Australian Mathematical Society (AustMS): E-Journals
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Hyperstability of generalised linear functional equations in several variables
No full texthttp://dx.doi.org/10.1017/S000497272000055
Degrees of Brauer characters and normal Sylow p-subgroups
No full texthttp://dx.doi.org/10.1017/S000497271900129
Extensions of autocorrelation inequalities with applications to additive combinatorics
No full textBarnard and Steinerberger show that for , the following autocorrelation inequality holds:
where the constant cannot be replaced by . In addition to being interesting and important in their own right, inequalities such as these have applications in additive combinatorics where some problems, such as those of minimal difference basis, can be encapsulated by a convolution inequality similar to the above integral. Barnard and Steinerberger suggest that future research may focus on the existence of functions extremizing the above inequality (which is itself related to Brascamp-Lieb type inequalities). We show that for to be extremal under the above, we must have
Our central technique for deriving this result is local perturbation of to increase the value of the autocorrelation, while leaving unchanged. These perturbation methods can be extended to examine a more general notion of autocorrelation. Let , , be a matrix with real entries and columns for , and be a constant. For a broad class of matrices , we prove necessary conditions for to extremize autocorrelation inequalities of the form \min_{ \mathbf{t} \in [0,1]^d } \int_{\R} \prod_{i=1}^n\ f(x+ \mathbf{t} \cdot a_i)\ \mathrm{d}x\ \leq\ C ||f||_{L^1}^n.$
Teaching algebra with digital technology: factors influencing secondary mathematics teachers' task development and implementation
No full textDOI:
10.1017/S000497271900142
On almost stable CMC hypersurfaces in manifolds of bounded sectional curvature
No full text10.1017/S000497271900093
Algebraic values of certain analytic functions defined by a canonical product
No full textDOI:
10.1017/S000497271900105
On the connection between differential polynomial rings and polynomial rings over nil rings
No full textDOI:
10.1017/S000497271900092
