In this paper, we discuss a strategy for reducing a complex single molecule kinetic process to a set of generic structures (motifs) that are building blocks for a general kinetic scheme. In general, these motifs have complex kinetics (i.e., waiting time distribution functions) which are composed of fundamental kinetic steps. (1) First, we treat four different experimental single molecule measur...

In this note, we prove the generic Kobayashi volume measure hyperbolicity of singular directed varieties (X,V ), as soon as the canonical sheaf KV of V is big in the sense of Demailly.

We investigate the structure of the nonlocal closure relation in the kinetic equation for a soliton gas. This kinetic equation represents an integro-differential nonlinear system which has been recently shown to possess a number of remarkable properties and seems to be a representative of an entirely new class of integrable systems. In this paper, we identify the nonlocal kinetic closure relati...

On the basis of the Kadanoff-Baym (KB) version of the time-dependent Green’s function method a new ansatz for the approximation of a spectral function is offered. The ansatz possesses all the advantages of quasiparticle (QP) and extended quasiparticle (EQP) approximations and satisfies the KB-equation for a spectral function in the case of slightly non-equilibrium system when disturbances in sp...

We present a first attempt to derive the cosmological evolution of the kinetic luminosity function of AGN based on the joint evolution of the flat spectrum radio and hard X-ray selected AGN luminosity functions. An empirical correlation between jet power and radio core luminosity is found, which is consistent with the theoretical assumption that, below a certain Eddington ratio, SMBH accrete in...

The Kompaneets theory of photon kinetic evolution due to the Compton effect in the absence of absorption and emission is extended to the case of the Vlasov plasma wave oscillations. Under the assumption that the electron distribution function at equilibrium is perturbed by a solution of the linearised Vlasov equation in the long-wavelength limit, a solution of the Kompaneets kinetic equation fo...

E-learning is popularized so fast and Collaborative Learning (CL) becomes so important an instructional strategy. There are huge Group Session (GS) texts needed to be analyzed to evaluate CL, thus the automatic or semi-automatic methods of analyzing the GS texts become very important. In this paper we present a method called Interaction Analysis depended on Knowledge Extraction (IAKE) to analyz...