We discuss the Bose-Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis's nonextensive statistical mechanics. We study the corrections to the standard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The re...

We define and study a family of Markov processes with state space the compact set of all partitions of N that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of exchangeable fragmentation as defined by Bertoin and of homogenous coalescence as defined by Pitman and Schweinsberg or Möhle and Sagitov. We show that they admit a unique invariant probabil...

In this chapter, we introduce a powerful solution for complex problems that are required to be solved by using neural nets. This is done by using modular neural nets (MNNs) that di‐ vide the input space into several homogenous regions. Such approach is applied to imple‐ ment XOR functions, 16 logic function on one bit level, and 2-bit digital multiplier. Compared to previous nonmodular designs,...

Stratified flows can develop powerful vertical drafts - resulting from a resonant interaction of gravity waves and turbulent motions when the system explores certain region parameter space which is geophysical interest. These extreme (detected through kurtosis velocity, ${K}_{w}$) do generate turbulence, leading to enhanced local-in-time-and-space kinetic (${\stackrel{\ifmmode \hat{}\else \^{}\...

The present investigation is to study the surface waves propagation with imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of Green-Lindsay (G-L model) theory. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velo...

In this paper we consider the class (θA, B) of parameter-dependent linear systems given by matrices A ∈ ℂn×n and B ℂn×m. This is interest for several applications frequently met task such to steer origin toward a target family f(θ) using an input that independent from parameter. provides collection necessary sufficient conditions ensemble reachability these systems.