In this article we have proposed a method using the apparatus of fuzzy sets theory in conjunction with the five-factor model of Altman to assess the creditworthiness of the investigated companies. The Altman model was improved in two ways: by using
RMS integral approximation for the exact calculation of the quantitative credit assessment (probability of bankruptcy) and the application of the apparatus of fuzzy sets for ordered sets by the degree of confidence resulting probability
Is given the analysis of the development of expert estimates in our country after the war. Are presented a diversity of expert technologies, the main ideas and publications that help identify the driving forces of development in this promising scientific and practical field
The article presents a project of the Yang-Mills
amplifier. Amplifier model is a multilayer spherical
shell with increasing density towards the center. In
the center of the amplifier is the core of high-density
material. It is shown that in such a system, the
amplitude of the Yang-Mills waves rises from the
periphery to the center of several orders of
magnitude. The role of the Yang-Mills field in the
processes occurring in the nuclei of galaxies, stars
and planets is discussed. The data modeling to
strengthen the Yang-Mills field in the bowels of the
planet, with an atomic explosion, and in some special
devices such as the voltaic pile. To describe the
mechanism of amplification chromodynamics field
used as accurate results in Yang-Mills theory and
numerical models developed based on an average and
the exact equations as well. Among the exact
solutions of the special role played by the centralsymmetric
metric describing the contribution of the
Yang-Mills field in the speed of recession of galaxies.
Among the approximate numerical models can be
noted the eight-scalar model we have developed for
the simulation of non-linear color oscillations and
chaos in the Yang-Mills theory. Earlier models were
investigated spatio-temporal oscillations of the YangMills
theory in the case of three and eight colors. The
results of numerical simulation show that the
nonlinear interaction does not lead to a spatial mixing
of colors as it might be in the case of turbulent
diffusion. Depending on the system parameters there
is a suppression of the amplitude of the oscillations
the first three by five colors or vice versa. The kinetic
energy fluctuations or shared equally between the
color components, or dominated by the kinetic energy
of repressed groups of colors. In the present study, we
found that amplification chromodynamic field leads
to a sharp increase in the amplitude of the suppressed
color, which can lead to an increase in entropy,
excitation of nuclear reactions and decays particles
The core of applied statistics is statistics in spaces of arbitrary nature, based on the use of distances and optimization problems. This article discusses the various distances in spaces of statistical data, in particular, their conclusions on the basis of appropriate systems of axioms. The conditions and proofs of theorems first published in scientific periodicals
The article discusses the excitation of electromagnetic radiation, nuclear reactions and decays of particles by the acceleration of charges, atomic nuclei and the macroscopic volumes of matter. The motion of charged particles in a magnetic trap used for plasma confinement was computed. We propose a model of the electromagnetic radiation of a charge moving in a non-inertial reference frame in general relativity. We have also constructed a theory of perturbation with using a wave equation with small parameters, taking into account a characteristic radius of the trajectory of the electrons as they move in a magnetic field. It was found that in the first approximation, the radiation back-reaction force depends on the acceleration of the charge. For the simulating of processes in hadrons and nuclei we used Yang-Mills theory and the metric, describes the acceleration and rotating reference frame in general relativity. We consider the scalar glueball model for an arbitrary dependence of acceleration and angular velocity of the system on time. The numerical model of wave propagation in non-inertial reference frame for the geometry of system of one, two or three spatial dimensions was tested. In the numerical experiments shown that the acceleration of the system leads to instability, leading to an unlimited increase in the amplitude of waves, which is interpreted as a decay of system. It was found that there are critical values of acceleration above which the instability develops
In the article we have concerned the researched mathematical method for the process of droplet dispersion on a horizontal surface. On the basis of the asymptotical method and the method of the division of variables we have found the approximate analytical solution of the problem
The fractal and prefractal graph are described in the
article. The basic definitions and notation are
proposed, the procedure for constructing prefractal
graph, the operation of replacement vertex by seed is
given
The article presents the theorem of Chebyshev on the
distribution of primes, considering functions that
approximated prime numbers. We have also
considered a new function, which is quite good for
approximation of prime numbers. A review of the
known results on distribution of prime numbers is
given as well
In this article, we consider quantum gravity in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation, and matter waves associated with gravitational waves by a simple equation. The mechanism of generation of baryonic matter of dark energy is discussed
This work deals with the numerical method of solution of integral equation with the kernel, which has the first order singularities by two variables. The solution is approximated by piecewise linear functions by every variable. The coefficients are
determined by the collocation method. The singular integrals of basic functions are calculated exact