Shannon[1] and Yavuz[2] estimated the entropy of real documents. This note drives an upper bound of entropy from the power law. Let D be a set of documents and f r(w) be the number of occurrences of a word w in the document. Given an interger k, we denote by F (k) the number of words whose frequency is k, i.e., F (k) = ♯{w ∈ D | f r(w) = k}. The entropy of the document set D is defined by E(D) ...

The struggle for power has been a persistent phenomenon throughout history, involving the rulers, general public, and various other interest groups. As one of these groups, the legal community has been in a unique position to regulate the relationship between the ruler and the public because of its dual responsibilities to provide services to the public and to impose constraints on the rulers. ...

Power-law distributions describe many phenomena related to rock fracture. Data collected to measure the parameters of such distributions only represent samples from some underlying population. Without proper consideration of the scale and size limitations of such data, estimates of the population parameters, particularly the exponent D, are likely to be biased. A Monte Carlo simulation of the s...

We perform time-resolved spectroscopy on the prompt emission in gammaray bursts (GRBs) and identify a thermal, photospheric component peaking at a temperature of a few hundreds keV. This peak does not necessarily coincide with the broad band (keV-GeV) power peak. We show that this thermal component exhibits a characteristic temporal behavior. We study a sample of 56 long bursts, all strong enou...

As part of a global analysis of deep star counts to constrain scenarii of galaxy formation and evolution, we investigate possible links between the galactic spheroid and the dark matter halo. A wide set of deep star counts at high and intermediate galactic latitudes is used to determine the large scale density law of the spheroid. Assuming a power density law, the exponent, flattening, local de...

A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the...

OBJECTIVE To determine the power-law exponents (D) of emphysema hole-size distributions as a competent emphysema index. Robustness to extreme breath-hold-level variations and correlations with clinical parameters for chronic obstructive pulmonary disease (COPD) were investigated and compared to a conventional emphysema index (EI%). PATIENTS AND METHODS A total of 100 patients with COPD (97 ma...

Many cosmological models of GRBs envision the energy source to be a cataclysmic stellar event leading to a relativistically expanding fireball. Particles are thought to be accelerated at shocks and produce nonthermal radiation. The highly variable temporal structure observed in most GRBs has significantly constrained models. By using different methods of statistical analysis in the time domain ...

We explore the behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form. We obtain expressions for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exh...

The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autoCorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral densit...