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Journal of the Australian Mathematical Society
Journal Prestige (SJR): 0.46  Citation Impact (citeScore): 1 Number of Followers: 0  Subscription journalISSN (Print) 1446-7887 - ISSN (Online) 1446-8107 Published by Cambridge University Press  [388 journals]
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- JAZ volume 109 Issue 1 Cover and Front matter
- PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S144678871900065X
Issue No: Vol. 109, No. 1 (2020)
- PubDate: 2020-08-01T00:00:00.000Z
- JAZ volume 109 Issue 1 Cover and Back matter
- PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000661
Issue No: Vol. 109, No. 1 (2020)
- PubDate: 2020-08-01T00:00:00.000Z
- A RESULT OF PALEY AND WIENER ON DAMEK–RICCI SPACES
- Authors: MITHUN BHOWMIK
Pages: 1 - 16
Abstract: A classical result due to Paley and Wiener characterizes the existence of a nonzero function in
$L^{2}(\mathbb{R})$ , supported on a half-line, in terms of the decay of its Fourier transform. In this paper, we prove an analogue of this result for Damek–Ricci spaces.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000077
Issue No: Vol. 109, No. 1 (2020)
- Authors: MITHUN BHOWMIK
- GROUP ALGEBRAS WHOSE UNIT GROUP IS LOCALLY NILPOTENT
- Authors: V. BOVDI
Pages: 17 - 23
Abstract: We present a complete list of groups
$G$ and fields 
$F$ for which: (i) the group of normalized units 
$V(FG)$ of the group algebra 
$FG$ is locally nilpotent; (ii) the set of nontrivial nilpotent elements of 
$FG$ is finite and nonempty, and 
$V(FG)$ is an Engel group.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000557
Issue No: Vol. 109, No. 1 (2020)
- Authors: V. BOVDI
- ON THE NUMBER OF SUBSEMIGROUPS OF DIRECT PRODUCTS INVOLVING THE FREE
MONOGENIC SEMIGROUP- Authors: ASHLEY CLAYTON; NIK RUŠKUC
Pages: 24 - 35
Abstract: The direct product
$\mathbb{N}\times \mathbb{N}$ of two free monogenic semigroups contains uncountably many pairwise nonisomorphic subdirect products. Furthermore, the following hold for 
$\mathbb{N}\times S$ , where 
$S$ is a finite semigroup. It contains only countably many pairwise nonisomorphic subsemigroups if and only if 
$S$ is a union of groups. And it contains only countably many pairwise nonisomorphic subdirect products if and only if every element of 
$S$ has a relative left or right identity element.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788718000605
Issue No: Vol. 109, No. 1 (2020)
- Authors: ASHLEY CLAYTON; NIK RUŠKUC
- GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS
- Authors: BRUNO L. M. FERREIRA; RUTH N. FERREIRA, HENRIQUE GUZZO
Pages: 36 - 43
Abstract: The purpose of this note is to prove the following. Suppose
$\mathfrak{R}$ is a semiprime unity ring having an idempotent element 
$e$ (
$e\neq 0,~e\neq 1$ ) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on 
$\mathfrak{R}$ is a generalized derivation.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000259
Issue No: Vol. 109, No. 1 (2020)
- Authors: BRUNO L. M. FERREIRA; RUTH N. FERREIRA, HENRIQUE GUZZO
- STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION WITH ALMOST
SPACE–TIME WHITE NOISE- Authors: JUSTIN FORLANO; TADAHIRO OH, YUZHAO WANG
Pages: 44 - 67
Abstract: We study the stochastic cubic nonlinear Schrödinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space–time white noise. We also discuss a notion of criticality in this stochastic context, comparing the situation with the stochastic cubic heat equation (also known as the stochastic quantization equation).
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000156
Issue No: Vol. 109, No. 1 (2020)
- Authors: JUSTIN FORLANO; TADAHIRO OH, YUZHAO WANG
- Authors: SHAHRINA ISMAIL
Pages: 68 - 80
Abstract: A Heron triangle is a triangle that has three rational sides
$(a,b,c)$ and a rational area, whereas a perfect triangle is a Heron triangle that has three rational medians 
$(k,l,m)$ . Finding a perfect triangle was stated as an open problem by Richard Guy [Unsolved Problems in Number Theory (Springer, New York, 1981)]. Heron triangles with two rational medians are parametrized by the eight curves 
$C_{1},\ldots ,C_{8}$ mentioned in Buchholz and Rathbun [‘An infinite set of heron triangles with two rational medians’, Amer. Math. Monthly 104(2) (1997), 106–115; ‘Heron triangles and elliptic curves’, Bull. Aust. Math.Soc. 58 (1998), 411–421] and Bácskái et al. [Symmetries of triangles with two rational medians, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.6533, 2003]. In this paper, we reveal results on the curve 
$C_{4}$ which has the property of satisfying conditions such that six of seven parameters given by three sides, two medians and area are rational. Our aim is to perform an extensive search to prove the nonexistence of a perfect triangle arising from this curve.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S144678871900003X
Issue No: Vol. 109, No. 1 (2020)
- Authors: SHAHRINA ISMAIL
- COMPLETE WEINGARTEN HYPERSURFACES SATISFYING AN OKUMURA TYPE INEQUALITY
- Authors: EUDES L. DE LIMA; HENRIQUE F. DE LIMA
Pages: 81 - 92
Abstract: In this paper we deal with complete linear Weingarten hypersurfaces immersed into Riemannian space forms. Assuming an Okumura type inequality on the total umbilicity tensor of such hypersurfaces, we prove that either the hypersurface is totally umbilical or it holds an estimate for the norm of the total umbilicity tensor, which is also shown be sharp in the sense that the product of space forms realize them. Our approach is based on a version of the Omori–Yau maximum principle for a suitable Cheng–Yau type operator.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000028
Issue No: Vol. 109, No. 1 (2020)
- Authors: EUDES L. DE LIMA; HENRIQUE F. DE LIMA
- ALGEBRAIC CUNTZ–KRIEGER ALGEBRAS
- Authors: ALIREZA NASR-ISFAHANI
Pages: 93 - 111
Abstract: We show that a directed graph
$E$ is a finite graph with no sinks if and only if, for each commutative unital ring 
$R$ , the Leavitt path algebra 
$L_{R}(E)$ is isomorphic to an algebraic Cuntz–Krieger algebra if and only if the 
$C^{\ast }$ -algebra 
$C^{\ast }(E)$ is unital and 
$\text{rank}(K_{0}(C^{\ast }(E)))=\text{rank}(K_{1}(C^{\ast }(E)))$ . Let 
$k$ be a field and 
$k^{\times }$ be the group of units of 
$k$ . When 
$\text{rank}(k^{\times })
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000375
Issue No: Vol. 109, No. 1 (2020)
- Authors: ALIREZA NASR-ISFAHANI
ALGEBRAS AND C*-ALGEBRAS- Authors: EBRAHIM SAMEI; JAFAR SOLTANI FARSANI
Pages: 112 - 130
Abstract: We introduce the concept of strong property
$(\mathbb{B})$ with a constant for Banach algebras and, by applying a certain analysis on the Fourier algebra of the unit circle, we show that all C*-algebras and group algebras have the strong property 
$(\mathbb{B})$ with a constant given by 
$288\unicode[STIX]{x1D70B}(1+\sqrt{2})$ . We then use this result to find a concrete upper bound for the hyperreflexivity constant of 
${\mathcal{Z}}^{n}(A,X)$ , the space of bounded 
$n$ -cocycles from 
$A$ into 
$X$ , where 
$A$ is a C*-algebra or the group algebra of a group with an open subgroup of polynomial growth and 
$X$ is a Banach 
$A$ -bimodule for which 
${\mathcal{H}}^{n+1}(A,X)$ ...
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788719000089
Issue No: Vol. 109, No. 1 (2020)
- Authors: EBRAHIM SAMEI; JAFAR SOLTANI FARSANI
$1/\unicode[STIX]{x1D70B}$- Authors: YUE ZHAO
Pages: 131 - 144
Abstract: In this article, we give new proofs of two of Ramanujan’s
$1/\unicode[STIX]{x1D70B}$ formulae 
$$\begin{eqnarray}\frac{1}{\unicode[STIX]{x1D70B}}=\frac{2\sqrt{2}}{99^{2}}\mathop{\sum }_{m=0}^{\infty }(26390m+1103)\frac{(4m)!}{396^{4m}(m!)^{4}}\end{eqnarray}$$ and 
$$\begin{eqnarray}\frac{1}{\unicode[STIX]{x1D70B}}=\frac{2}{84^{2}}\mathop{\sum }_{m=0}^{\infty }(21460m+1123)\frac{(-1)^{m}(4m)!}{(84\sqrt{2})^{4m}(m!)^{4}}\end{eqnarray}$$ using the theory of modular forms. The method can also be used to prove other classical 
$1/\unicode[STIX]{x1D70B}$ formulae.
PubDate: 2020-08-01T00:00:00.000Z
DOI: 10.1017/S1446788718000599
Issue No: Vol. 109, No. 1 (2020)
- Authors: YUE ZHAO
