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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 110 issue 2 Cover and Front matter
- PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788720000270
Issue No: Vol. 110, No. 2 (2021)
- PubDate: 2021-04-01T00:00:00.000Z
- JAZ volume 110 issue 2 Cover and Back matter
- PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788720000282
Issue No: Vol. 110, No. 2 (2021)
- PubDate: 2021-04-01T00:00:00.000Z
- ON 2-HOLONOMY
- Authors: HOSSEIN ABBASPOUR; FRIEDRICH WAGEMANN
Pages: 145 - 174
Abstract: We construct a cycle in higher Hochschild homology associated to the two-dimensional torus which represents 2-holonomy of a nonabelian gerbe in the same way as the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary Hochschild homology. This is done using the connection 1-form of Baez–Schreiber. A crucial ingredient in our work is the possibility to arrange that in the structure crossed module
$\unicode[STIX]{x1D707}:\mathfrak{h}\rightarrow \mathfrak{g}$ of the principal 2-bundle, the Lie algebra 
$\mathfrak{h}$ is abelian, up to equivalence of crossed modules.
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788719000314
Issue No: Vol. 110, No. 2 (2021)
- Authors: HOSSEIN ABBASPOUR; FRIEDRICH WAGEMANN
- A FRAMEWORK FOR TORSION THEORY COMPUTATIONS ON ELLIPTIC THREEFOLDS
- Authors: DAVID ANGELES; JASON LO, COURTNEY M. VAN DER LINDEN
Pages: 175 - 193
Abstract: We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new results on torsion pairs in the category of coherent sheaves on an elliptic threefold.
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S144678872000018X
Issue No: Vol. 110, No. 2 (2021)
- Authors: DAVID ANGELES; JASON LO, COURTNEY M. VAN DER LINDEN
- DIRICHLET FORMS AND ULTRAMETRIC CANTOR SETS ASSOCIATED TO HIGHER-RANK
GRAPHS- Authors: JAESEONG HEO; SOORAN KANG, YONGDO LIM
Pages: 194 - 219
Abstract: The aim of this paper is to study the heat kernel and the jump kernel of the Dirichlet form associated to the ultrametric Cantor set
$\unicode[STIX]{x2202}{\mathcal{B}}_{\unicode[STIX]{x1D6EC}}$ that is the infinite path space of the stationary 
$k$-Bratteli diagram 
${\mathcal{B}}_{\unicode[STIX]{x1D6EC}}$, where 
$\unicode[STIX]{x1D6EC}$ is a finite strongly connected 
$k$-graph. The Dirichlet form which we are interested in is induced by an even spectral triple 
$(C_{\operatorname{Lip}}(\unicode[STIX]{x2202}{\mathcal{B}}_{\unicode[STIX]{x1D6EC}}),\unicode[STIX]{x1D70B}_{\unicode[STIX]{x1D719}},{\mathcal{H}},D,\unicode[STIX]{x1D6E4})$ and is given by 
$$\begin{eqnarray}Q_{s}(f,g)=\frac{1}{2}\int _{\unicode[STIX]{x1D6EF}}\operatorname{Tr}(|D|^{-s}[D,\unicode[STIX]{x1D70B}_{\unicode[STIX]{x1D719}}(f)]^{\ast }[D,\unicode[STIX]{x1D70B}_{\unicode[STIX]{x1D719}}(g)])\,d\unicode[STIX]{x1D708}(\unicode[STIX]{x1D719}),\end{eqnarray}$$ where 
$\unicode[STIX]{x1D6EF}$ is the space of choice functions on 
$\unicode[STIX]{x2202}{\mathcal{B}}_{\unicode[STIX]{x1D6EC}}\times \unicode[STIX]{x2202}{\mathcal{B}}_{\unicode[STIX]{x1D6EC}}$. There are two ultrametrics, 
$d^{(s)}$ and
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788719000429
Issue No: Vol. 110, No. 2 (2021)
- Authors: JAESEONG HEO; SOORAN KANG, YONGDO LIM
- MONOTONE AND PSEUDO-MONOTONE EQUILIBRIUM PROBLEMS IN HADAMARD SPACES
- Authors: HADI KHATIBZADEH; VAHID MOHEBBI
Pages: 220 - 242
Abstract: As a continuation of previous work of the first author with Ranjbar [‘A variational inequality in complete CAT(0) spaces’, J. Fixed Point Theory Appl. 17 (2015), 557–574] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunctions in Hadamard spaces. Then, to approximate an equilibrium point, we consider the proximal point algorithm for pseudo-monotone bifunctions. We prove existence of the sequence generated by the algorithm in several cases in Hadamard spaces. Next, we introduce the resolvent of a bifunction in Hadamard spaces. We prove convergence of the resolvent to an equilibrium point. We also prove
$\triangle$-convergence of the sequence generated by the proximal point algorithm to an equilibrium point of the pseudo-monotone bifunction and also the strong convergence under additional assumptions on the bifunction. Finally, we study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point without any additional assumption on the pseudo-monotone bifunction. Some examples in fixed point theory and convex minimization are also presented.
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788719000041
Issue No: Vol. 110, No. 2 (2021)
- Authors: HADI KHATIBZADEH; VAHID MOHEBBI
- C
- Authors: MANSEOB LEE; LE HUY TIEN
Pages: 243 - 259
Abstract: Let M be a closed n-dimensional smooth Riemannian manifold, and let X be a
$C^1$-vector field of 
$M.$ Let 
$\gamma $ be a hyperbolic closed orbit of 
$X.$ In this paper, we show that X has the 
$C^1$-stably shadowing property on the chain component 
$C_X(\gamma )$ if and only if 
$C_X(\gamma )$ is the hyperbolic homoclinic class.
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788720000415
Issue No: Vol. 110, No. 2 (2021)
- Authors: MANSEOB LEE; LE HUY TIEN
$\widehat{{\mathcal{A}}}$- Authors: HIDEKI MURAHARA; TOMOKAZU ONOZUKA
Pages: 260 - 265
Abstract: Ihara et al. proved the derivation relation for multiple zeta values. The first-named author obtained its counterpart for finite multiple zeta values in
${\mathcal{A}}$. In this paper, we present its generalization in 
$\widehat{{\mathcal{A}}}$.
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788719000533
Issue No: Vol. 110, No. 2 (2021)
- Authors: HIDEKI MURAHARA; TOMOKAZU ONOZUKA
- THE QUOTIENT ALGEBRA OF COMPACT-BY-APPROXIMABLE OPERATORS ON BANACH SPACES
FAILING THE APPROXIMATION PROPERTY- Authors: HANS-OLAV TYLLI; HENRIK WIRZENIUS
Pages: 266 - 288
Abstract: We initiate a study of structural properties of the quotient algebra
${\mathcal{K}}(X)/{\mathcal{A}}(X)$ of the compact-by-approximable operators on Banach spaces 
$X$ failing the approximation property. Our main results and examples include the following: (i) there is a linear isomorphic embedding from 
$c_{0}$ into 
${\mathcal{K}}(Z)/{\mathcal{A}}(Z)$, where 
$Z$ belongs to the class of Banach spaces constructed by Willis that have the metric compact approximation property but fail the approximation property, (ii) there is a linear isomorphic embedding from a nonseparable space 
$c_{0}(\unicode[STIX]{x1D6E4})$ into 
${\mathcal{K}}(Z_{FJ})/{\mathcal{A}}(Z_{FJ})$, where 
$Z_{FJ}$ is a universal compact factorisation space arising from the work of Johnson and Figiel.
PubDate: 2021-04-01T00:00:00.000Z
DOI: 10.1017/S1446788719000211
Issue No: Vol. 110, No. 2 (2021)
- Authors: HANS-OLAV TYLLI; HENRIK WIRZENIUS
