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Publisher: Cambridge University Press   (Total: 373 journals)

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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  [373 journals]
• BAZ volume 99 Issue 2 Cover and Back matter
• PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001508
Issue No: Vol. 99, No. 2 (2019)

• BAZ volume 99 Issue 2 Cover and Front matter
• PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001491
Issue No: Vol. 99, No. 2 (2019)

• QUADRATIC NONRESIDUES AND NONPRIMITIVE ROOTS SATISFYING A COPRIMALITY
CONDITION
Pages: 177 - 183
Abstract: Let $q\geq 1$ be any integer and let $\unicode[STIX]{x1D716}\in [\frac{1}{11},\frac{1}{2})$ be a given real number. We prove that for all primes $p$ satisfying $$\begin{eqnarray}p\equiv 1\!\!\!\!\hspace{0.6em}({\rm mod}\hspace{0.2em}q),\quad \log \log p>\frac{2\log 6.83}{1-2\unicode[STIX]{x1D716}}\quad \text{and}\quad \frac{\unicode[STIX]{x1D719}(p-1)}{p-1}\leq \frac{1}{2}-\unicode[STIX]{x1D716},\end{eqnarray}$$ there exists a quadratic nonresidue $g$ which is not a primitive root modulo $p$ such that $\text{gcd}(g,(p-1)/q)=1$ .
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001065
Issue No: Vol. 99, No. 2 (2019)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$(k,l)$ ++++++++++++ ++++++++ ++++-SUM-FREE+SETS+IN+CYCLIC GROUPS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2019&rft.volume=99&rft.spage=184&rft.epage=194&rft.aulast=BAJNOK&rft.aufirst=BÉLA&rft.au=BÉLA+BAJNOK&rft.au=RYAN+MATZKE&rft_id=info:doi/10.1017/S000497271800117X">THE MAXIMUM SIZE OF $(k,l)$ -SUM-FREE SETS IN CYCLIC GROUPS
• Authors: BÉLA BAJNOK; RYAN MATZKE
Pages: 184 - 194
Abstract: A subset $A$ of a finite abelian group $G$ is called $(k,l)$ -sum-free if the sum of $k$ (not necessarily distinct) elements of $A$ never equals the sum of $l$ (not necessarily distinct) elements of  $A$ . We find an explicit formula for the maximum size of a $(k,l)$ -sum-free subset in $G$ for all $k$ and $l$ in the case when
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S000497271800117X
Issue No: Vol. 99, No. 2 (2019)

• ON MAXIMALLY FROBENIUS DESTABILISED VECTOR BUNDLES
• Authors: LINGGUANG LI
Pages: 195 - 202
Abstract: Let $X$ be a smooth projective curve of genus $g\geq 2$ over an algebraically closed field $k$ of characteristic $p>0$ . We show that for any integers $r$ and $d$ with $0 PubDate: 2019-04-01T00:00:00.000Z DOI: 10.1017/S0004972718001314 Issue No: Vol. 99, No. 2 (2019) • ON THE SECOND-LARGEST SYLOW SUBGROUP OF A FINITE SIMPLE GROUP OF LIE TYPE • Authors: S. P. GLASBY; ALICE C. NIEMEYER, TOMASZ POPIEL Pages: 203 - 211 Abstract: Let$T$be a finite simple group of Lie type in characteristic$p$, and let$S$be a Sylow subgroup of$T$with maximal order. It is well known that$S$is a Sylow$p$-subgroup except for an explicit list of exceptions and that$S$is always ‘large’ in the sense that$|T|^{1/3}
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718000928
Issue No: Vol. 99, No. 2 (2019)

• GROUPS SATISFYING THE DOUBLE CHAIN CONDITION ON ABELIAN SUBGROUPS
• Authors: MATTIA BRESCIA; ALESSIO RUSSO
Pages: 212 - 218
Abstract: If $\unicode[STIX]{x1D703}$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\unicode[STIX]{x1D703}$ -subgroups if it admits no infinite double sequences \begin{eqnarray}\cdots
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001004
Issue No: Vol. 99, No. 2 (2019)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++-HARMONIC+FUNCTIONS+ON+THE+HEISENBERG+GROUP&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2019&rft.volume=99&rft.spage=219&rft.epage=230&rft.aulast=LIU&rft.aufirst=HAIRONG&rft.au=HAIRONG+LIU&rft.au=FANG+LIU,+HUI+WU&rft_id=info:doi/10.1017/S0004972718001016">THE UNIQUE CONTINUATION PROPERTY OF $p$ -HARMONIC FUNCTIONS ON THE
HEISENBERG GROUP
• Authors: HAIRONG LIU; FANG LIU, HUI WU
Pages: 219 - 230
Abstract: We introduce an Almgren frequency function of the sub- $p$ -Laplace equation on the Heisenberg group to establish a doubling estimate under the assumption that the frequency function is locally bounded. From this, we obtain some partial results on unique continuation for the sub- $p$ -Laplace equation.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001016
Issue No: Vol. 99, No. 2 (2019)

• AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRÖDINGER
EQUATIONS WITH SUPER-LINEAR NONLINEARITIES
• Authors: SITONG CHEN; ZU GAO
Pages: 231 - 241
Abstract: By using variational and some new analytic techniques, we prove the existence of ground state solutions for the quasilinear Schrödinger equation with variable potentials and super-linear nonlinearities. Moreover, we establish a minimax characterisation of the ground state energy. Our result improves and extends the existing results in the literature.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001235
Issue No: Vol. 99, No. 2 (2019)

• EXISTENCE AND BLOW-UP OF SOLUTIONS TO A PARABOLIC EQUATION WITH
NONSTANDARD GROWTH CONDITIONS
• Authors: YANG LIU
Pages: 242 - 249
Abstract: We study the initial boundary value problem for a fourth-order parabolic equation with nonstandard growth conditions. We establish the local existence of weak solutions and derive the finite time blow-up of solutions with nonpositive initial energy.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001181
Issue No: Vol. 99, No. 2 (2019)

• QUANTITATIVE PROPERTIES OF MEROMORPHIC SOLUTIONS TO SOME
DIFFERENTIAL-DIFFERENCE EQUATIONS
• Authors: QIONG WANG; QI HAN, PEICHU HU
Pages: 250 - 261
Abstract: We investigate several quantitative properties of entire and meromorphic solutions to some differential-difference equations and generalised delay differential-difference equations. Our results are sharp in a certain sense as illustrated by several examples.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001247
Issue No: Vol. 99, No. 2 (2019)

• GEOMETRIC AND FIXED POINT PROPERTIES IN PRODUCTS OF NORMED SPACES
• Authors: M. VEENA SANGEETHA
Pages: 262 - 273
Abstract: Given two (real) normed (linear) spaces $X$ and $Y$ , let $X\otimes _{1}Y=(X\otimes Y,\Vert \cdot \Vert )$ , where $\Vert (x,y)\Vert =\Vert x\Vert +\Vert y\Vert$ . It is known that $X\otimes _{1}Y$ is $2$ -UR if and only if both $X$ and $Y$ are UR (where we use UR as an abbreviation for uniformly rotund). We prove that if $X$ is $m$ -dimensional and $Y$ is
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001144
Issue No: Vol. 99, No. 2 (2019)

• ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES
Pages: 274 - 283
Abstract: We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001363
Issue No: Vol. 99, No. 2 (2019)

• AMENABLE SEMIGROUPS OF NONLINEAR OPERATORS IN UNIFORMLY CONVEX BANACH
SPACES
Pages: 284 - 292
Abstract: In 1965, Browder proved the existence of a common fixed point for commuting families of nonexpansive mappings acting on nonempty bounded closed convex subsets of uniformly convex Banach spaces. The purpose of this paper is to extend this result to left amenable semigroups of nonexpansive mappings.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001077
Issue No: Vol. 99, No. 2 (2019)

• POSITIVE CENTRE SETS OF CONVEX CURVES AND A BONNESEN TYPE INEQUALITY
• Authors: YUNLONG YANG
Pages: 293 - 301
Abstract: We consider the positive centre sets of regular $n$ -gons, rectangles and half discs, and conjecture a Bonnesen type inequality concerning positive centre sets which is stronger than the classical isoperimetric inequality.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001284
Issue No: Vol. 99, No. 2 (2019)

• ON GENERALISED METRISABILITY AND CARDINAL INVARIANTS IN QUASITOPOLOGICAL
GROUPS
• Authors: ZHONGBAO TANG; SHOU LIN
Pages: 302 - 310
Abstract: We consider generalised metrisability and cardinal invariants in quasitopological groups. We construct examples to show that some equalities of cardinal invariants in topological groups cannot be extended to quasitopological groups.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S000497271800103X
Issue No: Vol. 99, No. 2 (2019)

• DIFFERENTIAL FORMS ON STRATIFIED SPACES II
• Authors: SERAP GÜRER; PATRICK IGLESIAS-ZEMMOUR
Pages: 311 - 318
Abstract: We prove that, for conelike stratified diffeological spaces, a zero-perverse form is the restriction of a global differential form if and only if its index is equal to one for every stratum.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S000497271800134X
Issue No: Vol. 99, No. 2 (2019)

• AN EXACT ENTANGLING GATE USING FIBONACCI ANYONS
• Authors: STEPHEN BIGELOW; CLAIRE LEVAILLANT
Pages: 319 - 326
Abstract: Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However, there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known ‘leakage-free’ entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001028
Issue No: Vol. 99, No. 2 (2019)

• THE DOMINATION GAME ON SPLIT GRAPHS
• Authors: TIJO JAMES; SANDI KLAVŽAR, AMBAT VIJAYAKUMAR
Pages: 327 - 337
Abstract: We investigate the domination game and the game domination number $\unicode[STIX]{x1D6FE}_{g}$ in the class of split graphs. We prove that $\unicode[STIX]{x1D6FE}_{g}(G)\leq n/2$ for any isolate-free $n$ -vertex split graph  $G$ , thus strengthening the conjectured $3n/5$ general bound and supporting Rall’s $\lceil n/2\rceil$ -conjecture. We also characterise split graphs of even order with $\unicode[STIX]{x1D6FE}_{g}(G)=n/2$ .
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001053
Issue No: Vol. 99, No. 2 (2019)

• ALGEBRAIC MODELS OF LARGE SCALE GENOME REARRANGEMENT EVENTS
• Authors: SANGEETA BHATIA
Pages: 338 - 339
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001417
Issue No: Vol. 99, No. 2 (2019)

• METRICS AND SPECIAL KÄHLER GEOMETRY ON THE MODULI SPACES OF HIGGS
BUNDLES AND HITCHIN SYSTEMS
• Authors: ZHENXI HUANG
Pages: 340 - 341
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001405
Issue No: Vol. 99, No. 2 (2019)

• POSITIVE SCALAR CURVATURE AND CALLIAS-TYPE INDEX THEOREMS FOR PROPER
ACTIONS
• Authors: HAO GUO
Pages: 342 - 343
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001338
Issue No: Vol. 99, No. 2 (2019)

• STOCHASTIC NAVIER–STOKES EQUATIONS ON 2D ROTATING SPHERES WITH
STABLE LÉVY NOISE
• Authors: LEANNE DONG
Pages: 344 - 345
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001351
Issue No: Vol. 99, No. 2 (2019)

• PARAMETER ESTIMATION FOR STAGE-DURATION MODELS
• Authors: HOA THI THU PHAM
Pages: 346 - 348
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001326
Issue No: Vol. 99, No. 2 (2019)

• JOINT MODELS FOR NONLINEAR LONGITUDINAL AND TIME-TO-EVENT DATA USING
PENALISED SPLINES
• Authors: HUONG THI THU PHAM
Pages: 349 - 352
PubDate: 2019-04-01T00:00:00.000Z
DOI: 10.1017/S0004972718001399
Issue No: Vol. 99, No. 2 (2019)

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