Zipf’s law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language communication systems emerge at an abrupt phase transition in the fidelity of mappings between symbols and objects. Since the phase transition approximates the Heavis...

The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass–luminosity relation to convert a luminosity function to a mass function, I predict the mass-luminosity relation from assumed mass functions and the luminosity functions of Jahreiss &Wielen (1997) and Gould, Bahcall & Flynn (1997). Comparison of the resulting mass–luminosity relations with data for bin...

We present numerical testing results of our mass function derived in our previous paper, and compare the testing results with those of the popular Press-Schechter (PS) mass function. Two fiducial models are considered for the test: the scale-free power-law spectra P (k) ∝ k with spectral indices n = −1, 0 and the standard cold dark matter (SCDM) model with Ω = 1 and h = 0.5. For the power-law m...

The macroscopic quantum states of a condensed neutral Bose gas in one-dimensional power-law traps are obtained by solving the Gross-Pitaevskii equation numerically. A suitable candidate for a trial wave function for the variational calculation of the ground-state energy is suggested. It is shown that the suggested function exp(−r), where k is the power of the trap, produces a lower ground-state...

We can observe a power law in critical phenomena in natural sciences. Such a power law is also empirically exhibited in many economic phenomena. In one of the older studies conducted approximately 120 years ago, Pareto first reported that the probability density function of personal wealth in Italy follows a power law [1]. Following this research, the power law was also found to hold for city s...

For single colloidal Ag nanoaggregates, covered with either large or small amounts of citrate anions, blinking surface-enhanced Raman scattering (SERS) of anionic thiacyanine was measured and analyzed by a truncated power law. The power law without and with an exponential function reproduces a probability distribution for bright and dark SERS events versus their duration times, respectively. On...

The paper deals with the numerical simulations of steady flows if incompressible fluids whose stress-strain relation is given through an implicit function. In particular, the stresspower law is studied and compared to the classical power law. We propose several formulations of the problem, their stable approximations and particular examples of finite element spaces. The method is demonstrated b...

| In this note a continuous feedback control law with time-periodic terms is derived for the control of non-holonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector elds are homogeneou...