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Publisher: Cambridge University Press   (Total: 371 journals)

 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  [371 journals]
• BAZ volume 98 Issue 1 Cover and Front matter
• PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972717001290
Issue No: Vol. 98, No. 1 (2018)

• BAZ volume 98 Issue 1 Cover and Back matter
• PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972717001307
Issue No: Vol. 98, No. 1 (2018)

• RESOLVABLE MENDELSOHN DESIGNS AND FINITE FROBENIUS GROUPS
• Authors: D. F. HSU; SANMING ZHOU
Pages: 1 - 13
Abstract: We prove the existence and give constructions of a $(p(k)-1)$ -fold perfect resolvable $(v,k,1)$ -Mendelsohn design for any integers $v>k\geq 2$ with $v\equiv 1\hspace{0.2em}{\rm mod}\hspace{0.2em}\,k$ such that there exists a finite Frobenius group whose kernel $K$ has order $v$ and whose complement contains an element $\unicode[STIX]{x1D719}$ of order $k$ , where $p(k)$ is the least prime factor of $k$ . Such a design admits $K\rtimes \langle \unicode[STIX]{x1D719}\rangle$ as a group of automorphisms and is per...
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000333
Issue No: Vol. 98, No. 1 (2018)

• ON THE TOTAL DISTANCE AND DIAMETER OF GRAPHS
• Authors: HONGBO HUA
Pages: 14 - 17
Abstract: The total distance (or Wiener index) of a connected graph $G$ is the sum of all distances between unordered pairs of vertices of $G$ . DeLaViña and Waller [‘Spanning trees with many leaves and average distance’, Electron. J. Combin. 15(1) (2008), R33, 14 pp.] conjectured in 2008 that if $G$ has diameter $D>2$ and order $2D+1$ , then the total distance of $G$ is at most the total distance of the cycle of the same order. In this note, we prove that this conjecture is true for 2-connected graphs.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000163
Issue No: Vol. 98, No. 1 (2018)

• THE COMPLEXITY OF THOMASON’S ALGORITHM FOR FINDING A SECOND
HAMILTONIAN CYCLE
• Authors: LIANG ZHONG
Pages: 18 - 26
Abstract: By Smith’s theorem, if a cubic graph has a Hamiltonian cycle, then it has a second Hamiltonian cycle. Thomason [‘Hamilton cycles and uniquely edge-colourable graphs’, Ann. Discrete Math. 3 (1978), 259–268] gave a simple algorithm to find the second cycle. Thomassen [private communication] observed that if there exists a polynomially bounded algorithm for finding a second Hamiltonian cycle in a cubic cyclically 4-edge connected graph $G$ , then there exists a polynomially bounded algorithm for finding a second Hamiltonian cycle in any cubic graph $G$ . In this paper we present a class of cyclically 4-edge connected cubic bipartite graphs $G_{i}$ with $16(i+1)$ vertices such that Thomason’s algorithm takes $12(2^{i}-1)+3$ steps to find a second Hamiltonian cycle in $G_{i}$ .
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000242
Issue No: Vol. 98, No. 1 (2018)

• ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++ +++++++++++++++-ADIC+GAMMA FUNCTIONS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=27&rft.epage=37&rft.aulast=LIU&rft.aufirst=JI-CAI&rft.au=JI-CAI+LIU&rft_id=info:doi/10.1017/S0004972718000278">SUPERCONGRUENCES INVOLVING $p$ -ADIC GAMMA FUNCTIONS
• Authors: JI-CAI LIU
Pages: 27 - 37
Abstract: We establish some supercongruences for the truncated $_{2}F_{1}$ and $_{3}F_{2}$ hypergeometric series involving the $p$ -adic gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated $_{3}F_{2}$ hypergeometric series. Related supercongruences modulo $p^{3}$ are proposed as conjectures.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000278
Issue No: Vol. 98, No. 1 (2018)

• COMMON SLOTS OF BILINEAR AND QUADRATIC PFISTER FORMS
• Authors: ADAM CHAPMAN
Pages: 38 - 47
Abstract: We show that over any field $F$ of characteristic 2 and 2-rank $n$ , there exist $2^{n}$ bilinear $n$ -fold Pfister forms that have no slot in common. This answers a question of Becher [‘Triple linkage’, Ann. $K$ -Theory, to appear] in the negative. We provide an analogous result also for quadratic Pfister forms.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000229
Issue No: Vol. 98, No. 1 (2018)

• THETA BLOCK FOURIER EXPANSIONS, BORCHERDS PRODUCTS AND A SEQUENCE OF
NEWMAN AND SHANKS
• Authors: CRIS POOR; JERRY SHURMAN, DAVID S. YUEN
Pages: 48 - 59
Abstract: The ‘Borcherds products everywhere’ construction [Gritsenko et al., ‘Borcherds products everywhere’, J. Number Theory 148 (2015), 164–195] creates paramodular Borcherds products from certain theta blocks. We prove that the $q$ -order of every such Borcherds product lies in a sequence  $\{C_{\unicode[STIX]{x1D708}}\}$ , depending only on the $q$ -order  $\unicode[STIX]{x1D708}$ of the theta block. Similarly, the $q$ -order of the leading Fourier–Jacobi coefficient of every such Borcherds product lies in a sequence  $\{A_{\unicode[STIX]{x1D708}}\}$ , and this is the sequence  $\{a_{n}\}$ from work of Newman and Shanks in connection with a family of series for  $\unicode[STIX]{x1D70B}$ . Our proofs use a combinatorial formula giving the Fourier expansion of any theta block in terms of its germ.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S000497271800031X
Issue No: Vol. 98, No. 1 (2018)

• A NOTE ON A COMPLETE SOLUTION OF A PROBLEM POSED BY K. MAHLER
• Authors: DIEGO MARQUES; CARLOS GUSTAVO MOREIRA
Pages: 60 - 63
Abstract: Let $\unicode[STIX]{x1D70C}\in (0,\infty ]$ be a real number. In this short note, we extend a recent result of Marques and Ramirez [‘On exceptional sets: the solution of a problem posed by K. Mahler’, Bull. Aust. Math. Soc. 94 (2016), 15–19] by proving that any subset of $\overline{\mathbb{Q}}\cap B(0,\unicode[STIX]{x1D70C})$ , which is closed under complex conjugation and contains $0$ , is the exceptional set of uncountably many analytic transcendental functions with rational coefficients and radius of convergence $\unicode[STIX]{x1D70C}$ . This solves the question posed by K. Mahler completely.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000187
Issue No: Vol. 98, No. 1 (2018)

• BOUNDS FOR TRIPLE EXPONENTIAL SUMS WITH MIXED EXPONENTIAL AND LINEAR
TERMS
• Authors: KAM HUNG YAU
Pages: 64 - 69
Abstract: We establish bounds for triple exponential sums with mixed exponential and linear terms. The method we use is by Shparlinski [‘Bilinear forms with Kloosterman and Gauss sums’, Preprint, 2016, arXiv:1608.06160] together with a bound for the additive energy from Roche-Newton et al. [‘New sum-product type estimates over finite fields’, Adv. Math. 293 (2016), 589–605].
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000205
Issue No: Vol. 98, No. 1 (2018)

• MAHLER MEASURE OF ‘ALMOST’ RECIPROCAL POLYNOMIALS
• Authors: J. C. SAUNDERS
Pages: 70 - 76
Abstract: We give a lower bound of the Mahler measure on a set of polynomials that are ‘almost’ reciprocal. Here ‘almost’ reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern may break down for the innermost coefficients.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000217
Issue No: Vol. 98, No. 1 (2018)

• ON THE DERIVATION LIE ALGEBRAS OF FEWNOMIAL SINGULARITIES
• Authors: NAVEED HUSSAIN; STEPHEN S.-T. YAU, HUAIQING ZUO
Pages: 77 - 88
Abstract: Let $V$ be a hypersurface with an isolated singularity at the origin defined by the holomorphic function $f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)$ . The Yau algebra, $L(V)$ , is the Lie algebra of derivations of the moduli algebra of $V$ . It is a finite-dimensional solvable algebra and its dimension $\unicode[STIX]{x1D706}(V)$ is the Yau number. Fewnomial singularities are those which can be defined by an $n$ -nomial in $n$ indeterminates. Yau and Zuo [‘A sharp upper estimate conjecture for the Yau number of weighted homogeneous isolated hypersurface singularity’, Pure Appl. Math. Q. 12(1) (2016), 165–181] conjectured a bound for the Yau number and proved that this conjecture holds for binomial isolated hypersurface singularities. In this paper, we verify this conjecture for weighted homogeneous fewnomial surface singularities.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000266
Issue No: Vol. 98, No. 1 (2018)

• CLASSIFICATION OF CUBIC HOMOGENEOUS POLYNOMIAL MAPS WITH JACOBIAN MATRICES
OF RANK TWO
• Authors: MICHIEL DE BONDT; XIAOSONG SUN
Pages: 89 - 101
Abstract: Let $K$ be any field with $\text{char}\,K\neq 2,3$ . We classify all cubic homogeneous polynomial maps $H$ over $K$ whose Jacobian matrix, ${\mathcal{J}}H$ , has $\text{rk}\,{\mathcal{J}}H\leq 2$ . In particular, we show that, for such an $H$ , if $F=x+H$ is a Keller map, then $F$ is invertible and furthermore $F$ is tame if the dimension $n\neq 4$ .
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000345
Issue No: Vol. 98, No. 1 (2018)

• TRANSFORMATIONS ON DENSITY OPERATORS PRESERVING GENERALISED ENTROPY OF A
CONVEX COMBINATION
• Authors: MARCELL GAÁL; GERGŐ NAGY
Pages: 102 - 108
Abstract: We aim to characterise those transformations on the set of density operators (which are the mathematical representatives of the states in quantum information theory) that preserve a so-called generalised entropy of one fixed convex combination of operators. The characterisation strengthens a recent result of Karder and Petek where the preservation of the same quantity was assumed for all convex combinations.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000254
Issue No: Vol. 98, No. 1 (2018)

• A NOTE ON NORMAL COMPLEMENTS FOR FINITE GROUPS
• Authors: NING SU; ADOLFO BALLESTER-BOLINCHES, HANGYANG MENG
Pages: 109 - 112
Abstract: Assume that $G$ is a finite group and $H$ is a 2-nilpotent Sylow tower Hall subgroup of $G$ such that if $x$ and $y$ are $G$ -conjugate elements of $H\cap G^{\prime }$ of prime order or order 4, then $x$ and $y$ are $H$ -conjugate. We prove that there exists a normal subgroup $N$ of
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000151
Issue No: Vol. 98, No. 1 (2018)

• BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES
• Authors: QING-GE KONG; HUO-JUN RUAN, SHENG ZHANG
Pages: 113 - 121
Abstract: Bilinear fractal interpolation surfaces were introduced by Ruan and Xu in 2015. In this paper, we present the formula for their box dimension under certain constraint conditions.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000321
Issue No: Vol. 98, No. 1 (2018)

• ON SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS OF BRIOT–BOUQUET TYPE
• Authors: FENGBAI LI
Pages: 122 - 133
Abstract: We study systems of partial differential equations of Briot–Bouquet type. The existence of holomorphic solutions to such systems largely depends on the eigenvalues of an associated matrix. For the noninteger case, we generalise the well-known result of Gérard and Tahara [‘Holomorphic and singular solutions of nonlinear singular first order partial differential equations’, Publ. Res. Inst. Math. Sci. 26 (1990), 979–1000] for Briot–Bouquet type equations to Briot–Bouquet type systems. For the integer case, we introduce a sequence of blow-up like changes of variables and give necessary and sufficient conditions for the existence of holomorphic solutions. We also give some examples to illustrate our results.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S000497271800014X
Issue No: Vol. 98, No. 1 (2018)

• ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\unicode[STIX]{x1D705}$ ++++++++++++ ++++++++ ++++ +++++++++++++++)+SPACES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=134&rft.epage=143&rft.aulast=CHOI&rft.aufirst=BYOUNG&rft.au=BYOUNG+JIN+CHOI&rft_id=info:doi/10.1017/S0004972718000230">CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT(
$\unicode[STIX]{x1D705}$ ) SPACES
• Authors: BYOUNG JIN CHOI
Pages: 134 - 143
Abstract: We study the convex feasibility problem in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to $\text{CAT}(\unicode[STIX]{x1D705})$ spaces with $\unicode[STIX]{x1D705}\geq 0$ , and then we prove the $\unicode[STIX]{x1D6E5}$ -convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces with $\unicode[STIX]{x1D705}\geq 0$ .
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000230
Issue No: Vol. 98, No. 1 (2018)

• ON OVERTWISTED CONTACT SURGERIES
• Authors: SINEM ONARAN
Pages: 144 - 148
Abstract: In this paper, we obtain a new result for overtwisted contact $(+1/n)$ -surgery. We also give a counterexample to a conjecture by James Conway on overtwistedness of manifolds obtained by contact surgery.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S000497271800028X
Issue No: Vol. 98, No. 1 (2018)

• INTERSECTIONS OF MULTICURVES FROM DYNNIKOV COORDINATES
• Authors: S. ÖYKÜ YURTTAŞ; TOBY HALL
Pages: 149 - 158
Abstract: We present an algorithm for calculating the geometric intersection number of two multicurves on the $n$ -punctured disk, taking as input their Dynnikov coordinates. The algorithm has complexity $O(m^{2}n^{4})$ , where  $m$ is the sum of the absolute values of the Dynnikov coordinates of the two multicurves. The main ingredient is an algorithm due to Cumplido for relaxing a multicurve.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000308
Issue No: Vol. 98, No. 1 (2018)

• ON LINEAR COMPLEMENTARY DUAL FOUR CIRCULANT CODES
• Authors: HONGWEI ZHU; MINJIA SHI
Pages: 159 - 166
Abstract: We study linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$ when $q$ is an odd prime power. When $q^{\unicode[STIX]{x1D6FF}}+1$ is divisible by $n$ , we obtain an exact count of linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$ . For certain values of $n$ and $q$ and assuming Artin’s conjecture for primitive roots, we show that the relative distance of these codes satisfies a modified Gilbert–Varshamov bound.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000175
Issue No: Vol. 98, No. 1 (2018)

• ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$R_{k}$ ++++++++++++ ++++++++ ++++ +++++++++++++++&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=98&rft.spage=167&rft.epage=174&rft.aulast=SHI&rft.aufirst=MINJIA&rft.au=MINJIA+SHI&rft.au=YUE+GUAN,+CHENCHEN+WANG,+PATRICK+SOLÉ&rft_id=info:doi/10.1017/S0004972718000291">FEW-WEIGHT CODES FROM TRACE CODES OVER $R_{k}$
• Authors: MINJIA SHI; YUE GUAN, CHENCHEN WANG, PATRICK SOLÉ
Pages: 167 - 174
Abstract: We construct two families of few-weight codes for the Lee weight over the ring $R_{k}$ based on two different defining sets. For the first defining set, taking the Gray map, we obtain an infinite family of binary two-weight codes which are in fact $2^{k}$ -fold replicated MacDonald codes. For the second defining set, we obtain two infinite families of few-weight codes. These few-weight codes can be used to implement secret-sharing schemes.
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000291
Issue No: Vol. 98, No. 1 (2018)

• TANGENT BUNDLES, MONOIDAL THEORIES AND WEIL ALGEBRAS
• Authors: POON LEUNG
Pages: 175 - 176
PubDate: 2018-08-01T00:00:00.000Z
DOI: 10.1017/S0004972718000102
Issue No: Vol. 98, No. 1 (2018)

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