36 research outputs found
Mathematical specification of hitomezashi designs
Two mathematical aspects of the centuries-old Japanese sashiko stitching form
hitomezashi are discussed: the encoding of designs using words from a binary
alphabet, and duality. Traditional hitomezashi designs are analysed using these
two ideas. Self-dual hitomezashi designs related to Fibonacci snowflakes, which
we term Pell persimmon polyomino patterns, are proposed. Both these designs and
the binary words used to generate them appear to be new to their respective
literatures.Comment: 25 pages; 21 figure
Curriculum Redesign to Provide Opportunities for a Diversity of Students
The Faculty decision in 2012 to change the prerequisite for the Bachelor of Science at La Trobe University from Mathematical Methods (intermediate) to “any mathematics” (elementary/intermediate), in conjunction with the introduction of a quantitative literacy requirement in first year, has presented both challenges and opportunities for the Department of Mathematics and Statistics. This paper describes the curriculum redesign undertaken to provide pathways to the mathematics or physics major for any student, whilst also satisfying the constraint that there be no proliferation of subjects or duplication of teaching. This careful redesign has also enabled the closure of a somewhat problematic summer bridging course, and permits mid-year transfer to engineering degrees for students whose subject choice at Year 12 would otherwise leave them ill-prepared for such programs
Stations, trains and small-world networks
The clustering coefficient, path length and average vertex degree of two
urban train line networks have been calculated. The results are compared with
theoretical predictions for appropriate random bipartite graphs. They have also
been compared with one another to investigate the effect of architecture on the
small-world properties.Comment: 6 pages, prepared in RevTe
Ising tricriticality and the dilute A model
Some universal amplitude ratios appropriate to the peturbation
of the c=7/10 minimal field theory, the subleading magnetic perturbation of the
tricritical Ising model, are explicitly demonstrated in the dilute A model,
in regime 1.Comment: 8 pages, LaTeX using iop macro
Off-Critical Logarithmic Minimal Models
We consider the integrable minimal models , corresponding
to the perturbation off-criticality, in the {\it logarithmic
limit\,} , where are coprime and the
limit is taken through coprime values of . We view these off-critical
minimal models as the continuum scaling limit of the
Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice.
Applying Corner Transfer Matrices to the Forrester-Baxter RSOS models in Regime
III, we argue that taking first the thermodynamic limit and second the {\it
logarithmic limit\,} yields off-critical logarithmic minimal models corresponding to the perturbation of the critical
logarithmic minimal models . Specifically, in accord with the
Kyoto correspondence principle, we show that the logarithmic limit of the
one-dimensional configurational sums yields finitized quasi-rational characters
of the Kac representations of the critical logarithmic minimal models . We also calculate the logarithmic limit of certain off-critical
observables related to One Point Functions and show that the
associated critical exponents
produce all conformal dimensions in the infinitely extended Kac table. The corresponding Kac labels
satisfy . The exponent is obtained from the logarithmic limit of the free energy giving the
conformal dimension for the perturbing field . As befits a non-unitary
theory, some observables diverge at criticality.Comment: 18 pages, 5 figures; version 3 contains amplifications and minor
typographical correction