CARMA supports the formation of the National Research Centre by the Australian Mathematical Sciences Institute. CARMA will be a foundation partner in the Centre when it is launched in 2016.

RESEARCH

CARMA renewed until 2020: read our presentation here

EVENTS

TOMORROW

CARMA Executive Meeting

10:00 am, Mon, 27th Feb 2017
V205, Mathematics Building

CARMA Colloquium

"Erdos-Selfridge and Supersingularity"
    Michael Bennett

4:00 pm, Tue, 28th Feb 2017
V205, Mathematics Building

School Meeting

12:00 pm, Wed, 1st Mar 2017
V111, Mathematics Building

School Research Seminar

"Plasma fusion"
   Dr David Green

1:00 pm, Thu, 2nd Mar 2017
PG03, Physics Building

"I Wish I'd Known..." Seminar

4:00 pm, Thu, 2nd Mar 2017
V205, Mathematics Building

These are the events in the next 7 days. For more, see the events page.

NEWS

"Sound Advice" Leads George Willis to Gavin Brown Prize

Gavin Brown Best Paper Prize winner Professor George Willis from the University of Newcastle was recognised for his outstanding joint original research paper with Yehuda Shalom, Commens... [READ MORE]

Bernhard Neumann Prize honourable mention for Scott Lindstrom

CARMA PhD student Scott Lindstrom received an honourable mention for the Bernhard Neumann Prize for his presentation in the Annual Meeting of Australian Mathematical Society in Canberra... [READ MORE]

AMS' Levi L. Conant Prize for Bailey, Borwein, Mattingly and Wightwick

David Bailey, Jonathan Borwein, Andrew Mattingly, and Glenn Wightwick received the 2017 Conant Prize for their article "The Computation of Previously Inaccessible Digits of π2 and Cata... [READ MORE]

HIGHLIGHTS

Selected paper from DocServer
Jonathan M. Borwein, Neil J. Calkin, Scott Lindstrom, A. Mattingly

ABSTRACT

We investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical experimentation we discover that, for one such formulation, the exponent terms have �nite arithmetic means for almost all real numbers. This set of means, which we call the logarithmic Khintchine numbers, has a pleasing relationship with the geometric means of the corresponding continued fraction terms. While the classical Khintchine's constant is believed not to be related to any naturally occurring number, we �find surprisingly that the logarithmic Khintchine numbers are elementary.

MEMBERSHIP

Membership to CARMA offers many benefits and is available by invitation to all University of Newcastle academic staff. Associate membership, also by invitation, is available to external researchers and practitioners for three-year renewable terms. Associate members are expected to visit CARMA with some frequency, typically for a total of three to four weeks in a year, and to be involved in one or more ongoing research projects with CARMA members. CARMA is able to assist with the travel and living costs of such visits.