Intensity parameters of neodymium ions in doped SrWO4 monocrystals, grown by modified Czochralski method, are calculated. Changes in the values of these parameters when replacing the tungsten atoms W6+ atoms of molybdenum Ðœo6+ in the matrices SrMeO4 with the scheelite structure due to less screening of the nucleus Ðœo6+ compared with W6+ are shown
The purpose of mathematical statistics is
development of methods for the data analysis
intended to solve applied problems. Over time,
approaches to the development of data analysis
methods have changed. A hundred years ago, it was
assumed, that the distributions of the data have a
certain type, for example, they are normal
distributions, and on that assumption they developed
a statistical theory. The next stage, in the first place
in theoretical studies there are limit theorems. By
"small sample" we mean a sample, which can not be
applied to conclusions based on the limit theorems.
In each statistical problem there is a need to divide
the final sample sizes into two classes - those for
which you can apply the limit theorems, and those
for which you can not do it because of the risk of
incorrect conclusions. To solve this problem we
often used the Monte Carlo method. More complex
problems arise when studying the effect on the
properties of statistical procedures for data analysis
of various deviations from the original assumptions.
To study such impact, we often used the Monte
Carlo method as well. The basic (and not solved in a
general way) problem of the study of the stability of
the findings in the presence of deviations from the
parametric families of distributions is the problem of
choosing some distributions for using in modeling.
We consider some examples of application of the
Monte Carlo method, relating to the activities of our
research team. We have also formulated basic
unsolved problems
The analysis of the various conditions of the two (four) laser radiation streams coherent addition was realized. It is shown that it is possible to create devices providing continuous subtraction of waves. In such radiation stream a continuous subtraction on the line can be replaced by the continuous addition on the photomultiplier by using a dispersive delay line. The research results can be used for creation of modern open atmospheric connection lines
The article presents the model of the large-scale clustering
of the matter in the universe. The base for mathematical
calculations is interval mathematics
The article presents the problem of spanning trees with
topological criteria and interval scales. We have
introduced relationship preferences and
incomparability to find the complete set of alternatives
in the case of interval scales. The base for
mathematical calculations is interval mathematics
Classic quantitative measure of the reliability of the models: F-measure by van Rijsbergen is based on counting the total number of correctly and incorrectly classified and not classified objects in the training sample. In multiclass classification systems, the facility can simultaneously apply to multiple classes. Accordingly, when the synthesis of the model description is used for formation of generalized images of many of the classes it belongs to. When using the model for classification, it is determined by the degree of similarity or divergence of the object with all classes, and a true-positive decision may be the membership of the object to several classes. The result of this classification may be that the object is not just rightly or wrongly relates or does not relate to different classes, both in the classical F-measure, but rightly or wrongly relates or does not relate to them in varying degrees. However, the classic F-measure does not count the fact that the object may in fact simultaneously belongs to multiple classes (multicrossover) and the fact that the classification result can be obtained with a different degree of similarity-differences of object classes (blurring). In the numerical example, the author states that with true-positive and true-negative decisions, the module similarities-differences of the object classes are much higher than for false-positive and false-negative decisions. It would therefore be rational to the extent that the reliability of the model to take into account not just the fact of true or false positive or negative decisions, but also to take into account the degree of confidence of the classifier in these decisions. In classifying big data we have revealed a large number of false-positive decisions with a low level of similarity, which, however, in total, contribute to reducing the reliability of the model. To overcome this problem, we propose a L2-measure, in which instead of the sum of levels of similarity we use the average similarity by different classifications. Thus, this work offers measures of the reliability of the models, called L1-measure and the L2 measure, mitigating and overcoming the shortcomings of the F-measures; these measures are described mathematically and their application is demonstrated on a simple numerical example. In the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we have implemented all these measures of the reliability of the models: F, L1 and L2
The article continues the cycle of their studies
associated with the formulation and development of
methods of construction of nonnegative solutions of
inverse problems for dynamic systems. In this article
the authors formulated and investigated inverse
problems for dynamic systems: model of Samuelsson–
Hicks. The technique of constructing non-negative
solutions of the studied inverse problems. This method
is based on the following scheme of the solution. First,
we have to identify the formulation of the direct
problem, then the formulation of the inverse. This
work investigates how correct the mathematical
models describing the dynamic economic system are.
Further, in the specified tabular solutions of the direct
problem, we have built a system of algebraic equations
containing the unknown estimated parameters of the
studied model. Then posed inverse problem is reduced
to solution of a problem of quadratic programming, the
solutions of which are defined in MS Excel. The
theoretical material is accompanied by the specific
example
The scientific publications review about a high-frequency electromagnetic field influence on the conductivity, the acidity and the reaction constant of different compounds of water solutions was made. It is shown, that a high-frequency electromagnetic field influence decreases with the impurity concentration growth
This work is a continuation of [1], which was devoted to
the investigation of the hydrodynamics of the experimental electrochemical cell with rotating disk cation exchange membrane. This article focuses on the transport of salt ions in a closed cell at different initial experimentation with modes of exact current regimes. The main regularities of transport of salt ions and membrane equal accessible surface were set
Researches in plasma methods for isotopes separation and analyze of the results were done. Results show high values of separation coefficient for intermediate products during the last years. It is shown by us, that these factors will be considerably reduced in the subsequent plasma processes and a way of freezing of high value of factor of division of isotopes