New Zealand Journal of Mathematics
https://nzjmath.org/index.php/NZJMATH
<p>Welcome to the official website of the New Zealand Journal of Mathematics. From 2020, the old website will be gradually phased out and past issues will be uploaded to this website.</p> <p>The New Zealand Journal of Mathematics seeks to publish high quality research papers in diverse areas of pure and applied mathematics. Well-written survey articles are also warmly invited.</p> <p>Papers should be of general interest and of moderate length. The journal is more likely to publish papers on topics that overlap with the interests of the Editorial Board or that are of interest to at least one mathematician in New Zealand.</p> <p>The online ISSN is 1179-4984.</p>New Zealand Mathematical Society and Department of Mathematics at the University of Aucklanden-USNew Zealand Journal of Mathematics1179-4984Nearly self-conjugate integer partitions
https://nzjmath.org/index.php/NZJMATH/article/view/217
<p>We investigate integer partitions $\lambda$ of $n$ that are nearly self-conjugate in the sense that there are $n - 1$ overlapping cells among the Ferrers diagram of $\lambda$ and its transpose, by establishing a correspondence, through the method of combinatorial telescoping, to partitions of $n$ in which (i).~there exists at least one even part; (ii).~any even part is of size $2$; (iii).~the odd parts are distinct; and (iv).~no odd part is of size $1$. In particular, this correspondence confirms a conjecture that had been given in the OEIS.</p>John CampbellShane Chern
Copyright (c) 2023 The author
2023-06-252023-06-25541710.53733/217Amendment to "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]
https://nzjmath.org/index.php/NZJMATH/article/view/218
<p>We give a counterexample in this amendment to show that there is an error in consideration of the statement "{\it if $f : X \to Y$ and ${\bf J}$ is an ideal on $Y$, then $f^{-1}({\bf J}) = \{f^{-1}(J) : J \in {\bf J}\}$ is an ideal on $X$}" by Hamlett in his paper "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]. We also modify it here in a new way and henceforth put forward correctly all the results that were based on the said statement derived therein.</p>Jiarul HoqueShyamapada Modak
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2023-06-252023-06-255491110.53733/218The 2-fold pure extensions need not split
https://nzjmath.org/index.php/NZJMATH/article/view/277
<p>In this paper, we give an example of locally compact abelian groups $A$ and $C$ such that ${\rm Pext}^{2}(C,A)\neq 0$.</p>Aliakbar Alijani
Copyright (c) 2023 The author
2023-06-252023-06-2554131510.53733/277The conjugate locus in convex 3-manifolds
https://nzjmath.org/index.php/NZJMATH/article/view/139
<p>In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent space; this provides a natural coordinate system to study and classify the singularities of the conjugate locus. We pay particular attention to 3-dimensional manifolds, and describe a novel method for determining conjugate points. We then make a study of a special case: the 3-dimensional (quadraxial) ellipsoid. We emphasise the similarities with the focal sets of 2-dimensional ellipsoids.</p>Thomas WatersMatthew Cherrie
Copyright (c) 2023 New Zealand Journal of Mathematics
2023-07-012023-07-0154173010.53733/139Corrigendum to: Two new proofs of the fact that triangle groups are distinguished by their finite quotients
https://nzjmath.org/index.php/NZJMATH/article/view/361
<p>This brief corrigendum corrects some minor errors in the paper `"Two new proofs of the fact that triangle groups are distinguished by their finite quotients", published in the <em>New Zealand Journal of Mathematics</em> <strong>52</strong> (2022), 827--844.</p>Marston Conder
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2023-10-032023-10-0354313110.53733/361Group Actions on Product Systems
https://nzjmath.org/index.php/NZJMATH/article/view/311
<p>We introduce the concept of a crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system. We generalize a theorem of Hao and Ng about the crossed product of the Cuntz-Pimsner algebra of a $C^{\ast}$-correspondence by a group action to the context of product systems. We present examples related to group actions on $k$-graphs and to higher rank Doplicher-Roberts algebras.</p>Valentin DeaconuLeonard Huang
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2023-10-192023-10-1954334710.53733/311Yamabe solitons in contact geometry
https://nzjmath.org/index.php/NZJMATH/article/view/286
<p>It is shown that the scalar curvature of a Yamabe soliton as a Sasakian manifold is constant and the soliton vector field is Killing. The same conclusion is shown to hold for a Yamabe soliton as a $K$-contact manifold $M^{2n+1}$ if any one of the following conditions hold: (i) its scalar curvature is constant along the soliton vector field $V$, (ii) $V$ is an eigenvector of the Ricci operator with eigenvalue $2n$, (iii) $V$ is gradient.</p>Rahul PoddarS. BalasubramanianRamesh Sharma
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2023-12-202023-12-2054495510.53733/286A note on the regularity criterion for the micropolar fluid equations in homogeneous Besov spaces
https://nzjmath.org/index.php/NZJMATH/article/view/315
<p>This paper gives a further investigation on the regularity criteria for three-dimensional micropolar equations in Besov spaces. More precisely, it is proved that the weak solution $(u, \omega)$ is regular if the velocity $u$ satisfies</p> <p>$$\int_{0}^{T}\| \nabla_{h}u_{h}\|_{\dot{B}_{p,\frac{2p}{3}}^{0}}^{q} d t<\infty,\ with\ \ \frac{3}{p}+\frac{2}{q}=2,\ \frac{3}{2}<p\leq\infty,$$<br />or $$\int_{0}^{T}\| \nabla_{h}u\|_{\dot{B}_{\infty ,\infty}^{-1}}^{\frac{8}{3}} d t<\infty,$$<br />or $$\int_{0}^{T}\|\nabla_{h} u_{h}\|_{\dot{B}_{\infty,\infty}^{-\alpha}}^{\frac{2}{2-\alpha}} d t<\infty,\ with\ 0< \alpha< 1. $$</p>Qiang LiMianlu Zou
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2023-12-202023-12-2054576710.53733/315