Joint