We give a method for obtaining radially symmetric solutions for the critical exponent problem ?u + a(x)u = u q + u 2 ?1 in R N u > 0 and R R N jruj 2 < 1 where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant ao > 0. We remark that, diierently from the literature, we do not require any conditions on a at innnity.

This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are also given on real data, both new data sets and well-studied data sets. All data and tools used are freely available for download along with simple “recipes” wh...

A one-dimensional tight-binding Hamiltonian describes the evolution of a single impurity interacting locally with N electrons. The impurity spectral function has a power-law singularity A(ω) ∝| ω− ω0 |−1+β with the same exponent β that characterizes the logarithmic decay of the quasiparticle weight Z with the number of electrons N , Z ∝ N−β. The exponent β is computed by (1) perturbation theory...

We study the asymptotic expansions with respect to h of

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent α ≈ 1.1 for intermediate and with exponent γ ≈ 0.6 for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a ...

We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: D t u(t, x) = Bu + u · Ẇ , where D t is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R and Ẇ a time homogeneous fractional ...

We consider the role of finite size effects on the value of the effective Hurst exponent H . This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer’s identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H = 1/2) i...

An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent alpha(min) that characterizes the "hottest" region of the harmonic measure and the fractal dimension D of the cluster, i.e., D=1+alpha(min). Due to lack of accurate direct measurements of both D and alpha(min), this conjecture ...

The results of kinetic Monte Carlo simulations of epitaxial growth on fcc~100! and bcc~100! surfaces in which the correct crystal geometry is taken into account are reported. The existence of downward funneling to fourfold hollow sites leads to a downward current for large angles and to angle selection as observed in a variety of experiments. We have used our model to simulate Fe/Fe~100! deposi...