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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  [395 journals]
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- JAZ volume 109 issue 3 Cover and Front matter
- PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000697
Issue No: Vol. 109, No. 3 (2020)
- PubDate: 2020-12-01T00:00:00.000Z
- JAZ volume 109 issue 3 Cover and Back matter
- PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000703
Issue No: Vol. 109, No. 3 (2020)
- PubDate: 2020-12-01T00:00:00.000Z
- CUNTZ–KRIEGER ALGEBRAS AND ONE-SIDED CONJUGACY OF SHIFTS OF FINITE TYPE
AND THEIR GROUPOIDS- Authors: KEVIN AGUYAR BRIX; TOKE MEIER CARLSEN
Pages: 289 - 298
Abstract: A one-sided shift of finite type
$(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines on the one hand a Cuntz–Krieger algebra 
${\mathcal{O}}_{A}$ with a distinguished abelian subalgebra 
${\mathcal{D}}_{A}$ and a certain completely positive map 
$\unicode[STIX]{x1D70F}_{A}$ on 
${\mathcal{O}}_{A}$. On the other hand, 
$(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines a groupoid 
${\mathcal{G}}_{A}$ together with a certain homomorphism 
$\unicode[STIX]{x1D716}_{A}$ on 
${\mathcal{G}}_{A}$. We show that each of these two sets of data completely characterizes the one-sided conjugacy class of 
$\mathsf{X}_{A}$. This strengthens a result of Cuntz and Krieger. We also exhibit an example of two irreducible shifts of finite type which are eventually conjugate but not conjugate. This provides a negative answer to a question of Matsumoto of whether eventual conjugacy implies conjugacy.
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000168
Issue No: Vol. 109, No. 3 (2020)
- Authors: KEVIN AGUYAR BRIX; TOKE MEIER CARLSEN
- SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA
PARTIAL SKEW GROUP RING THEORY- Authors: DANIEL GONÇALVES; DANILO ROYER
Pages: 299 - 319
Abstract: We realize Leavitt ultragraph path algebras as partial skew group rings. Using this realization we characterize artinian ultragraph path algebras and give simplicity criteria for these algebras.
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S144678871900020X
Issue No: Vol. 109, No. 3 (2020)
- Authors: DANIEL GONÇALVES; DANILO ROYER
- WEIGHTED WEAK TYPE ENDPOINT ESTIMATES FOR THE COMPOSITIONS OF
CALDERÓN–ZYGMUND OPERATORS- Authors: GUOEN HU
Pages: 320 - 339
Abstract: Let
$T_{1}$, 
$T_{2}$ be two Calderón–Zygmund operators and 
$T_{1,b}$ be the commutator of 
$T_{1}$ with symbol 
$b\in \text{BMO}(\mathbb{R}^{n})$. In this paper, by establishing new bilinear sparse dominations and a new weighted estimate for bilinear sparse operators, we prove that the composite operator 
$T_{1}T_{2}$ satisfies the following estimate: for 
$\unicode[STIX]{x1D706}>0$ and weight 
$w\in A_{1}(\mathbb{R}^{n})$, 
$$\begin{eqnarray}\displaystyle & & \displaystyle w(\{x\in \mathbb{R}^{n}:\,|T_{1}T_{2}f(x)|>\unicode[STIX]{x1D706}\})\nonumber\\ \displaystyle & & \displaystyle \qquad \lesssim [w]_{A_{1}}[w]_{A_{\infty }}\log (\text{e}+[w]_{A_{\infty }})\int _{\mathbb{R}^{n}}\frac{|f(x)|}{\unicode[STIX]{x1D706}}\log \bigg(\text{e}+\frac{|f(x)|}{\unicode[STIX]{x1D706}}\bigg)w(x)\,dx,\nonumber\end{eqnarray}$$ while the composite operator 
$T_{1,b}T_{2}$ satisfies 
$$\begin{eqnarray}\displaystyle & & \displaystyle w(\{x\in \mathbb{R}^{n}:\,|T_{1,b}T_{2}f(x)|>\unicode[STIX]{x...
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000107
Issue No: Vol. 109, No. 3 (2020)
- Authors: GUOEN HU
- RIGHT ENGEL-TYPE SUBGROUPS AND LENGTH PARAMETERS OF FINITE GROUPS
- Authors: E. I. KHUKHRO; P. SHUMYATSKY, G. TRAUSTASON
Pages: 340 - 350
Abstract: Let
$g$ be an element of a finite group 
$G$ and let 
$R_{n}(g)$ be the subgroup generated by all the right Engel values 
$[g,_{n}x]$ over 
$x\in G$. In the case when 
$G$ is soluble we prove that if, for some 
$n$, the Fitting height of 
$R_{n}(g)$ is equal to 
$k$, then 
$g$ belongs to the 
$(k+1)$th Fitting subgroup 
$F_{k+1}(G)$. For nonsoluble
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000181
Issue No: Vol. 109, No. 3 (2020)
- Authors: E. I. KHUKHRO; P. SHUMYATSKY, G. TRAUSTASON
- SHORT INTERVALS ASYMPTOTIC FORMULAE FOR BINARY PROBLEMS WITH PRIME POWERS,
II- Authors: ALESSANDRO LANGUASCO; ALESSANDRO ZACCAGNINI
Pages: 351 - 370
Abstract: We improve some results in our paper [A. Languasco and A. Zaccagnini, ‘Short intervals asymptotic formulae for binary problems with prime powers’, J. Théor. Nombres Bordeaux 30 (2018) 609–635] about the asymptotic formulae in short intervals for the average number of representations of integers of the forms
$n=p_{1}^{\ell _{1}}+p_{2}^{\ell _{2}}$ and 
$n=p^{\ell _{1}}+m^{\ell _{2}}$, where 
$\ell _{1},\ell _{2}\geq 2$ are fixed integers, 
$p,p_{1},p_{2}$ are prime numbers and 
$m$ is an integer. We also remark that the techniques here used let us prove that a suitable asymptotic formula for the average number of representations of integers 
$n=\sum _{i=1}^{s}p_{i}^{\ell }$, where 
$s$, 
$\ell$ are two integers such that 
$2\leq s\leq \ell -1$, 
$\ell \geq 3$ and 
$p_{i}$,
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000120
Issue No: Vol. 109, No. 3 (2020)
- Authors: ALESSANDRO LANGUASCO; ALESSANDRO ZACCAGNINI
- NOTES ON VANISHING CYCLES AND APPLICATIONS
- Authors: LAURENŢIU G. MAXIM
Pages: 371 - 415
Abstract: Vanishing cycles, introduced over half a century ago, are a fundamental tool for studying the topology of complex hypersurface singularity germs, as well as the change in topology of a degenerating family of projective manifolds. More recently, vanishing cycles have found deep applications in enumerative geometry, representation theory, applied algebraic geometry, birational geometry, etc. In this survey, we introduce vanishing cycles from a topological perspective and discuss some of their applications.
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788720000403
Issue No: Vol. 109, No. 3 (2020)
- Authors: LAURENŢIU G. MAXIM
- LYAPUNOV-TYPE INEQUALITY FOR EXTREMAL PUCCI’S EQUATIONS
- Authors: J. TYAGI; R. B. VERMA
Pages: 416 - 430
Abstract: In this article, we establish a Lyapunov-type inequality for the following extremal Pucci’s equation:
$$\begin{eqnarray}\left\{\begin{array}{@{}ll@{}}{\mathcal{M}}_{\unicode[STIX]{x1D706},\unicode[STIX]{x1D6EC}}^{+}(D^{2}u)+b(x)|Du|+a(x)u=0 & \text{in}~\unicode[STIX]{x1D6FA},\\ u=0 & \text{on}~\unicode[STIX]{x2202}\unicode[STIX]{x1D6FA},\end{array}\right.\end{eqnarray}$$ where 
$\unicode[STIX]{x1D6FA}$ is a smooth bounded domain in 
$\mathbb{R}^{N}$, 
$N\geq 2$. This work generalizes the well-known works on the Lyapunov inequality for extremal Pucci’s equations with gradient nonlinearity.
PubDate: 2020-12-01T00:00:00.000Z
DOI: 10.1017/S1446788719000569
Issue No: Vol. 109, No. 3 (2020)
- Authors: J. TYAGI; R. B. VERMA
