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 Bulletin of the Australian Mathematical SocietyJournal Prestige (SJR): 0.44 Number of Followers: 2      Subscription journal ISSN (Print) 0004-9727 - ISSN (Online) 1755-1633 Published by Cambridge University Press  [387 journals]
• BAZ volume 101 Issue 1 Cover and Front matter
• PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001461
Issue No: Vol. 101, No. 1 (2020)

• BAZ volume 101 Issue 1 Cover and Back matter
• PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001473
Issue No: Vol. 101, No. 1 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$ax^{2}+by^{2}+cz^{2}$ ++++++++++++ ++++++++ +++++AND+ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$ax^{2}+by^{2}+cz^{2}+dw^{2}$ ++++++++++++ ++++++++ ++++&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=1&rft.epage=12&rft.aulast=DOYLE&rft.aufirst=GREG&rft.au=GREG+DOYLE&rft.au=KENNETH+S.+WILLIAMS&rft_id=info:doi/10.1017/S0004972719001023">PRIME-UNIVERSAL QUADRATIC FORMS $ax^{2}+by^{2}+cz^{2}$ AND
$ax^{2}+by^{2}+cz^{2}+dw^{2}$
• Authors: GREG DOYLE; KENNETH S. WILLIAMS
Pages: 1 - 12
Abstract: A positive-definite diagonal quadratic form $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}\;(a_{1},\ldots ,a_{n}\in \mathbb{N})$ is said to be prime-universal if it is not universal and for every prime $p$ there are integers $x_{1},\ldots ,x_{n}$ such that $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}=p$ . We determine all possible prime-universal ternary quadratic forms $ax^{2}+by^{2}+cz^{2}$ and all possible prime-universal quaternary quadratic forms $ax^{2}+by^{2}+cz^{2}+dw^{2}$ . The prime-universal ternary forms are completely determined. The prime-universal quaternary forms are determined subject to the validity of two conjectures. We make no use of a result of Bhargava concerning quadratic forms representing primes which is stated but not proved in the literature.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001023
Issue No: Vol. 101, No. 1 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$L$ ++++++++++++ ++++++++ ++++-VALUE+OF+THE+CONGRUENT+NUMBER+ELLIPTIC+CURVES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=13&rft.epage=22&rft.aulast=SAMART&rft.aufirst=DETCHAT&rft.au=DETCHAT+SAMART&rft_id=info:doi/10.1017/S000497271900056X">ON A NONCRITICAL SYMMETRIC SQUARE $L$ -VALUE OF THE CONGRUENT NUMBER
ELLIPTIC CURVES
• Authors: DETCHAT SAMART
Pages: 13 - 22
Abstract: The congruent number elliptic curves are defined by $E_{d}:y^{2}=x^{3}-d^{2}x$ , where $d\in \mathbb{N}$ . We give a simple proof of a formula for $L(\operatorname{Sym}^{2}(E_{d}),3)$ in terms of the determinant of the elliptic trilogarithm evaluated at some degree zero divisors supported on the torsion points on $E_{d}(\overline{\mathbb{Q}})$ .
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S000497271900056X
Issue No: Vol. 101, No. 1 (2020)

• ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES
AND FINITE MULTIPLE ZETA VALUES
• Authors: HIDEKI MURAHARA; TAKUYA MURAKAMI
Pages: 23 - 34
Abstract: We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000790
Issue No: Vol. 101, No. 1 (2020)

• PARTITIONS WITH AN ARBITRARY NUMBER OF SPECIFIED DISTANCES
• Authors: BERNARD L. S. LIN
Pages: 35 - 39
Abstract: For positive integers $t_{1},\ldots ,t_{k}$ , let $\tilde{p}(n,t_{1},t_{2},\ldots ,t_{k})$ (respectively $p(n,t_{1},t_{2},\ldots ,t_{k})$ ) be the number of partitions of $n$ such that, if $m$ is the smallest part, then each of $m+t_{1},m+t_{1}+t_{2},\ldots ,m+t_{1}+t_{2}+\cdots +t_{k-1}$ appears as a part and the largest part is at most (respectively equal to) $m+t_{1}+t_{2}+\cdots +t_{k}$ . Andrews et al. [‘Partitions with fixed differences between largest and smallest parts’, Proc. Amer. Math. Soc.143 (2015), 4283–4289] found an explicit formula for the generating function of $p(n,t_{1},t_{2},\ldots ,t_{k})$ . We establish a $q$ -series identity from which the formulae for the generating functions of $\tilde{p}(n,t_{1},t_{2},\ldots ,t_{k})$ and
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000650
Issue No: Vol. 101, No. 1 (2020)

• PERMUTATION POLYNOMIALS OF DEGREE 8 OVER FINITE FIELDS OF ODD
CHARACTERISTIC
• Authors: XIANG FAN
Pages: 40 - 55
Abstract: We give an algorithmic generalisation of Dickson’s method of classifying permutation polynomials (PPs) of a given degree $d$ over finite fields. Dickson’s idea is to formulate from Hermite’s criterion several polynomial equations satisfied by the coefficients of an arbitrary PP of degree $d$ . Previous classifications of PPs of degree at most 6 were essentially deduced from manual analysis of these polynomial equations, but this approach is no longer viable for $d>6$ . Our idea is to calculate some radicals of ideals generated by the polynomials, implemented by a computer algebra system. Our algorithms running in SageMath 8.6 on a personal computer work very fast to determine all PPs of degree 8 over an arbitrary finite field of odd order $q>8$ . Such PPs exist if and only if $q\in \{11,13,19,23,27,29,31\}$ and are explicitly listed in normalised form.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000674
Issue No: Vol. 101, No. 1 (2020)

• A NEW PROOF OF THE CARLITZ–LUTZ THEOREM
• Authors: RACHID BOUMAHDI; OMAR KIHEL, JESSE LARONE, MAKHLOUF YADJEL
Pages: 56 - 60
Abstract: A polynomial $f$ over a finite field $\mathbb{F}_{q}$ can be classified as a permutation polynomial by the Hermite–Dickson criterion, which consists of conditions on the powers $f^{e}$ for each $e$ from $1$ to $q-2$ , as well as the existence of a unique solution to $f(x)=0$ in $\mathbb{F}_{q}$ . Carlitz and Lutz gave a variant of the criterion. In this paper, we provide an alternate proof to the theorem of Carlitz and Lutz.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000728
Issue No: Vol. 101, No. 1 (2020)

• ALGEBRAIC SURFACES WITH INFINITELY MANY TWISTOR LINES
• Authors: A. ALTAVILLA; E. BALLICO
Pages: 61 - 70
Abstract: We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalisation map of a surface, we give constructive existence results for even degrees.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000534
Issue No: Vol. 101, No. 1 (2020)

• THE FACTORIAL CONJECTURE AND IMAGES OF LOCALLY NILPOTENT DERIVATIONS
• Authors: DAYAN LIU; XIAOSONG SUN
Pages: 71 - 79
Abstract: The factorial conjecture was proposed by van den Essen et al. [‘On the image conjecture’, J. Algebra 340(1) (2011), 211–224] to study the image conjecture, which arose from the Jacobian conjecture. We show that the factorial conjecture holds for all homogeneous polynomials in two variables. We also give a variation of the result and use it to show that the image of any linear locally nilpotent derivation of $\mathbb{C}[x,y,z]$ is a Mathieu–Zhao subspace.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000546
Issue No: Vol. 101, No. 1 (2020)

• ON A PROBLEM OF PRAEGER AND SCHNEIDER
• Authors: EGLE BETTIO; ENRICO JABARA
Pages: 80 - 87
Abstract: This note provides an affirmative answer to Problem 2.6 of Praeger and Schneider [‘Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type’, Israel J. Math. 228(2) (2018), 1001–1023]. We will build groups $G$ (abelian, nonabelian and simple) for which there are two automorphisms $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD}$ of $G$ such that the map $$\begin{eqnarray}T=T_{\unicode[STIX]{x1D6FC}}\times T_{\unicode[STIX]{x1D6FD}}:G\longrightarrow G\times G,\quad g\mapsto (g^{-1}g^{\unicode[STIX]{x1D6FC}},g^{-1}g^{\,\unicode[STIX]{x1D6FD}})\end{eqnarray}$$ is surjective.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000649
Issue No: Vol. 101, No. 1 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$2\times+2$ ++++++++++++ ++++++++ +++++MATRICES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=88&rft.epage=104&rft.aulast=ZHANG&rft.aufirst=WEN&rft.au=WEN+TING+ZHANG&rft.au=YAN+FENG+LUO&rft_id=info:doi/10.1017/S0004972719001035">THE FINITE BASIS PROBLEM FOR INVOLUTION SEMIGROUPS OF TRIANGULAR $2\times 2$ MATRICES
• Authors: WEN TING ZHANG; YAN FENG LUO
Pages: 88 - 104
Abstract: Let $T_{n}(\mathbb{F})$ be the semigroup of all upper triangular $n\times n$ matrices over a field $\mathbb{F}$ . Let $UT_{n}(\mathbb{F})$ and $UT_{n}^{\pm 1}(\mathbb{F})$ be subsemigroups of $T_{n}(\mathbb{F})$ , respectively, having $0$ s and/or $1$ s on the main diagonal and $0$ s and/or $\pm 1$ s on the main diagonal. We give some sufficient conditions under which an involution semigroup is nonfinitely based. As an application, we show that $UT_{2}(\mathbb{F}),UT_{2}^{\pm 1}(\mathbb{F})$ and
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001035
Issue No: Vol. 101, No. 1 (2020)

• HOMOLOGY AND MATUI’S HK CONJECTURE FOR GROUPOIDS ON ONE-DIMENSIONAL
SOLENOIDS
• Authors: INHYEOP YI
Pages: 105 - 117
Abstract: We show that Matui’s HK conjecture holds for groupoids of unstable equivalence relations and their corresponding $C^{\ast }$ -algebras on one-dimensional solenoids.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000522
Issue No: Vol. 101, No. 1 (2020)

• WEAKENING OF THE HARDY PROPERTY FOR MEANS
• Authors: PAWEŁ PASTECZKA
Pages: 118 - 129
Abstract: The aim of this paper is to find a broad family of means defined on a subinterval of $I\subset [0,+\infty )$ such that \begin{eqnarray}\mathop{\sum }_{n=1}^{\infty }\mathscr{M}(a_{1},\ldots ,a_{n})
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000686
Issue No: Vol. 101, No. 1 (2020)

• ON SOME SUBCLASSES OF HARMONIC MAPPINGS
• Authors: NIRUPAM GHOSH; VASUDEVARAO ALLU
Pages: 130 - 140
Abstract: Let ${\mathcal{P}}_{{\mathcal{H}}}^{0}(M)$ denote the class of normalised harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ satisfying $\text{Re}\,(zh^{\prime \prime }(z))>-M+|zg^{\prime \prime }(z)|$ , where $h^{\prime }(0)-1=0=g^{\prime }(0)$ and $M>0$ . Let ${\mathcal{B}}_{{\mathcal{H}}}^{0}(M)$ denote the class of sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ satisfying $|zh^{\prime \prime }(z)|\leq M-|zg^{\prime \prime }(z)|$ , where $M>0$ . We discuss the coefficient bound problem, the growth theorem for fu...
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000698
Issue No: Vol. 101, No. 1 (2020)

• NEW GLOBAL LOGARITHMIC STABILITY RESULTS ON THE CAUCHY PROBLEM FOR
ELLIPTIC EQUATIONS
Pages: 141 - 145
Abstract: We prove the global logarithmic stability of the Cauchy problem for $H^{2}$ -solutions of an anisotropic elliptic equation in a Lipschitz domain. The result is based on existing techniques used to establish stability estimates for the Cauchy problem combined with related tools used to study an inverse medium problem.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000789
Issue No: Vol. 101, No. 1 (2020)

• LARGE DEVIATIONS FOR THE LONGEST GAP IN POISSON PROCESSES
• Authors: JOSEPH OKELLO OMWONYLEE
Pages: 146 - 156
Abstract: The longest gap $L(t)$ up to time $t$ in a homogeneous Poisson process is the maximal time subinterval between epochs of arrival times up to time $t$ ; it has applications in the theory of reliability. We study the Laplace transform asymptotics for $L(t)$ as $t\rightarrow \infty$ and derive two natural and different large-deviation principles for $L(t)$ with two distinct rate functions and speeds.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000972
Issue No: Vol. 101, No. 1 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$q$ ++++++++++++ ++++++++ ++++-ARY+LINEAR+CODES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2020&rft.volume=101&rft.spage=157&rft.epage=162&rft.aulast=WEI&rft.aufirst=YILUN&rft.au=YILUN+WEI&rft.au=BO+WU,+QIJIN+WANG&rft_id=info:doi/10.1017/S0004972719000637">ON THE GENERALISATION OF SIDEL’NIKOV’S THEOREM TO $q$ -ARY LINEAR
CODES
• Authors: YILUN WEI; BO WU, QIJIN WANG
Pages: 157 - 162
Abstract: We generalise Sidel’nikov’s theorem from binary codes to $q$ -ary codes for $q>2$ . Denoting by $A(z)$ the cumulative distribution function attached to the weight distribution of the code and by $\unicode[STIX]{x1D6F7}(z)$ the standard normal distribution function, we show that $|A(z)-\unicode[STIX]{x1D6F7}(z)|$ is bounded above by a term which tends to $0$ when the code length tends to infinity.
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719000637
Issue No: Vol. 101, No. 1 (2020)

• NUMERICAL INVESTIGATION AND APPLICATION OF FRACTIONAL DYNAMICAL SYSTEMS
• Authors: LIBO FENG
Pages: 163 - 165
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S000497271900114X
Issue No: Vol. 101, No. 1 (2020)

• COPULA-BASED STATISTICAL MODELLING OF SYNOPTIC-SCALE CLIMATE INDICES FOR
QUANTIFYING AND MANAGING AGRICULTURAL RISKS IN AUSTRALIA
• Authors: THONG NGUYEN-HUY
Pages: 166 - 169
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001217
Issue No: Vol. 101, No. 1 (2020)

• DEGREE BOUNDED GEOMETRIC SPANNING TREES WITH A BOTTLENECK OBJECTIVE
FUNCTION
• Authors: PATRICK JOHN ANDERSEN
Pages: 170 - 171
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001126
Issue No: Vol. 101, No. 1 (2020)

• CANONICAL DUAL FINITE ELEMENT METHOD FOR SOLVING NONCONVEX MECHANICS AND
TOPOLOGY OPTIMISATION PROBLEMS
• Authors: ELAF J. ALI
Pages: 172 - 173
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001205
Issue No: Vol. 101, No. 1 (2020)

• MECHANISTIC AND STATISTICAL MODELS OF SKIN DISEASE TRANSMISSION
• Authors: MICHAEL J. LYDEAMORE
Pages: 174 - 176
PubDate: 2020-02-01T00:00:00.000Z
DOI: 10.1017/S0004972719001072
Issue No: Vol. 101, No. 1 (2020)

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