We find the almost sure Hausdorff and box-counting dimensions of random subsets of self-affine fractals obtained by selecting subsets at each stage of the hierarchical construction in a statistically self-similar manner.

We construct two families of binary quadratic bent functions in a combinatorial way. They are self-dual and anti-self-dual quadratic bent functions, respectively, which are not of the Maiorana-McFarland type, but affine equivalent to it.

We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpets that are not self-similar.

This paper proposes an adaptive backstepping control strategy for a class of uncertain non affine systems using self recurrent neural networks. To assure the stable tracking of nonlinear non affine system, it is first converted to an affine like form and subsequently a wavelet based adaptive backstepping controller is developed. Self recurrent wavelet neural network (SRWNN) is used to approxima...

Abstract. Gröchenig and Madych showed that a Haar-type wavelet basis of L2(Rn) can be constructed from the characteristic function χΩ of a compact set Ω if and only if Ω is an integral self-affine tile of Lebesgue measure one. In this paper we generalize their result to the multiwavelet settings. We give a complete characterization of Haar-type scaling function vectors χΩ(x) := [χΩ1 (x), . . . ...

We provide several constructions of self-affine probability measures on the unit square with uniform marginals. These constructions include and extend constructions of previous authors and are parameterized in a natural way. In addition, for each different construction we determine the dimension of the parameter space and thus the level of flexibility (for instance, for approximation purposes) ...

Equilibrium and nonequilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of underlying phenomena. Here, we analyze scaling properties of the cumulative distribution of iso-height loops (i.e., contour lines) of rough self-affine surfaces i...

A tile is a bounded subset of the plane, copies of which may be used to cover the whole plane without gaps or overlap. There are many sources (such as [1]) of beautiful images involving tiling, from medieval Islamic art, through Escher, to more modern work. Perhaps the simplest example of a tile, though, is a solid square, which may tile the plane in a familiar checkerboard pattern. The square ...

We study the box dimensions of self-affine sets in R3 which are generated by a finite collection generalised permutation matrices. obtain bounds for hold with very minimal assumptions and give rise to sharp results many cases. There issues extending well-established planar theory including that principal projections (affine distortions of) overlaps (rather than self-similar sets) natural modifi...

The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger–Wang, Chau–Weinkove and the author solved this global problem in W4,p under some restricti...