Resource-bounded dimension is a complexity-theoretic extension of classical Hausdorff dimension introduced by Lutz (2000) in order to investigate the fractal structure of sets that have resource-bounded measure 0. For example, while it has long been known that the Boolean circuit-size complexity class SIZE ( α n

We derive a new lower bound p c > 0:8107 for the critical value of Mandelbrot's dyadic fractal percolation model. This is achieved by taking the random fractal set (to be denoted A 1) and adding to it a countable number of straight line segments, chosen in a certain (non-random) way as to simplify greatly the connectivity structure. We denote the modiied model thus obtained by C 1 , and write C...

As Part III of a comprehensive evaluation of CMAQ for the summer 1999 Southern Oxidants Study episode, the observed number (N), volume (V), surface area (S), and size distributions of accumulation-mode particles during the Aerosol Research Inhalation Epidemiological Study (ARIES) are used to evaluate CMAQ’s capability in reproducing PM size distributions. CMAQ underpredicts V, S, and geometric ...

Different fractal antennas based on aperture coupled feeding technique are studied, analysed and compared for size reduction, low profile, and good omini‐dirctional pattern suitable for RFID applications. The results are used as a guideline to propose modified fractal shapes patch antennas having lower size reduction parameters. All the designed antennas are bas...

Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from Ndimensional hypercomplex numbers (N a power of 2, and at least 4) can represent singularities and, as N → ∞, fractals – and thereby, scale-free networks. Any integer > 8 and not a power of 2 generates a meta-fractal or Sky when it is interpreted as the strut constant (S) of an ensemble of octahedral vertex figures called Box-Kite...

We consider asymptotic bounds for the discrepancy of point sets on a class of fractal sets. By a method of R. Alexander, we prove that for a wide class of fractals, the L 2-discrepancy (and consequently also the worst-case discrepancy) of an N-point set with respect to halfspaces is at least of the order N ?1=2?1=2s , where s is the Hausdorr dimension of the fractal. We also show that for many ...

We study an aggregation-disaggregation model which is relevant to biological processes such as the growth of senile plaques in Alzheimer disease. In this model, during the aggregation each deposited particle has a probability of producing a new particle in its vicinity, while during disaggregation the particles are anihilated randomly. The model is held in a dynamic equilibrium by a feedback me...

We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to the distribution of galaxies. If the distribution of galaxies forms a fractal set, then this property results in a number of scaling laws to be fulfilled by...

The distribution function of local amplitudes, t = ~@(ro)~, of single-particle states in disordered conductors is calculated on the basis of a reduced version of the supersymmetric o model solved using the saddle-point method. Although the distribution of relatively small amplitudes can be approxixnated by the universal Porter-Thomas formulas known from the random-matrix theory, the asymptotica...