arXiv subjects
Publications and source records attributed to Kim Chol-jun.
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a ``superposition'' model, which leads to an asymptotic power-law distribution of the number of occurrences (or frequency) of words, that is, Zipf's law. The model is well consistent with observations.
Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without introduction of delicate economic models but only on the statistical way. A convexity in the low-size part of the distribution is one peculiarity of the theory, which is absent in the power-law distribution. We found that the distribution of the geometrically growing system could have a trend to flatten in the evolution of the system so that the relative ratio of size within the system increases. The system can act as a reverse machine to covert a diffusion in parametric space to a concentration in the size distribution.
We show that while the Fourier transform can figure only an "intensity" of a periodic signal, there is an additional information embedded, which is a "coherence" of the signal. Supposing that the periodicity is reflected only on the "coherence," we introduce a time stability as a measure of "coherence" excluding the "intensity," i.e. amplitude of signal. In stead of classical strength-based significance, where strength implies the power or amplitude, we adopt a stability-based significance as criterion to choose cycles in a random signal. We inspect the time-stable solar periodicities and show that most periodicities discovered in exterior solar activities such as the solar wind inhere in interior solar activity such as the sunspot and that the time stability can be an effective tool in spectral analysis of stochastic solar activity.
The spectral analysis with stochastic significance cannot distinguish the spurious cycles effectively, because a non-stationary signal can make a significant peak in spectrum. I show that the random separation between the grand extremes such as grand maxima and minima in solar activity can make a spurious but significant peak in spectrum. And it is possible to pick even the weak stable cycle by applying an averaging down-sampling and the differencing to a random signal. This is because both operations variously change the height of peak in spectrum and the spurious cycle is in turn unstable in both operations. I introduce a samplogram showing these operations and stability intuitively.
We investigated the Korean records of naked-eye sunspot observations and found an implication of periodicity of about 200-year. Adding the Chinese records we showed that the historical naked-eye sunspot observations have the similar periodicity. Recent some works showed that there would be no intrinsic periodicities except 11-year cycle. We adopt the new approach called samplogram to test sampling stability of cycles in terms of power spectra and difference series and show that the Suess/de Vries cycle of about 207-year is a deterministic cycle of the stochastic solar activity. Also we show that occurrences of grand minimum are not necessarily expected with the Suess/de Vries cycle and it is possible to appear double or multiple grand maxima without a grand minimum within them.
A role of the scalar-matter direct coupling in the evolution of scalar-tensor gravity was studied. If the coupling functions in the generalized scalar-tensor gravity satisfy a definite equation the scalar-tensor gravity is reduced to Einstein's tensor gravity. We consider the issue in Jordan frame and then Einstein frame. It is shown that the coupling strength in the right hand side of the master equation obtained in Damour and Nordtvedt(1993) must be added by a coupling strength $\hatβ$ which characterizes the scalar-matter direct coupling. If a minimum of potential $\ln C(φ)$ does not coincide with one of the potential $\ln A(φ)$ or the potential $\ln C(φ)$ does not have any minimum and is a monotonic function, then the attractor mechanism of scalar-tensor gravity toward pure general relativity should be modified, and the combined potential $\ln A(φ)+\ln C(φ)$ will determine the attractor mechanism.