Zipf’s law appears in many application areas but does not have a closed form expression, which may make its use cumbersome. Since it coincides with the truncated version of the Zeta distribution, in this paper we propose three approximate closed form expressions for the truncated Zeta distribution, which may be employed for Zipf’s law as well. The three approximations are based on the replaceme...

The Shilkret integral is maxitive (i.e., the integral of a pointwise supremum of functions is the supremum of their integrals), but defined only for nonnegative functions. In the present paper, some properties of this integral (such as subadditivity and a law of iterated expectations) are studied, in comparison with the additive and Choquet integrals. Furthermore, the definition of a maxitive i...

in this paper, the problem of finite time stabilization for guidance system is investigated and a novel nonlinear guidance law against maneuvering targets is proposed based on the principles of parallel navigation. the proposed law is developed using two variable structure control techniques. by applying finite time integral sliding mode and combining it with terminal sliding mode, a new guidan...

Techniques for using the Monte Carlo method to evaluate fuzzy Riemann integrals and improper fuzzy Riemann integrals are proposed in this paper. Owing to the α-level set of the (improper) fuzzy Riemann integral being the closed interval whose end points are the classical (improper) Riemann integrals, it is possible to invoke the Monte Carlo method to approximate the end points of the α-level cl...

We present an INTEGRAL data analysis of the X-ray transient SAX J2103.5+4545 during two outbursts detected in December 2002. The INTEGRAL coordinates and error circle agree with the position of the recently proposed optical counterpart. A power-law plus cutoff model provided a good fit to the 4–150 keV spectrum yielding a photon index of 1.0±0.1, a cutoff energy E cut = 7.6 ± 2.0 keV and a fold...

The recent (14 July 2015) flyby of NASA’s New Horizons spacecraft of the dwarf planet Pluto resulted in the first high-resolution images of the geological surfacefeatures of Pluto. Since previous studies showed that the impact crater size-frequency distribution (SFD) of different celestial objects of our solar system follows power-laws, the aim of the present analysis was to determine, for the ...

We study self-similar solutions of the kinetic equation for MHD wave turbulence derived in (Galtier S et al 2000 J. Plasma Phys. 63 447–88). Motivated by finding the asymptotic behaviour of solutions for initial value problems, we formulate a nonlinear eigenvalue problem comprising in finding a number x∗ such that the self-similar shape function f (η) would have a powerlaw asymptotic η−x ∗ at...