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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  [367 journals]
• BAZ volume 97 Issue 3 Cover and Front matter
• PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972717001277
Issue No: Vol. 97, No. 3 (2018)

• BAZ volume 97 Issue 3 Cover and Back matter
• PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972717001289
Issue No: Vol. 97, No. 3 (2018)

• VISIBLE POINTS ON EXPONENTIAL CURVES
• Authors: SIMON MACOURT
Pages: 353 - 359
Abstract: We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible points on exponential curves modulo a prime for almost all primes.
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972717001186
Issue No: Vol. 97, No. 3 (2018)

• Authors: L. A. FERREIRA
Pages: 360 - 362
Abstract: An additive basis $A$ is finitely stable when the order of $A$ is equal to the order of $A\cup F$ for all finite subsets $F\subseteq \mathbb{N}$ . We give a sufficient condition for an additive basis to be finitely stable. In particular, we prove that $\mathbb{N}^{2}$ is finitely stable.
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972717001204
Issue No: Vol. 97, No. 3 (2018)

• A NOTE ON THE ERDŐS–GRAHAM THEOREM
• Authors: WENHUI WANG; MIN TANG
Pages: 363 - 366
Abstract: Let ${\mathcal{A}}=\{a_{1} PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000126 Issue No: Vol. 97, No. 3 (2018) • A VARIATION ON THE THEME OF NICOMACHUS • Authors: FLORIAN LUCA; GEREMÍAS POLANCO, WADIM ZUDILIN Pages: 367 - 373 Abstract: In this paper, we prove some conjectures of K. Stolarsky concerning the first and third moments of the Beatty sequences with the golden section and its square. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001411 Issue No: Vol. 97, No. 3 (2018) • IMPROVING AN INEQUALITY FOR THE DIVISOR FUNCTION • Authors: JEFFREY P. S. LAY Pages: 374 - 381 Abstract: Using elementary means, we improve an explicit bound on the divisor function due to Friedlander and Iwaniec [Opera de Cribro, American Mathematical Society, Providence, RI, 2010]. Consequently, we modestly improve a result regarding a sieving inequality for Gaussian sequences. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000084 Issue No: Vol. 97, No. 3 (2018) • A NOTE ON THE FUNDAMENTAL THEOREM OF ALGEBRA • Authors: MOHSEN ALIABADI Pages: 382 - 385 Abstract: The algebraic proof of the fundamental theorem of algebra uses two facts about real numbers. First, every polynomial with odd degree and real coefficients has a real root. Second, every nonnegative real number has a square root. Shipman [‘Improving the fundamental theorem of algebra’, Math. Intelligencer 29(4) (2007), 9–14] showed that the assumption about odd degree polynomials is stronger than necessary; any field in which polynomials of prime degree have roots is algebraically closed. In this paper, we give a simpler proof of this result of Shipman. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000035 Issue No: Vol. 97, No. 3 (2018) • ALEXANDER POLYNOMIALS OF COMPLEX PROJECTIVE PLANE CURVES • Authors: QUY THUONG LÊ Pages: 386 - 395 Abstract: We compute the Alexander polynomial of a nonreduced nonirreducible complex projective plane curve with mutually coprime orders of vanishing along its irreducible components in terms of certain multiplier ideals. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001198 Issue No: Vol. 97, No. 3 (2018) • PT-GROUPS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=396&rft.epage=405&rft.aulast=HU&rft.aufirst=BIN&rft.au=BIN+HU&rft.au=JIANHONG+HUANG,+ALEXANDER+N.+SKIBA&rft_id=info:doi/10.1017/S0004972717001083">A GENERALISATION OF FINITE PT-GROUPS • Authors: BIN HU; JIANHONG HUANG, ALEXANDER N. SKIBA Pages: 396 - 405 Abstract: Let$G$be a group and$\unicode[STIX]{x1D70E}=\{\unicode[STIX]{x1D70E}_{i}\mid i\in I\}$some partition of the set of all primes. A subgroup$A$of$G$is$\unicode[STIX]{x1D70E}$-subnormal in$G$if there is a subgroup chain$A=A_{0}\leq A_{1}\leq \cdots \leq A_{m}=G$such that either$A_{i-1}\unlhd A_{i}$or$A_{i}/(A_{i-1})_{A_{i}}$is a finite$\unicode[STIX]{x1D70E}_{j}$-group for some$j=j(i)$for PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001083 Issue No: Vol. 97, No. 3 (2018) • ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$++++++++++++ ++++++++ ++++ +++++++++++++++-PARTS+OF+CONJUGACY+CLASS+SIZES+OF+FINITE GROUPS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=406&rft.epage=411&rft.aulast=YANG&rft.aufirst=YONG&rft.au=YONG+YANG&rft.au=GUOHUA+QIAN&rft_id=info:doi/10.1017/S0004972718000072">ON$p$-PARTS OF CONJUGACY CLASS SIZES OF FINITE GROUPS • Authors: YONG YANG; GUOHUA QIAN Pages: 406 - 411 Abstract: Let$G$be a finite group. Let$\operatorname{cl}(G)$be the set of conjugacy classes of$G$and let$\operatorname{ecl}_{p}(G)$be the largest integer such that$p^{\operatorname{ecl}_{p}(G)}$divides$|C|$for some$C\in \operatorname{cl}(G)$. We prove the following results. If$\operatorname{ecl}_{p}(G)=1$, then$|G:F(G)|_{p}\leq p^{4}$if$p\geq 3$. Moreover, if$G$is solvable, then PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000072 Issue No: Vol. 97, No. 3 (2018) • ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\text{Out}(F_{N})$++++++++++++ ++++++++ ++++ +++++++++++++++&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=412&rft.epage=421&rft.aulast=HULL&rft.aufirst=MICHAEL&rft.au=MICHAEL+HULL&rft.au=ILYA+KAPOVICH&rft_id=info:doi/10.1017/S0004972718000047">COUNTING CONJUGACY CLASSES IN$\text{Out}(F_{N})$• Authors: MICHAEL HULL; ILYA KAPOVICH Pages: 412 - 421 Abstract: We show that if a finitely generated group$G$has a nonelementary WPD action on a hyperbolic metric space$X$, then the number of$G$-conjugacy classes of$X$-loxodromic elements of$G$coming from a ball of radius$R$in the Cayley graph of$G$grows exponentially in$R$. As an application we prove that for$N\geq 3$the number of distinct$\text{Out}(F_{N})$-conjugacy classes of fully irreducible elements$\unicode[STIX]{x1D719}$from an PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000047 Issue No: Vol. 97, No. 3 (2018) • LEE MONOIDS ARE NONFINITELY BASED WHILE THE SETS OF THEIR ISOTERMS ARE FINITELY BASED • Authors: OLGA SAPIR Pages: 422 - 434 Abstract: We establish a new sufficient condition under which a monoid is nonfinitely based and apply this condition to Lee monoids$L_{\ell }^{1}$, obtained by adjoining an identity element to the semigroup generated by two idempotents$a$and$b$with the relation$0=abab\cdots \,$(length$\ell$). We show that every monoid$M$which generates a variety containing$L_{5}^{1}$and is contained in the variety generated by$L_{\ell }^{1}$for some$\ell \geq 5$is nonfinitely based. We establish this result by analysing$\unicode[STIX]{x1D70F}$-terms for$M$PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000023 Issue No: Vol. 97, No. 3 (2018) • THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS • Authors: BOGUMIŁA KOWALCZYK; ADAM LECKO, YOUNG JAE SIM Pages: 435 - 445 Abstract: We prove the sharp inequality$|H_{3,1}(f)|\leq 4/135$for convex functions, that is, for analytic functions$f$with$a_{n}:=f^{(n)}(0)/n!,~n\in \mathbb{N}$, such that $$\begin{eqnarray}Re\bigg\{1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\bigg\}>0\quad \text{for}~z\in \mathbb{D}:=\{z\in \mathbb{C}:|z| PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001125 Issue No: Vol. 97, No. 3 (2018) • ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++L^{p} ++++++++++++ ++++++++ ++++ +++++++++++++++-APPROXIMATION+OF+HOLOMORPHIC+FUNCTIONS+ON+A+CLASS+OF+CONVEX+DOMAINS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=446&rft.epage=452&rft.aulast=HA&rft.aufirst=LY&rft.au=LY+KIM+HA&rft_id=info:doi/10.1017/S0004972718000114">L^{p} -APPROXIMATION OF HOLOMORPHIC FUNCTIONS ON A CLASS OF CONVEX DOMAINS • Authors: LY KIM HA Pages: 446 - 452 Abstract: Let \unicode[STIX]{x1D6FA} be a member of a certain class of convex ellipsoids of finite/infinite type in \mathbb{C}^{2} . In this paper, we prove that every holomorphic function in L^{p}(\unicode[STIX]{x1D6FA}) can be approximated by holomorphic functions on \bar{\unicode[STIX]{x1D6FA}} in L^{p}(\unicode[STIX]{x1D6FA}) -norm, for 1\leq p PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000114 Issue No: Vol. 97, No. 3 (2018) • INEQUALITIES ASSOCIATED WITH RATIOS OF GAMMA FUNCTIONS • Authors: JENICA CRINGANU Pages: 453 - 458 Abstract: We use properties of the gamma function to estimate the products \prod _{k=1}^{n}(4k-3)/4k and \prod _{k=1}^{n}(4k-1)/4k , motivated by the work of Chen and Qi [‘Completely monotonic function associated with the gamma function and proof of Wallis’ inequality’, Tamkang J. Math. 36(4) (2005), 303–307] and Mortici et al. [‘Completely monotonic functions and inequalities associated to some ratio of gamma function’, Appl. Math. Comput. 240 (2014), 168–174]. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000138 Issue No: Vol. 97, No. 3 (2018) • ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++\unicode[STIX]{x1D70E} ++++++++++++ ++++++++ ++++ +++++++++++++++-QUADRATIC+FUNCTIONAL+EQUATION+ON+SEMIGROUPS&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=459&rft.epage=470&rft.aulast=EL-FASSI&rft.aufirst=IZ-IDDINE&rft.au=IZ-IDDINE+EL-FASSI&rft.au=JANUSZ+BRZDĘK&rft_id=info:doi/10.1017/S0004972717001137">ON THE HYPERSTABILITY OF A PEXIDERISED \unicode[STIX]{x1D70E} -QUADRATIC FUNCTIONAL EQUATION ON SEMIGROUPS • Authors: IZ-IDDINE EL-FASSI; JANUSZ BRZDĘK Pages: 459 - 470 Abstract: Motivated by the notion of Ulam stability, we investigate some inequalities connected with the functional equation$$\begin{eqnarray}f(xy)+f(x\unicode[STIX]{x1D70E}(y))=2f(x)+h(y),\quad x,y\in G,\end{eqnarray}$$for functions f and h mapping a semigroup (G,\cdot ) into a commutative semigroup (E,+) , where the map \unicode[STIX]{x1D70E}:G\rightarrow G is an endomorphism of G with \unicode[STIX]{x1D70E}(\unicode[STIX]{x1D70E}(x))=x for all x\in G . We derive from these results some characterisations of inner product spaces. We also obtain a description of solutions to the equation and hyperstability results for the \unicode[STIX]{x1D70E} -quadratic and PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001137 Issue No: Vol. 97, No. 3 (2018) • STABILITY OF AN EXPONENTIAL-MONOMIAL FUNCTIONAL EQUATION • Authors: CHANG-KWON CHOI Pages: 471 - 479 Abstract: Let N be a fixed positive integer and f:\mathbb{R}\rightarrow \mathbb{C} . As a generalisation of the superstability of the exponential functional equation we consider the functional inequalities$$\begin{eqnarray}\displaystyle & \displaystyle \big|f\big(\!\sqrt[N]{x^{N}+y^{N}}\big)-f(x)f(y)\big|\leq \unicode[STIX]{x1D719}(x), & \displaystyle \nonumber\\ \displaystyle & \displaystyle \big|f\big(\!\sqrt[N]{x^{N}+y^{N}}\big)-f(x)f(y)\big|\leq \unicode[STIX]{x1D713}(x,y) & \displaystyle \nonumber\end{eqnarray}$$for all$x,y\in \mathbb{R}$, where$\unicode[STIX]{x1D719}:\mathbb{R}\rightarrow \mathbb{R}^{+}$is an arbitrary function and$\unicode[STIX]{x1D713}:\mathbb{R}^{2}\rightarrow \mathbb{R}^{+}$satisfies a certain condition. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972718000011 Issue No: Vol. 97, No. 3 (2018) • THE HARDY AND HEISENBERG INEQUALITIES IN MORREY SPACES • Authors: HENDRA GUNAWAN; DENNY IVANAL HAKIM, EIICHI NAKAI, YOSHIHIRO SAWANO Pages: 480 - 491 Abstract: We use the Morrey norm estimate for the imaginary power of the Laplacian to prove an interpolation inequality for the fractional power of the Laplacian on Morrey spaces. We then prove a Hardy-type inequality and use it together with the interpolation inequality to obtain a Heisenberg-type inequality in Morrey spaces. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001216 Issue No: Vol. 97, No. 3 (2018) • A REMARK ON THE TRACIAL ROKHLIN PROPERTY • Authors: YUAN HANG ZHANG Pages: 492 - 498 Abstract: To explore the difficulties of classifying actions with the tracial Rokhlin property using K-theoretic data, we construct two$\mathbb{Z}_{2}$actions$\unicode[STIX]{x1D6FC}_{1},\unicode[STIX]{x1D6FC}_{2}$on a simple unital AF algebra$A$such that$\unicode[STIX]{x1D6FC}_{1}$has the tracial Rokhlin property and$\unicode[STIX]{x1D6FC}_{2}$does not, while$(\unicode[STIX]{x1D6FC}_{1})_{\ast }=(\unicode[STIX]{x1D6FC}_{2})_{\ast }$, where$(\unicode[STIX]{x1D6FC}_{i})_{\ast }$is the induced map by$\unicode[STIX]{x1D6FC}_{i}$acting on$K_{0}(A)$for$i=1,2$. PubDate: 2018-06-01T00:00:00.000Z DOI: 10.1017/S0004972717001162 Issue No: Vol. 97, No. 3 (2018) • ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\unicode[STIX]{x1D6FC}$++++++++++++ ++++++++ ++++ +++++++++++++++-MODULATION+SPACES+IN+THE+FULL+RANGE&rft.title=Bulletin+of+the+Australian+Mathematical+Society&rft.issn=0004-9727&rft.date=2018&rft.volume=97&rft.spage=499&rft.epage=512&rft.aulast=ZHAO&rft.aufirst=GUOPING&rft.au=GUOPING+ZHAO&rft.au=WEICHAO+GUO,+XIAO+YU&rft_id=info:doi/10.1017/S0004972718000096">FRACTIONAL INTEGRAL OPERATORS ON$\unicode[STIX]{x1D6FC}$-MODULATION SPACES IN THE FULL RANGE • Authors: GUOPING ZHAO; WEICHAO GUO, XIAO YU Pages: 499 - 512 Abstract: We use a unified approach to study the boundedness of fractional integral operators on$\unicode[STIX]{x1D6FC}\$ -modulation spaces and find sharp conditions for boundedness in the full range.
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972718000096
Issue No: Vol. 97, No. 3 (2018)

• A SIMPLE PROOF OF THE STRONG LAW OF LARGE NUMBERS WITH RATES
• Authors: NUNO LUZIA
Pages: 513 - 517
Abstract: We give a simple proof of the strong law of large numbers with rates, assuming only finite variance. This note also serves as an elementary introduction to the theory of large deviations, assuming only finite variance, even when the random variables are not necessarily independent.
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972718000059
Issue No: Vol. 97, No. 3 (2018)

• THE OCEAN’S GLOBAL IRON, PHOSPHORUS AND SILICON CYCLES: INVERSE
MODELLING AND NOVEL DIAGNOSTICS
• Authors: BENOÎT PASQUIER
Pages: 518 - 519
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972718000060
Issue No: Vol. 97, No. 3 (2018)

• NONSTANDARD ESTIMATION FOR THE VON MISES FISHER
DISTRIBUTION
• Authors: MARYAM GHODSI
Pages: 520 - 522
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972717001228
Issue No: Vol. 97, No. 3 (2018)

• NONLINEAR THERMOMAGNETIC INSTABILITIES IN FERROMAGNETIC NANOFLUIDS
• Authors: PINKEE DEY
Pages: 523 - 524
PubDate: 2018-06-01T00:00:00.000Z
DOI: 10.1017/S0004972717001423
Issue No: Vol. 97, No. 3 (2018)

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