Frequency fluctuations of lasers cause a broadening of their line shapes. Although the relation between the frequency noise spectrum and the laser line shape has been studied extensively, no simple expression exists to evaluate the laser linewidth for frequency noise spectra that does not follow a power law. We present a simple approach to this relation with an approximate formula for evaluatio...

The gluon condensation in the proton as a dynamical model is used to treat series of unsolved puzzles sub-TeV gamma ray spectra, they include broken power-law blazar's radiation, hardening confusion 1ES 1426+428, Mkn 501, and recently recorded spectra GRB 180720B 190114C. We find that above anomalous phenomena energy can be understood with simple power law based on QCD effect.

Many self-gravitating systems often show scaling properties in their mass density, system size, velocities, and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse power law interaction. As a simple case, we consider the self-similar stationary solution in the collisionless Boltzmann equation with power law potential ...

1=f D noise occurs in an impressive variety of physical systems, and numerous complex theories have been proposed to explain it. We construct two relatively simple renewal processes whose power spectral densities vary as 1=f D : 1) a standard renewal point process, with 0 < D < 1; and 2) a nite-valued alternating renewal process, with 0 < D < 2. The resulting event number statistics, coincidenc...

Power-law distributions are essential in computational and statistical investigations of extreme events complex systems. The usual technique to generate power-law distributed data is first infer the scale exponent $\alpha$ using observed interest then sample from associated distribution. This approach has important limitations because it relies on a fixed (e.g., limited applicability testing {\...