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 Bulletin of the Australian Mathematical SocietyJournal Prestige (SJR): 0.44 Number of Followers: 1      Subscription journal ISSN (Print) 0004-9727 - ISSN (Online) 1755-1633 Published by Cambridge University Press  [372 journals]
• BAZ volume 98 Issue 2 Cover and Front matter
• PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972717001319
Issue No: Vol. 98, No. 2 (2018)

• BAZ volume 98 Issue 2 Cover and Back matter
• PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972717001320
Issue No: Vol. 98, No. 2 (2018)

• A GENERAL POSITION PROBLEM IN GRAPH THEORY
• Authors: PAUL MANUEL; SANDI KLAVŽAR
Pages: 177 - 187
Abstract: The paper introduces a graph theory variation of the general position problem: given a graph $G$ , determine a largest set $S$ of vertices of $G$ such that no three vertices of $S$ lie on a common geodesic. Such a set is a max-gp-set of $G$ and its size is the gp-number $\text{gp}(G)$ of $G$ . Upper bounds on $\text{gp}(G)$ in terms of different isometric covers are given and used to determine the gp-number of several classes of graphs. Connections between general position sets and packings are investigated and used to give lower bounds on the gp-number. It is also proved that the general position problem is NP-complete.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000473
Issue No: Vol. 98, No. 2 (2018)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$x^{2}+(2c-1)^{m}=c^{n}$ ++++++++++++ ++++++++ ++++&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=188&rft.epage=195&rft.aulast=DENG&rft.aufirst=MOU-JIE&rft.au=MOU-JIE+DENG&rft.au=JIN+GUO,+AI-JUAN+XU&rft_id=info:doi/10.1017/S0004972718000369">A NOTE ON THE DIOPHANTINE EQUATION $x^{2}+(2c-1)^{m}=c^{n}$
• Authors: MOU-JIE DENG; JIN GUO, AI-JUAN XU
Pages: 188 - 195
Abstract: Let $c\geq 2$ be a positive integer. Terai [‘A note on the Diophantine equation $x^{2}+q^{m}=c^{n}$ ’, Bull. Aust. Math. Soc.90 (2014), 20–27] conjectured that the exponential Diophantine equation $x^{2}+(2c-1)^{m}=c^{n}$ has only the positive integer solution $(x,m,n)=(c-1,1,2)$ . He proved his conjecture under various conditions on $c$ and $2c-1$ . In this paper, we prove Terai’s conjecture under a wider range of conditions on $c$ and $2c-1$ . In particular, we show that the conjecture is true if $c\equiv 3\hspace{0.6em}({\rm mod}\hspace{0.2em}4)$ and $3\leq c\leq 499$ .
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000369
Issue No: Vol. 98, No. 2 (2018)

• A SIMPLE PROOF OF CHEBOTAREV’S DENSITY THEOREM OVER FINITE FIELDS
• Authors: STEVE MEAGHER
Pages: 196 - 202
Abstract: We present a simple proof of the Chebotarev density theorem for finite morphisms of quasi-projective varieties over finite fields following an idea of Fried and Kosters for function fields. The key idea is to interpret the number of rational points with a given Frobenius conjugacy class as the number of rational points of a twisted variety, which is then bounded by the Lang–Weil estimates.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000448
Issue No: Vol. 98, No. 2 (2018)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++-ADIC+NUMBERS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=203&rft.epage=211&rft.aulast=BUGEAUD&rft.aufirst=YANN&rft.au=YANN+BUGEAUD&rft.au=GÜLCAN+KEKEÇ&rft_id=info:doi/10.1017/S0004972718000515">ON MAHLER’S CLASSIFICATION OF $p$ -ADIC NUMBERS
• Authors: YANN BUGEAUD; GÜLCAN KEKEÇ
Pages: 203 - 211
Abstract: We give transcendence measures for $p$ -adic numbers $\unicode[STIX]{x1D709}$ , having good rational (respectively, integer) approximations, that force them to be either $p$ -adic $S$ -numbers or $p$ -adic $T$ -numbers.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000515
Issue No: Vol. 98, No. 2 (2018)

• ALGEBRAIC NUMBERS WITH BOUNDED DEGREE AND WEIL HEIGHT
• Authors: ARTŪRAS DUBICKAS
Pages: 212 - 220
Abstract: For a positive integer $d$ and a nonnegative number $\unicode[STIX]{x1D709}$ , let $N(d,\unicode[STIX]{x1D709})$ be the number of $\unicode[STIX]{x1D6FC}\in \overline{\mathbb{Q}}$ of degree at most $d$ and Weil height at most $\unicode[STIX]{x1D709}$ . We prove upper and lower bounds on $N(d,\unicode[STIX]{x1D709})$ . For each fixed $\unicode[STIX]{x1D709}>0$ , these imply the asymptotic formula $\log N(d,\unicode[STIX]{x1D709})\sim \unicode[STIX]{x1D709}d^{2}$ as $d\rightarrow \infty$ , which was conjectured in a question at Mathoverflow [https://mathoverflow.net/questions/177206/].
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000497
Issue No: Vol. 98, No. 2 (2018)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$j$ ++++++++++++ ++++++++ ++++-WISE+RELATIVELY+ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$r$ ++++++++++++ ++++++++ ++++-PRIME+ALGEBRAIC+INTEGERS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=221&rft.epage=229&rft.aulast=SITTINGER&rft.aufirst=BRIAN&rft.au=BRIAN+D.+SITTINGER&rft_id=info:doi/10.1017/S0004972718000382">THE DENSITY OF $j$ -WISE RELATIVELY $r$ -PRIME ALGEBRAIC INTEGERS
• Authors: BRIAN D. SITTINGER
Pages: 221 - 229
Abstract: Let $K$ be a number field with a ring of integers ${\mathcal{O}}$ . We follow Ferraguti and Micheli [‘On the Mertens–Cèsaro theorem for number fields’, Bull. Aust. Math. Soc.93(2) (2016), 199–210] to define a density for subsets of ${\mathcal{O}}$ and use it to find the density of the set of $j$ -wise relatively $r$ -prime $m$ -tuples of algebraic integers. This provides a generalisation and analogue for several results on natural densities of integers and ideals of algebraic integers.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000382
Issue No: Vol. 98, No. 2 (2018)

• LIFTINGS OF A MONOMIAL CURVE
• Authors: MESUT ŞAHİN
Pages: 230 - 238
Abstract: We study an operation, that we call lifting, creating nonisomorphic monomial curves from a single monomial curve. Our main result says that all but finitely many liftings of a monomial curve have Cohen–Macaulay tangent cones even if the tangent cone of the original curve is not Cohen–Macaulay. This implies that the Betti sequence of the tangent cone is eventually constant under this operation. Moreover, all liftings have Cohen–Macaulay tangent cones when the original monomial curve has a Cohen–Macaulay tangent cone. In this case, all the Betti sequences are just the Betti sequence of the original curve.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000400
Issue No: Vol. 98, No. 2 (2018)

• ON BASE RADICAL OPERATORS FOR CLASSES OF FINITE ASSOCIATIVE RINGS
• Authors: R. G. MCDOUGALL; L. K. THORNTON
Pages: 239 - 250
Abstract: In this paper, class operators are used to give a complete listing of distinct base radical and semisimple classes for universal classes of finite associative rings. General relations between operators reveal that the maximum order of the semigroup formed is 46. In this setting, the homomorphically closed semisimple classes are precisely the hereditary radical classes and hence radical–semisimple classes, and the largest homomorphically closed subclass of a semisimple class is a radical–semisimple class.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000461
Issue No: Vol. 98, No. 2 (2018)

• ON VANISHING CRITERIA THAT CONTROL FINITE GROUP STRUCTURE II
• Authors: JULIAN BROUGH; QINGJUN KONG
Pages: 251 - 257
Abstract: The first author [J. Brough, ‘On vanishing criteria that control finite group structure’, J. Algebra458 (2016), 207–215] has shown that for certain arithmetical results on conjugacy class sizes it is enough to consider only the vanishing conjugacy class sizes. In this paper we further weaken the conditions to consider only vanishing elements of prime power order.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000540
Issue No: Vol. 98, No. 2 (2018)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$h$ ++++++++++++ ++++++++ ++++-POLYNOMIALS+OF+CLUSTER+SUBDIVISIONS+HAVE+ONLY+REAL+ZEROS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=258&rft.epage=264&rft.aulast=ZHANG&rft.aufirst=PHILIP&rft.au=PHILIP+B.+ZHANG&rft_id=info:doi/10.1017/S0004972718000564">THE LOCAL $h$ -POLYNOMIALS OF CLUSTER SUBDIVISIONS HAVE ONLY REAL ZEROS
• Authors: PHILIP B. ZHANG
Pages: 258 - 264
Abstract: Athanasiadis [‘A survey of subdivisions and local $h$ -vectors’, in The Mathematical Legacy of Richard P. Stanley (American Mathematical Society, Providence, RI, 2017), 39–51] asked whether the local $h$ -polynomials of type $A$ cluster subdivisions have only real zeros. We confirm this conjecture and prove that the local $h$ -polynomials for all the Cartan–Killing types have only real roots. Our proofs use multiplier sequences and Chebyshev polynomials of the second kind.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000564
Issue No: Vol. 98, No. 2 (2018)

• ON THE WEAK-HASH METRIC FOR BOUNDEDLY FINITE INTEGER-VALUED MEASURES
• Authors: MAXIME MORARIU-PATRICHI
Pages: 265 - 276
Abstract: It is known that the space of boundedly finite integer-valued measures on a complete separable metric space becomes a complete separable metric space when endowed with the weak-hash metric. It is also known that convergence under this topology can be characterised in a way that is similar to the weak convergence of totally finite measures. However, the original proofs of these two fundamental results assume that a certain term is monotonic, which is not the case as we show by a counterexample. We clarify these original proofs by addressing the parts that rely on this assumption and finding alternative arguments.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000485
Issue No: Vol. 98, No. 2 (2018)

• A REACTION–DIFFUSION–ADVECTION EQUATION WITH COMBUSTION
NONLINEARITY ON THE HALF-LINE
• Authors: FANG LI; QI LI, YUFEI LIU
Pages: 277 - 285
Abstract: We study the dynamics of a reaction–diffusion–advection equation $u_{t}=u_{xx}-au_{x}+f(u)$ on the right half-line with Robin boundary condition $u_{x}=au$ at $x=0$ , where $f(u)$ is a combustion nonlinearity. We show that, when $0 PubDate: 2018-10-01T00:00:00.000Z DOI: 10.1017/S0004972718000370 Issue No: Vol. 98, No. 2 (2018) • A NEW EXTENSION OF DARBO’S FIXED POINT THEOREM USING RELATIVELY MEIR–KEELER CONDENSING OPERATORS • Authors: MOOSA GABELEH; CALOGERO VETRO Pages: 286 - 297 Abstract: We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations. PubDate: 2018-10-01T00:00:00.000Z DOI: 10.1017/S000497271800045X Issue No: Vol. 98, No. 2 (2018) • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$b$++++++++++++ ++++++++ ++++-METRIC+SPACES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=298&rft.epage=304&rft.aulast=DUNG&rft.aufirst=NGUYEN&rft.au=NGUYEN+VAN+DUNG&rft.au=VO+THI+LE+HANG&rft_id=info:doi/10.1017/S0004972718000394">ON THE COMPLETION OF$b$-METRIC SPACES • Authors: NGUYEN VAN DUNG; VO THI LE HANG Pages: 298 - 304 Abstract: Based on the metrisation of$b$-metric spaces of Paluszyński and Stempak [‘On quasi-metric and metric spaces’, Proc. Amer. Math. Soc.137(12) (2009), 4307–4312], we prove that every$b$-metric space has a completion. Our approach resolves the limitation in using the quotient space of equivalence classes of Cauchy sequences to obtain a completion of a$b\$ -metric space.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000394
Issue No: Vol. 98, No. 2 (2018)

• WEIGHT ELEMENTS OF THE KNOT GROUPS OF SOME THREE-STRAND PRETZEL KNOTS
• Authors: MASAKAZU TERAGAITO
Pages: 305 - 318
Abstract: A knot group has weight one, so is normally generated by a single element called a weight element of the knot group. A meridian is a typical weight element, but some knot groups admit other weight elements. We show that for some infinite classes of three-strand pretzel knots and all prime knots with up to eight crossings, the knot groups admit weight elements that are not automorphic images of meridians.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000539
Issue No: Vol. 98, No. 2 (2018)

• DIFFERENTIAL FORMS ON STRATIFIED SPACES
• Authors: SERAP GÜRER; PATRICK IGLESIAS-ZEMMOUR
Pages: 319 - 330
Abstract: First, we extend the notion of stratified spaces to diffeology. Then we characterise the subspace of stratified differential forms, or zero-perverse forms in the sense of Goresky–MacPherson, which can be extended smoothly into differential forms on the whole space. For that we introduce an index which outlines the behaviour of the perverse forms on the neighbourhood of the singular strata.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000436
Issue No: Vol. 98, No. 2 (2018)

• INITIAL IMPROVEMENT OF THE HYBRID ACCELERATED GRADIENT DESCENT PROCESS
• Authors: STEFAN PANIĆ; MILENA J. PETROVIĆ, MIROSLAVA MIHAJLOV CAREVIĆ
Pages: 331 - 338
Abstract: We improve the convergence properties of the iterative scheme for solving unconstrained optimisation problems introduced in Petrovic et al. [‘Hybridization of accelerated gradient descent method’, Numer. Algorithms (2017), doi:10.1007/s11075-017-0460-4] by optimising the value of the initial step length parameter in the backtracking line search procedure. We prove the validity of the algorithm and illustrate its advantages by numerical experiments and comparisons.
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000552
Issue No: Vol. 98, No. 2 (2018)

• MATHEMATICAL ANALYSIS OF COMBUSTION WAVES IN COMPETITIVE EXOTHERMIC
REACTIONS
• Authors: ZHEJUN HUANG
Pages: 339 - 342
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000527
Issue No: Vol. 98, No. 2 (2018)

• STOCHASTIC MODELS FOR OPTICALLY TRAPPED NANOWIRES
• Authors: IGNACIO ORTEGA-PIWONKA
Pages: 343 - 344
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000199
Issue No: Vol. 98, No. 2 (2018)

• MODELLING JOINT AUTOREGRESSIVE MOVING AVERAGE PROCESSES
• Authors: ROSS S. BOWDEN
Pages: 345 - 347
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S000497271800062X
Issue No: Vol. 98, No. 2 (2018)

• EXPLORING THE ROLE OF SMALL-SCALE THERMOHALINE STRUCTURE ON MIXING AND
TRANSPORT IN THE OCEAN
• Authors: YUEHUA LI
Pages: 348 - 349
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000412
Issue No: Vol. 98, No. 2 (2018)

• A+PRIORI+IDENTIFIABILITY+OF+MODELS+OF+FLOW-CELL+OPTICAL+BIOSENSOR+EXPERIMENTS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=350&rft.epage=352&rft.aulast=WHYTE&rft.aufirst=JASON&rft.au=JASON+M.+WHYTE&rft_id=info:doi/10.1017/S0004972718000357">GLOBAL A PRIORI IDENTIFIABILITY OF MODELS OF FLOW-CELL OPTICAL BIOSENSOR
EXPERIMENTS
• Authors: JASON M. WHYTE
Pages: 350 - 352
PubDate: 2018-10-01T00:00:00.000Z
DOI: 10.1017/S0004972718000357
Issue No: Vol. 98, No. 2 (2018)

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