
I.P. Bestsennyi
On the Reduction of Modalities in Deontic Calculi
Formal theories of deontic logic based on the Gensentype
propositional calculus are considered. Syntactic and semantic differences
between the aletic and deontological calculi are analyzed in the aspect of
reduction of sequences of successive modal signs
Keywords: modal logic, deontic calculi, Kripke semantic.
V.V. Varlamov
Mass Quantization and Lorentz Group
Mass spectrum of localized states of quantum microobjects is studied
in the framework of holistic (nonlocal) Heisenberg's scheme. As an object of a
fundamental level (potential reality), the quantum microobject exists outside
of spacetime. It is shown that state masses of lepton (except the neutrino)
and hadron sectors of matter spectrum are proportional to the rest mass of
electron with an accuracy of 0,41%.
Keywords: mass spectrum, Lorentz group, cyclic representations, mass formulae,
mass quantization.
V.A. Shaptsev
About Dependence in the Bernoulli Trials
Analytical representation of scheme is discussed in independent
Bernoulli trials by means of the ordered subsets of \(m\) (\(m < n\)) numbers of
successful and \(n  m\) numbers of failed tests. The probabilistic description of
\(P_{n}(m)\) is determined by summing the binomial formula \({p^{m}(1p)^{nm}}\) for all such
subsets rather than a simple multiplication by the number of combinations \(C_{n}^{m}\).
Some appropriate expressions are given for the probability of success with \(k > 2\) outcome of the experiments for the cases of equal and different probabilities of outcomes in different trials. In these symbolics, expressions for
calculating the corresponding probabilities of the number of successful tests
is specified in the presence of dependence of outcomes probabilities on a
parameter varying in time (from test to test), regularly or accidentally. Thus,
the basis is created for application of the scheme of dependent tests to
estimate the probabilistic characteristics of complex stochastic systems,
network architectures, in particular, characterized by some varying measure of
quality. In conclusion, we present the expression for the mathematical
expectation of the probability of m successful trials out of $n$ in the case of
random parameter on which the probabilities of outcomes depend. Hypothesis
about the possibility of using finitedimensional characteristic function of
the random parameter in the corresponding expression for the case of
exponential dependence of the probability of the outcome from the random
parameter is written.
Keywords: independent Bernoulli trials, ordered subsets of tests numbers,
dependent tests.
V.N. Stepanov
The Method of Spherical Harmonics for Integral Transforms on a Sphere
The integral convolutiontype equations of the first
kind on the sphere are important for the geometric tomography.
They have been studied by many researchers. In this paper, we
consider the uniqueness and stability of solutions of such
equations. We prove the uniqueness of the solution for the
equation with the kernel of convolution type and obtain a formula for
the average value of a function on a subsphere. The latter is used
for the deriving of the inversion formula of Radon spherical
transformation on sphere. For the BlaschkeLevy equation and for
the convolution type singular integral equations of the linear
transfer theory, the uniqueness theorems are proved and find
estimates for the stability of solutions are found.
In all the cases we use the expansion of a function into series of spherical harmonics.
Keywords: geometric tomography, convolutiontype equations of
the first kind, uniqueness, stability, Radon spherical transform,
inversion formula, BlaschkeLevy equation, equation with a
singular kernel.
Applied Mathematics and Modeling
S.V. Belim,
T.B. Smirnova,
A.N. Mironenko
Application of an Associative Rules Method to the Activities
Analysis of Public Organizations
In the article the activities indicators analysis method of public
organizations is developed. The method of the associative rules is used.
Transactions are created of polling questionnaires. From coded responses of
questionnaires the associative rules are obtained. The rules possessing high support and
confidence are selected. On the basis of the associative rules the oriented weighted
correlations graph is constructed. On this graph search of communities is executed. The
selected community allowed to reveal activities factors of public organizations the most
tightly connected with each other.
Keywords: associative rules, public organizations, community, Data Mining.
V.P. Golubyatnikov
The Existence of a Stable Cycle in a Model of a Molecular Repressor
We consider nonlinear 6dimensional dynamical system which describes a
model of functioning of one simple molecular repressilator. We find sufficient conditions
of existence of a stable cycle in the phase portrait of this system.
Keywords: nonlinear dynamical system, gene network models, hyperbolic stationary points,
cycles, Brouwer's fixedpoint theorem, stability.
L.A. Volodchenkova, A.K. Guts
Equilibrium Dynamics of Forest Ecosystems Based on the Relationship ”VegetationSoil”
In the article the Nash equilibrium state for the forest ecosystems based on
the relationship ”vegetationsoil” and the theory of differential games are investigated.
Keywords: The Nash equilibrium, forest ecosystem, soil, vegetation, differential games.
V.A. Shovin, V.V. Goltyapin
Latency Analysis Based on Penalty Method for Multidimensional Binary Indicators
A comparison of following classification algorithms with learning is carried
out: FORDIASIMPT, latency analysis based on penalty method, KORA, naive Bayes classifier,
knearest neighbors algorithm, decision tree based on information growth and reduction of
the average entropy in an example of multidimensional binary indicators.
Keywords: classification with learning, FORDIASIMPT, latency analysis, penalty
method, KORA, naive Bayes classifier, knearest neighbors algorithm, decision tree.
V.A. Shovin
FRiSCompactness of Groups of Patients with Hypertension
The compactness of groups of patients with hypertension before and after
physiotherapy calculates by FRiS function. The ”defenses” of groups of patients is
determined by counting the number of nearest neighbors of each group of objects that
alternate FRiS function. The article offers a special FRiS function that improves the
accuracy of statistical estimates of the compactness of classes. As the result of the
calculations, it turned out that from the group of the patients ”after physical therapy”
a compact group is allocated, while the objects of the third part were not protected by
objects of the own group. From a medical point of view, it seems to be interpreted as a
positive effect of treatment for some patients.
Keywords: FRiS compact function, hypertension.
N.S. Novakovskiy
Analytical and Numerical Reconstruction of Generalized Central Compression Wave’s Sound Characteristics
Abstract. The results of analytical and numerical simulations of onedimensional ideal
gas shockfree strong compression problem while compression piston’s radius is not
decrease are presented. The analytic formula for generalized compression Riemann wave’s
sound characteristics is the main result. Comparison of the formula with calculation of
the problem by characteristic method in time decreasing case is also presented. Obtained
formulas for sound characteristics was used to calculate gasdynamic characteristic
(velocity, density, etc.) of ideal gas layer while time increase. The computational
domain is the area between compression piston and the last sound characteristic of
generalized Riemann wave. The main results of numerical simulations are shown in
graphs and tables.
Keywords: gas strong compression, the characteristic series method, solution feature.
D.N. Lavrov,
A.A. Laptev,
M.A Mamontova
Identification of a Parametric Model of Changes in the Number of Students Enrolled on a Small Sample
A parametric model of changes in the number of students of the University
with a small sample is built. The number of high school graduates in the region
is taken as an input parameter. With the help of information criteria, the order of
autoregressive movingaverage is selected. Applying the identification system feature
of Scilab, the forecast of the number of applicants for admission campaign in 2017
was made. A similar result was obtained through the identification of the model in
the form of the transfer function.
Keywords: parametric identification, autoregressivemovingaverage model, forecast
of the number of high school students, Akaike information criterion.
O. Kosheleva, V. Kreinovich
What is the Best Way to Add Large Number of Integers: NumberbyNumber as Computers Do or LowestDigitsThanNextDigitsEtc as we Humans Do?
When we need to add several integers, computers add them one by
one, while we usually add them digit by digit: first, we add all
the lowest digits, then we add all next lowest digits, etc. Which
way is faster? Should we learn from computers or should we teach
computers to add several integers our way?
In this paper, we show that the computer way is faster. This adds
one more example to the list of cases when computerbased
arithmetic algorithms are much more efficient than the algorithms
that we humans normally use.
Keywords: digits, adding, calculating
Computer Science
A.A. Senkovskaya, I.I. Furayeva
Modelling and Optimization of Allocation of Human Resources and Classroom University Fund on the Basis of the Curriculum Analysis
The main reasons for the need for a preliminary analysis of the initial data
for the calculation of teaching loads are presented. We confirmed the presence of factors
that affect the optimal distribution of the teaching load, such as a classroom university
fund, threading of groups and other. The study is based on the analysis and
subsequent optimization of the university curriculum. The curricula for the current
academic year of Kazakh University of Economy, Finance and International Trade
(Astana, Kazakhstan) were used as the initial data, as well as academic calendars and
rules for the organization of educational process on credit technology in the Republic of
Kazakhstan.
Keywords: optimization, modelling, curriculum, teaching load, classroom fund.
G. Muela, C. Servin, V. Kreinovich
How to Make Machine Learning Robust Against Adversarial Inputs
It has been recently shown that it is possible
to "cheat" many machine learning algorithms  i.e., to perform
minor modifications of the inputs that would lead to a wrong
classification. This feature can be used by adversaries to avoid
spam detection, to create a wrong identification allowing access
to classified information, etc. In this paper, we propose a
solution to this problem: namely, instead of applying the original
machine learning algorithm to the original inputs, we should first
perform a random modification of these inputs. Since machine
learning algorithms perform well on random data, such a random
modification ensures us that the algorithm will, with a high
probability, work correctly on the modified inputs. An additional
advantage of this idea is that it also provides an additional
privacy protection.
Keywords: machine learning, adversarial inputs, robust learning
Information Security
D.M. Brechka, A.A. Litvinenko
Ðàçðàáîòêà ñèñòåìû ìàíäàòíîãî óïðàâëåíèÿ äîñòóïîì äëÿ îïåðàöèîííûõ ñèñòåì ñåìåéñòâà Windows
Abstract. The article describes a development of Mandatory Access Control System
for Windows operating system. It is proposed the approach of creating the minifilter
driver for the file system to intercept application calls. The interface of the Mandatory
Access Control system, and the results of testing are described.
Keywords: Mandatory Access Control, operating system, Windows, driver, access
control, subjects, objects.