We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from natural numbers. Solvability such (systems of) has been intensively studied for various classes groups recent years. In many cases, it turns out that set all solutions on an equation is a semilinear can be constructed effectively. Such ...

Knowledge of current vegetation dynamics and an ability to make accurate predictions of ecological changes are essential for minimizing food scarcity in developing countries. Vegetation trends are also closely related to sustainability issues, such as management of conservation areas and wildlife habitats. In this study, AVHRR and MODIS NDVI datasets have been used to assess the spatial tempora...

We present direct numerical simulations and Lagrangian averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling beha...

We study the regularity of a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is ut = ∇·(u∇(−∆)−1/2u). For definiteness, the problem is posed in {x ∈ RN , t ∈ R} with nonnegative initial data u(x, 0) that are integrable and decay at infinity. Previous papers have established the existence of mass-preserving, nonnegative ...

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We construct, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by "stat...

Von Bertalanffy proposed the differential equation m'(t) = p × m(t) a  - q × m(t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (Von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would p...

For a layered probabilistic shaping (PS) scheme with a general decoding metric, an achievable rate is derived using Gallager’s error exponent approach. Several instances for specific decoding metrics are discussed, including bit-metric decoding, interleaved coded modulation, and hard-decision decoding. It is shown that important previously known achievable rates can also be achieved by layered ...

We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C.A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.

We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created. The memory required to grow a cluster of mass s is of the order of s(strai...

Executive Summary In an ideal world, review and changes to computing curricula should be driven solely by academic concerns for the needs of students. The process should be informed by industry accreditation processes and international best practice (Hurst et al., 2001). However, Australian computing curricular review is often driven by the need for financial viability of programs with declinin...