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Publisher: Cambridge University Press   (Total: 365 journals)

 Bulletin of the Australian Mathematical Society   [SJR: 0.488]   [H-I: 30]   [1 followers]  Follow        Subscription journal    ISSN (Print) 0004-9727 - ISSN (Online) 1755-1633    Published by Cambridge University Press  [365 journals]
• BAZ volume 97 Issue 2 Cover and Front matter
• PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001253
Issue No: Vol. 97, No. 2 (2018)

• BAZ volume 97 Issue 2 Cover and Back matter
• PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001265
Issue No: Vol. 97, No. 2 (2018)

• ON SOME PROPERTIES OF QUASI-DISTANCE-BALANCED GRAPHS
Pages: 177 - 184
Abstract: For an edge $uv$ in a graph $G$ , $W_{u,v}^{G}$ denotes the set of all vertices of $G$ that are closer to $u$ than to $v$ . A graph $G$ is said to be quasi-distance-balanced if there exists a constant $\unicode[STIX]{x1D706}>1$ such that $|W_{u,v}^{G}|=\unicode[STIX]{x1D706}^{\pm 1}|W_{v,u}^{G}|$ for every pair of adjacent vertices $u$ and $v$ ...
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S000497271700096X
Issue No: Vol. 97, No. 2 (2018)

• ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A PARTIALLY ORDERED SET
• Authors: SARIKA DEVHARE; VINAYAK JOSHI, JOHN LAGRANGE
Pages: 185 - 193
Abstract: In this paper, it is proved that the complement of the zero-divisor graph of a partially ordered set is weakly perfect if it has finite clique number, completely answering the question raised by Joshi and Khiste [‘Complement of the zero divisor graph of a lattice’, Bull. Aust. Math. Soc. 89 (2014), 177–190]. As a consequence, the intersection graph of an intersection-closed family of nonempty subsets of a set is weakly perfect if it has finite clique number. These results are applied to annihilating-ideal graphs and intersection graphs of submodules.
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717000867
Issue No: Vol. 97, No. 2 (2018)

• Authors: XIAOLAN HU; YUNQING ZHANG, YANBO ZHANG
Pages: 194 - 199
Abstract: For two given graphs $G_{1}$ and $G_{2}$ , the planar Ramsey number $PR(G_{1},G_{2})$ is the smallest integer $N$ such that every planar graph $G$ on $N$ vertices either contains $G_{1}$ , or its complement contains $G_{2}$ . Let $C_{4}$ be a quadrilateral, $T_{n}$ a tree of order $n\geq 3$ with maximum degree ...
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001022
Issue No: Vol. 97, No. 2 (2018)

• PARTITIONS OF THE SET OF NONNEGATIVE INTEGERS WITH THE SAME REPRESENTATION
FUNCTIONS
• Authors: JIA-WEN LI; MIN TANG
Pages: 200 - 206
Abstract: Let $\mathbb{N}$ be the set of all nonnegative integers. For a given set $S\subset \mathbb{N}$ the representation function $R_{S}(n)$ counts the number of solutions of the equation $n=s+s^{\prime }$ with $s PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717000818 Issue No: Vol. 97, No. 2 (2018) • AN EQUIVARIANT DESCRIPTION OF CERTAIN HOLOMORPHIC SYMPLECTIC VARIETIES • Authors: PETER CROOKS Pages: 207 - 214 Abstract: Varieties of the form$G\times S_{\!\text{reg}}$, where$G$is a complex semisimple group and$S_{\!\text{reg}}$is a regular Slodowy slice in the Lie algebra of$G$, arise naturally in hyperkähler geometry, theoretical physics and the theory of abstract integrable systems. Crooks and Rayan [‘ integrable systems on hyperkähler manifolds arising from Slodowy slices’, Math. Res. Let., to appear] use a Hamiltonian$G$-action to endow$G\times S_{\!\text{reg}}$with a canonical abstract integrable system. To understand examples of abstract integrable systems arising from Hamiltonian$G$-actions, we consider a holomorphic symplectic variety$X$carrying an abstract integrable system induced by a Hamiltonian$G$-action. Under certain hypotheses, we show that there must exist a$G$-equivariant var... PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717001095 Issue No: Vol. 97, No. 2 (2018) • ITÔ’S THEOREM AND MONOMIAL BRAUER CHARACTERS II • Authors: XIAOYOU CHEN; MARK L. LEWIS Pages: 215 - 217 Abstract: Let$G$be a finite solvable group and let$p$be a prime. We prove that the intersection of the kernels of irreducible monomial$p$-Brauer characters of$G$with degrees divisible by$p$is$p$-closed. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717000879 Issue No: Vol. 97, No. 2 (2018) • ++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\unicode[STIX]{x1D70B}$++++++++++++ ++++++++ ++++ ++++++++++++++++++ +++++++++++++++-DECOMPOSABILITY&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=218&rft.epage=228&rft.aulast=KAZARIN&rft.aufirst=L.&rft.au=L.+S.+KAZARIN&rft.au=A.+MARTÍNEZ-PASTOR,+M.+D.+PÉREZ-RAMOS&rft_id=info:doi/10.1017/S0004972717001034">FINITE TRIFACTORISED GROUPS AND$\unicode[STIX]{x1D70B}$-DECOMPOSABILITY • Authors: L. S. KAZARIN; A. MARTÍNEZ-PASTOR, M. D. PÉREZ-RAMOS Pages: 218 - 228 Abstract: We derive some structural properties of a trifactorised finite group$G=AB=AC=BC$, where$A$,$B$, and$C$are subgroups of$G$, provided that$A=A_{\unicode[STIX]{x1D70B}}\times A_{\unicode[STIX]{x1D70B}^{\prime }}$and$B=B_{\unicode[STIX]{x1D70B}}\times B_{\unicode[STIX]{x1D70B}^{\prime }}$are$\unicode[STIX]{x1D70B}$-decomposable groups, for a set of primes$\unicode[STIX]{x1D70B}$. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717001034 Issue No: Vol. 97, No. 2 (2018) • GROUPS OF FINITE NORMAL LENGTH • Authors: FRANCESCO DE GIOVANNI; ALESSIO RUSSO Pages: 229 - 239 Abstract: Let$k$be a nonnegative integer. A subgroup$X$of a group$G$has normal length$k$in$G$if all chains between$X$and its normal closure$X^{G}$have length at most$k$, and$k$is the length of at least one of these chains. The group$G$is said to have finite normal length if there is a finite upper bound for the normal lengths of its subgroups. The aim of this paper is to study groups of finite normal length. Among other results, it is proved that if all subgroups of a locally (soluble-by-finite) group PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717001101 Issue No: Vol. 97, No. 2 (2018) • REALISABLE SETS OF CATENARY DEGREES OF NUMERICAL MONOIDS • Authors: CHRISTOPHER O’NEILL; ROBERTO PELAYO Pages: 240 - 245 Abstract: The catenary degree is an invariant that measures the distance between factorisations of elements within an atomic monoid. In this paper, we classify which finite subsets of$\mathbb{Z}_{\geq 0}$occur as the set of catenary degrees of a numerical monoid (that is, a co-finite, additive submonoid of$\mathbb{Z}_{\geq 0}$). In particular, we show that, with one exception, every finite subset of$\mathbb{Z}_{\geq 0}$that can possibly occur as the set of catenary degrees of some atomic monoid is actually achieved by a numerical monoid. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717000995 Issue No: Vol. 97, No. 2 (2018) • DENSITY, SMITAL PROPERTY AND QUASICONTINUITY • Authors: GRAŻYNA HORBACZEWSKA; SEBASTIAN LINDNER Pages: 246 - 252 Abstract: Based on the abstract version of the Smital property, we introduce an operator$DS$. We use it to characterise the class of semitopological abelian groups, for which addition is a quasicontinuous operation. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717000922 Issue No: Vol. 97, No. 2 (2018) • TOEPLITZ DETERMINANTS WHOSE ELEMENTS ARE THE COEFFICIENTS OF ANALYTIC AND UNIVALENT FUNCTIONS • Authors: MD FIROZ ALI; D. K. THOMAS, A. VASUDEVARAO Pages: 253 - 264 Abstract: Let${\mathcal{S}}$denote the class of analytic and univalent functions in$\mathbb{D}:=\{z\in \mathbb{C}:|z|
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001174
Issue No: Vol. 97, No. 2 (2018)

• AN ENTIRE FUNCTION SHARING TWO VALUES WITH ITS LINEAR DIFFERENTIAL
POLYNOMIAL
• Authors: INDRAJIT LAHIRI
Pages: 265 - 273
Abstract: We consider the uniqueness of an entire function and a linear differential polynomial generated by it. One of our results improves a result of Li and Yang [‘Value sharing of an entire function and its derivatives’, J. Math. Soc. Japan 51(4) (1999), 781–799].
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S000497271700079X
Issue No: Vol. 97, No. 2 (2018)

• ++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\unicode[STIX]{x1D711}$ ++++++++++++ ++++++++ ++++ ++++++++++++++++++ +++++++++++++++-CONTRACTIBILITY+AND+ ++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\unicode[STIX]{x1D711}$ ++++++++++++ ++++++++ ++++ ++++++++++++++++++ +++++++++++++++-CONNES+AMENABILITY+COINCIDE+WITH+SOME+OLDER+NOTIONS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=274&rft.epage=278&rft.aulast=MAHMOODI&rft.aufirst=AMIN&rft.au=AMIN+MAHMOODI&rft_id=info:doi/10.1017/S0004972717000909">$\unicode[STIX]{x1D711}$ -CONTRACTIBILITY AND $\unicode[STIX]{x1D711}$
-CONNES AMENABILITY COINCIDE WITH SOME OLDER NOTIONS
• Authors: AMIN MAHMOODI
Pages: 274 - 278
Abstract: It is shown that various definitions of $\unicode[STIX]{x1D711}$ -Connes amenability and $\unicode[STIX]{x1D711}$ -contractibility are equivalent to older and simpler concepts.
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717000909
Issue No: Vol. 97, No. 2 (2018)

• ++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++${\mathcal{L}}^{\infty+}(\unicode[STIX]{x1D6E4})$ ++++++++++++ ++++++++ ++++ ++++++++++++++++++ +++++++++++++++-TYPE+SPACES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=279&rft.epage=284&rft.aulast=JIA&rft.aufirst=WEIKE&rft.au=WEIKE+JIA&rft.au=DONGNI+TAN&rft_id=info:doi/10.1017/S0004972717000910">WIGNER’S THEOREM IN ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$
-TYPE SPACES
• Authors: WEIKE JIA; DONGNI TAN
Pages: 279 - 284
Abstract: We investigate surjective solutions of the functional equation $$\begin{eqnarray}\displaystyle \{\Vert f(x)+f(y)\Vert ,\Vert f(x)-f(y)\Vert \}=\{\Vert x+y\Vert ,\Vert x-y\Vert \}\quad (x,y\in X), & & \displaystyle \nonumber\end{eqnarray}$$ where $f:X\rightarrow Y$ is a map between two real ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$ -type spaces. We show that all such solutions are phase equivalent to real linear isometries. This can be considered as an extension of Wigner’s theorem on symmetry for real ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$ -type spaces.
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717000910
Issue No: Vol. 97, No. 2 (2018)

• ++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\ell+_{1}$ ++++++++++++ ++++++++ ++++ ++++++++++++++++++ +++++++++++++++-SUM+OF+STRICTLY+CONVEX+BANACH+SPACES&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=285&rft.epage=292&rft.aulast=KADETS&rft.aufirst=V.&rft.au=V.+KADETS&rft.au=O.+ZAVARZINA&rft_id=info:doi/10.1017/S0004972717001150">NONEXPANSIVE BIJECTIONS TO THE UNIT BALL OF THE $\ell _{1}$ -SUM OF
STRICTLY CONVEX BANACH SPACES
• Authors: V. KADETS; O. ZAVARZINA
Pages: 285 - 292
Abstract: Extending recent results by Cascales et al. [‘Plasticity of the unit ball of a strictly convex Banach space’, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 110(2) (2016), 723–727], we demonstrate that for every Banach space $X$ and every collection $Z_{i},i\in I$ , of strictly convex Banach spaces, every nonexpansive bijection from the unit ball of $X$ to the unit ball of the sum of $Z_{i}$ by $\ell _{1}$ is an isometry.
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001150
Issue No: Vol. 97, No. 2 (2018)

• IMPROVED INEQUALITIES FOR THE NUMERICAL RADIUS: WHEN INVERSE COMMUTES WITH
THE NORM
• Authors: BRYAN E. CAIN
Pages: 293 - 296
Abstract: New inequalities relating the norm $n(X)$ and the numerical radius $w(X)$ of invertible bounded linear Hilbert space operators were announced by Hosseini and Omidvar [‘Some inequalities for the numerical radius for Hilbert space operators’, Bull. Aust. Math. Soc. 94 (2016), 489–496]. For example, they asserted that $w(AB)\leq$ $2w(A)w(B)$ for invertible bounded linear Hilbert space operators $A$ and $B$ . We identify implicit hypotheses used in their discovery. The inequalities and their proofs can be made good by adding the extra hypotheses which take the form $n(X^{-1})=n(X)^{-1}$ . We give counterexamples in the absence of such additional hypotheses. Finally, we show that these hypotheses yield even stronger conclusions, for example, $w(AB)=w(A)w(B)$ .
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001046
Issue No: Vol. 97, No. 2 (2018)

• THE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES
• Authors: YUFEI LI; YUFENG LU, TAO YU
Pages: 297 - 307
Abstract: Let $\unicode[STIX]{x1D711}$ be an analytic self-map of the unit disc. If $\unicode[STIX]{x1D711}$ is analytic in a neighbourhood of the closed unit disc, we give a precise formula for the essential norm of the composition operator $C_{\unicode[STIX]{x1D711}}$ on the weighted Dirichlet spaces ${\mathcal{D}}_{\unicode[STIX]{x1D6FC}}$ for $\unicode[STIX]{x1D6FC}>0$ . We also show that, for a univalent analytic self-map $\unicode[STIX]{x1D711}$ of $\mathbb{D}$ , if $\unicode[STIX]{x1D711}$ has an angular derivative at some point of $\unicode[STIX]{x2202}\mathbb{D}$ , then the essential norm of $C_{\unicode[STIX]{x1D711}}$ on the Dirichlet space is equal to one.
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717000983
Issue No: Vol. 97, No. 2 (2018)

• PRODUCTS OF ROTATIONS BY A GIVEN ANGLE IN THE ORTHOGONAL GROUP
• Authors: M. G. MAHMOUDI
Pages: 308 - 312
Abstract: For every rotation $\unicode[STIX]{x1D70C}$ of the Euclidean space $\mathbb{R}^{n}$ ( $n\geq 3$ ), we find an upper bound for the number $r$ such that $\unicode[STIX]{x1D70C}$ is a product of $r$ rotations by an angle $\unicode[STIX]{x1D6FC}$ ( $0 PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717000946 Issue No: Vol. 97, No. 2 (2018) • DEFORMING A CONVEX DOMAIN INTO A DISK BY KLAIN’S CYCLIC REARRANGEMENT • Authors: YUNLONG YANG; DEYAN ZHANG Pages: 313 - 319 Abstract: For a convex domain, we use Klain’s cyclic rearrangement to obtain a sequence of convex domains with increasing area and the same perimeter which converges to a disk. As a byproduct, we give a proof of the classical isoperimetric inequality in the plane. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717001113 Issue No: Vol. 97, No. 2 (2018) • CONTINUITY ON GENERALISED TOPOLOGICAL SPACES VIA HEREDITARY CLASSES • Authors: P. MONTAGANTIRUD; W. THAIKUA Pages: 320 - 330 Abstract: A generalised topology is a collection of subsets of a given nonempty set containing the empty set and arbitrary unions of the elements in the collection. By using the concept of hereditary classes, a generalised topology can be extended to a new one, called a generalised topology via a hereditary class. We study continuity on generalised topological spaces via hereditary classes in various situations. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717001071 Issue No: Vol. 97, No. 2 (2018) • HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES • Authors: SAMI LAZAAR; TOM RICHMOND, HOUSSEM SABRI Pages: 331 - 339 Abstract: A function$f:X\rightarrow X$determines a topology$P(f)$on$X$by taking the closed sets to be those sets$A\subseteq X$with$f(A)\subseteq A$. The topological space$(X,P(f))$is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces. PubDate: 2018-04-01T00:00:00.000Z DOI: 10.1017/S0004972717000934 Issue No: Vol. 97, No. 2 (2018) • ++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\mathbb{Z}_{2}$++++++++++++ ++++++++ ++++ ++++++++++++++++++ +++++++++++++++-ACTIONS+ON+SOME+DOLD+MANIFOLDS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=340&rft.epage=348&rft.aulast=MORITA&rft.aufirst=ANA&rft.au=ANA+MARIA+M.+MORITA&rft.au=DENISE+DE+MATTOS,+PEDRO+L.+Q.+PERGHER&rft_id=info:doi/10.1017/S0004972717001058">THE COHOMOLOGY RING OF ORBIT SPACES OF FREE$\mathbb{Z}_{2}$-ACTIONS ON SOME DOLD MANIFOLDS • Authors: ANA MARIA M. MORITA; DENISE DE MATTOS, PEDRO L. Q. PERGHER Pages: 340 - 348 Abstract: We determine the possible$\mathbb{Z}_{2}$-cohomology rings of orbit spaces of free actions of$\mathbb{Z}_{2}$(or fixed point free involutions) on the Dold manifold$P(1,n)$, where$n\$ is an odd natural number.
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001058
Issue No: Vol. 97, No. 2 (2018)

• MATHEMATICAL MODELS FOR QUANTIFYING COLLECTIVE CELL BEHAVIOUR
• Authors: STUART T. JOHNSTON
Pages: 349 - 352
PubDate: 2018-04-01T00:00:00.000Z
DOI: 10.1017/S0004972717001149
Issue No: Vol. 97, No. 2 (2018)

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