A study of the subdiffusion of small molecules in charged polyelectrolyte multilayers

A theoretical approach has been developed here to describe the slow diffusion of small charged molecules of sodium dithionite (S2O42−) in polyelectrolyte multilayers (PEMs) composed of polyallylamine hydrochloride (PAH) and polystyrene sulfonate (PSS), which is demonstrated here to be a case of subdifussion. Diffusion is measured experimentally by recording the quenching of the fluorescence of (7-nitrobenz-2-oxa-1,3-diazol-4yl) amino (NBD) labelled PAH layers assembled on silica particles by flow cytometry. NBD is reduced when it encounters dithionite leading to the disappearance of the fluorescence. The fluorescence decay curves show a slow diffusion of dithionite, that does not follow classical Fickean law. Dithionite diffusion in the PEMs is shown to be a non-Markovian process and the slow diffusion can be described via diffusion equations with fractional time derivatives. Results are explained assuming subdifussion of dithionite in the PEMs, as a result of the trapping of the negatively charged dithionite in the positively charged layers of PAH.

An estimation of efficiency of filtering algorithms of state vector of small-sized observed object with non-Markovian approximation of trajectory

The article discusses the possibilities of estimating the states vectors of observation objects with the nonMarkovian approximation of the trajectories. The introduction discusses the problem consisting in the fact that the use of the approximation of the trajectory of the observed object by Markov processes in some cases can lead to a discrepancy between theory and practice. In the first section, we simulate the trajectories of observed objects when approximated by a Markovian process and indicate the limitations of this approach. It is proposed to use a multidimensional Gaussian distribution law for generating the trajectory of the observed object. In the second section, a study of the accuracy characteristics of a single-position angular-rangefinder radar and a three-position rangefinder radar are considered. Algorithms α-β, Kalman and nonlinear estimation are used in the modeling as estimation algorithms in these systems. The parameters and characteristics of the simulation are given. In the third part, the results of modeling the process of estimating the location of objects of observation with trajectories of movement approximated by non-Markov processes are presented. Modeling confirms the possibility of using submitted algorithms to estimate the trajectory of a smallsized object of observation, a trajectory model of which uses a multidimensional normal distribution law. It is pointed out that in several cases the filtering errors exceed the errors of a single measurement. This leads to the conclusion that further modification of the algorithms is necessary. In the final part, a recommendation is given on how to further reduce the estimation errors when using Kalman algorithms and nonlinear estimation.

Witnessing quantum memory in non-Markovian processes

We present a method to detect quantum memory in a non-Markovian process. We call a process Markovian when the environment does not provide a memory that retains correlations across different system-environment interactions. We define two types of non-Markovian processes, depending on the required memory being classical or quantum. We formalise this distinction using the process matrix formalism, through which a process is represented as a multipartite state. Within this formalism, a test for entanglement in a state can be mapped to a test for quantum memory in the corresponding process. This allows us to apply separability criteria and entanglement witnesses to the detection of quantum memory. We demonstrate the method in a simple model where both system and environment are single interacting qubits and map the parameters that lead to quantum memory. As with entanglement witnesses, our method of witnessing quantum memory provides a versatile experimental tool for open quantum systems.

Method of using the transitive graph of a Markovian process as part of ranking of heterogeneous items

Hierarchy analysis developed by Thomas Saaty is a closed logical structure that uses simple and well-substantiated rules that allow solving multicriterial problems that include both quantitative, and qualitative factors, whereby the quantitative factors can differ in terms of their dimensionality. The method is based on problem decomposition and its representation as a hierarchical arrangement, which allows including into such hierarchy all the knowledge the decision-maker has regarding the problem at hand and subsequent processing of decision-makers’ judgements. As the result, the relative degree of the interaction between the elements of such hierarchy can be identified and later quantified. Hierarchy analysis includes the procedure of multiple judgement synthesis, criteria priority definition and rating of the compared alternatives. The method’s significant limitation consists in the requirement of coherence of pairwise comparison matrices for correct definition of the weights of compared alternatives. The Aim of the paper is to examine a non-conventional method of solving the problem of alternative ratings estimation based on their pairwise comparisons that arises in the process of expert preference analysis in various fields of research. Approaches are discussed to the generation of pairwise comparison matrices taking into consideration the problem of coherence of such matrices and expert competence estimation. Method. The methods of hierarchy analysis, models and methods of the Markovian process theory were used. Result. The paper suggested a method of using the transitive graph of a Markovian process as part of expert ranking of items of a certain parent entity subject to the competence and qualification of the experts involved in the pairwise comparison. It is proposed to use steady-state probabilities of a Markovian process as the correlation of priorities (weights) of the compared items. The paper sets forth an algorithm for constructing the final scale of comparison taking into consideration the experts’ level of competence. Conclusion. The decision procedures, in which the experts are expected to choose the best alternatives out of the allowable set, are quite frequently used in a variety of fields for the purpose of estimation and objective priority definition, etc. The described method can be applied not only for comparing items, but also for solving more complicated problems of expert group estimation, i.e., planning and management, prediction, etc. The use of the method contributes to the objectivity of analysis, when comparing alternatives, taking into consideration various aspects of their consequences, as well as the decision-maker’s attitude to such consequences. The suggested model-based approach allows the decision-maker identifying and adjusting his/her preferences and, consequently, choosing the decisions according to such preferences, avoiding logical errors in long and complex reasoning chains. This approach can be used in group decision-making, description of the procedures that compensate a specific expert’s insufficient knowledge by using information provided by the other experts.

Stochastic Periodic Solution and Permanence of a Holling–Leslie Predator-Prey System with Impulsive Effects

Considering the environmental effects, a Holling–Leslie predator-prey system with impulsive and stochastic disturbance is proposed in this paper. Firstly, we prove that existence of periodic solution, the mean time boundness of variables is found by integral inequality, and we establish some sufficient conditions assuring the existencle of periodic Markovian process. Secondly, for periodic impulsive differential equation and system, it is different from previous research methods, by defining three restrictive conditions, we study the extinction and permanence in the mean of all species. Thirdly, by stochastic analysis method, we investigate the stochastic permanence of the system. Finally, some numerical simulations are given to illustrate the main results.

Determination of failure rate function on the basis оf the markovian process

The life cycle of a construction (or its element) is considered as markovian process with discrete states and continuous time. Five operational states have been accepted, in which the construction may be. The corresponding system of differential equations is obtained for the case of a homogeneous markovian process with a constant conversion rate (Kolmogorov system). The method of uncertain coefficients is applied to solve the system of equations in analytical form. The obtained solutions make it possible to determine the probability of finding the construction in a particular state as well as the most likely transition time from one operational state to another. Security function defined as the probability of not finding the construction in its last (inoperable) state and the failure rate function. The graphs of the probability of finding a construction in each of the five states, reliability and failure rate functions are presented and investigated. The obtained analytical dependences make it possible to determine the longevity and residual life of the work both individual elements and structures as a whole and optimize scheduling for ongoing maintenance work, significantly improve the performance of the structure, reduce the cost of repair work and extend the life of the structure.