The article presents a mathematical model of the effect on ion transport electro convection salt in non-smooth camera channel desalting electro dialysis apparatus in the presence of forced convection. The basic rules of process of electro convection are revealed
We propose a mathematical model of ion transport binary salt in electroosmotic flow in a capillary. The capillary is open on one side and immersed in a vessel of large volume, in which the concentration of the solution is maintained constant, and the other side closed ion exchange membrane. The walls are considered wettable, i.e. the solution adheres to the walls. This means that the mathematical modeling used to rate the condition of sticking. We study the boundary value problem for a coupled system of equations Nernst, Planck, Poisson and Navier-Stokes equations. Used boundary conditions of general form. The mathematical model is based on the general laws of transport and contains no adjustable parameters. Using this model, the basic laws of ion transport salt solution liquid flow, the emergence and development electroconvection, distribution of concentration of salt ions in the capillary with a small change in time, ie, in the initial (transitional) regime. We have identified the presence of ion-exchange membrane surface electroconvective vortices and their influence on the mechanisms of ion transport of salt and fluid movement in different areas of the capillary. A feature of the capillary transport is to the right of the vortex region stagnant areas with a higher concentration of ions
The article analyzes the various approaches to the mathematical modeling of financial pyramids. It considered “economically rational subject”, game approach and the approach of Dubovsky. In this article, the mathematical models of the unproblematic approaches examined; we also analyzed their characteristics, including the dependence of the lifetime of the pyramid of accrued interest and the number of clients, the maximum possible profit of the founders of the pyramid, etc. This work analyzes the various options of the campaign, including whether the implicit advertising company, which arises from the spread of the financial company clients and rumors about their income
This article is devoted to the analysis of different cases of changing the number of customers of the financial pyramid and the establishment of the basic rules of the pyramid schemes on the basis of continuous models, and it is a continuation of works [1, 2], which had formulas to simulate the amount collected by the pyramid scheme and it considers the discrete models
This article analyzes the changes in the number of cases of various clients of the pyramid and the establishment of the basic rules of the pyramid schemes based on discrete models. The article is also a continuation of previous work [1], which had formulas to simulate the amount collected by the pyramid scheme
In the article we build a mathematical model of elec-tro-diffusion of ions in the diffusion layer of a mem-brane system complicated by the occurrence of the previous slow homogeneous chemical reaction with the condition of electrical neutrality of the solution. We have set a two-point boundary value problem and developed a method to solve it; we have given an algorithm and a numerical method for solving it in Comsol 3.5 environment. The formula for limiting kinetic current was derived. Some of the model’s capabilities to describe the properties of the system are given
This article continues the works [1,2], devoted to the theoretical study of the basic laws of electroconvection
caused by natural or artificial inhomogeneous conductivity of ion-exchange membranes in a smooth rectangular channel electrodialysis desalination unit. For this purpose, a mathematical model was created for a binary electrolyte electroconvection at overlimiting current modes in the form of a boundary value problem for a coupled system of the Nernst-Planck-Poisson and Navier-Stokes equations. We have studied the influence of heterogeneity on the ion-exchange membranes and ion transport electroconvection salt, calculated currentvoltage characteristic. The possibility of intensification of mass transfer due to the surface modification of ion exchange membranes was also shown
The article is devoted to development of effective and adequate mathematical models of an estimation of a financial and economic condition of region and meeting program toolkit with use of multivariate statistical models and fuzzy logic systems
The federal program on essential drugs provision
(EDP) is one of the most significant and socially
important state projects; it is directed to the reduction
of morbidity and mortality together with the
improvement of life quality of the society and its
social climate. In accordance with the federal law “On
social state assistance” from 17.07.1999 №178- FL,
the essence of the program is that medical recipes are
dispensed for preferential medicines to be received by
federal program participants. The medical-economic
control (MEC) of the drugs designation and provision
of federal benefit recipients is performed basing on the
automated registries examination of released drugs.
The number of passed and failed examination recipes
is determined according to the registers processing
results. A certain percentage of the accepted for
payment prescriptions is a subject for MEC. For the
purpose of the recipes selection for testing, the paper
proposes the mathematical models of criteria
application and MEC-planning. The game model of
organization and MEC performance in health care
organizations is build basing on the theory of games.
The considered play model suggests that the health
services quality examination need to be adjusted and
some strategies are to be improved. The solution on
the planning of checked recipes number allows to
perform the inspection of all the health care
organizations, involved in EDP program
When developing management solutions with the
aim of joint consideration and comparison of
various factors, partial removal of uncertainty is
widely used ratings. In the theory of decisionmaking
in almost the same sense, we use the terms
"composite index" or "integrated indicator". The
article is devoted to the mathematical theory of
ratings as tools for studying socio-economic
systems. We considered, primarily, linear ratings
which is a linear function from a single (private)
indicators (factors, criteria), constructed using the
coefficients of importance (weightiness,
importance). The study discusses the factors
affecting the magnitude of the ratings. Three groups
of causes affect the value of a line ranking: the ways
of measurement of individual indicators, the choice
of the set of indicators; the values of the coefficients
of importance. We considered binary ratings when
the rating takes two values. To compare the
proposed rankings we use a new indicator of the
quality of diagnostics and prognostic power.
Significantly, in many managerial situations,
significant differences between objects are identified
using any rating. According to the fundamental
results of stability theory, the same source data
should be processed in several ways. Matching
findings, obtained using multiple methods, likely
reflect the properties of reality. The difference is the
result of a subjective selection method. When using
the results of the comparison of objects according to
several indicators (criteria ratings), including in
dynamics, very useful is the selection of the Pareto
set. We discuss the examples of the application of
the decision theory, expert evaluations and rankings
when developing complex technical systems