IKBFU's Vestnik

# Physics, mathematics, and technology

### Mathematical Modeling

#### Application of dimension reduction methods in objects homogeneity evaluation: airport network analysis

Abstract

An application of dimension reduction methods in the analysis of the phenomena of socio-economic systems by analyzing the choice of direction of development of socio-economic development is considered. In particular it is shown that the use of algorithms dimension reduction methods the probability of error when estimating posterior probabilities of belonging to the class of homogeneous objects, obtained in the result of solving the problem of discriminant analysis

#### Joint modeling of elastic and acoustic waves in the Arctic

Abstract

Numerical solutions of seismic prospecting problems in the Arctic is presented. Results of numerical modeling of the explosive impact on the iceberg and earthquake impact on the oil storage are considered as well. The complete system of equations describing the state elastic body and a system of equations describing the acoustic field are solved using grid-characteristic method, the contact condition between the liquid and the solid is used on the border

### Differential geometry

#### Strongly mutual threefold distributions of projective space

Abstract

Construction of a general theory of a special class ( -distribution) of the regular threefold distributions ( -distribution ) of the projective space   consisting of a basic distribution of the 1st kind of r-dimensional planes   are equipped with the distribution of the 1st kind of m-dimensional planes   and equip distribution 1st the first kind of hyperplane elements (hyperplanes)   with the ratio of the incidence of the corresponding elements in the common center   is considered in this article. In this paper, these three distributions is considered as a immersed manifold. By virtue of the  -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements , (n-1)-dimensional linear elements   and hyperband distribution . However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately.

#### About horizontally vector lifts of tensor fields from the base to its tangent bundle

Abstract

The vector field of the type  , obtained fr om the tensor field   on a smooth manifold M to the tangent bundle  , arises in the study of infinitesimal affine transformations with a complete lift. The H-lift was introduced S. Tanno in 1974 in infinitesimal isometries on the tangent bundle with the complete lift. The definition of H’-lift given by the author in this paper. There are established the properties of the entered lift and founded the commutator  , wh ere  .

### Artificial Intelligence

#### Examples of the mathematical model of the management company

Abstract

The article discusses Two mathematical models of housing and utilities services organization as an example of a managing company are considered. The first model is based on balance equations of the organization. It takes into account and systematizes income and expenses of a managing company. The second model is presented in the form of the optimal control problem. Wherein, the discounted profit of the company was selected as an optimization element, whereas the costs of housing modernization were chosen as a control element.

### Theoretical and experimental physics

#### iltering of signals from noise by maximum likelihood method

Abstract

A method of filtering radar pulse on the background of the focus obtained by frequency interference. The basis of the method are the principles of the theory of optimal reception and position of the linear space of signals. Derived the basic expressions when filtering of the signal strength in the area of orthogonality of signal and noise, and their non-orthogonality. Equations for impulse and hour-tonyh characteristics of filters.

#### Modeling studies of filtering process of the radio pulse from noise

Abstract

Presents the results of model studies of the possibilities of a filtration of pulse centered on the background frequency interference maximum likelihood method. Basis are the principles of the theory of optimal reception and submission of the linear space of signals. Shows odnosno-ness of the solution of the filtering problem in the field of orthogonality of signal and noise, and their reorthogonalize . Submitted to evaluation of the dynamic range of the filter.

### Informatics and mathematical geophysics

#### Algorithms and software for building three-dimensional models of microseismic monitoring data

Abstract

Algorithms for constructing three-dimensional models of microseismic activity fields are described. The first approach is based on voxel models and involves the construction of polygonal surfaces of interpolated parameters of microseismic events. The second approach uses a triangulation algorithm based on the Delaunay criterion and α-shapes method. Software developed on the basis of the proposed algorithms, offers advanced graphical tools for the analysis and interpretation of microseismic multiparameter data

#### Experience of applying microseismic monitoring for control waterflood into Northern Truva deposits

Abstract

Results of passive microseismic monitoring of water injection into one of the wells of the carbonate deposits are presented. The maps of the spatial distribution of sources have prepared and the analysis of the dynamic parameters of microseismic events together with graphs of pressure and injection volumes has done. The possibility of operational control of the process of flooding is shown on the example of Northern Truva.

#### The structure of Vendian-Cambrian sediments of the Ilbokichskoye field

Abstract

The structure of Vendian sediments and overlying usolskaya formation sediments of the Lower Cambrian is described. The Vendian sediment (oskobinskaya formation) contaisn gas condensate deposit. The  sediments of vanavarskaya formation, carbonate Vendian and osinskiy horizon are perspective to search for hydrocarbons in the Ilbokichskiy license area. Therefore, learning the structure of Vendian and osinskiy horizon sediments is one of the most important factors in hydrocarbon deposits prediction.

#### An interpolation of a supervision system by RTD method

Abstract

One of the problems of interpretation of seismic data is that they are often measured on an irregular grid with large distances between the sources and receivers, which affects the outcome of processing. The article discusses the possibility of using the procedure RTD (Reverse Time Datuming) [1-4] to ob-tain the wave field with a dense and regular geometry of sources and receivers at some depth. The results of numerical testing are presented.

#### Algorithms of determining of bodies in a 3D irregular point cloud

Abstract

A technique for recognition of shapes of bodies in a 3D point cloud is de-scribed. At the first step cloud clustering is conducted using the criterion of maximum distance between the points to identify the bodies being determined. Then proceeding to voxel presentation is being done. Existence of a tetrahe-dron with its points in cloud points and size-limited sides for which the voxel being tested is internal is treated as a criterion of belongment of voxel to a body. A fast algorithm for voxel tetrahedron filling is developed and used for optimization. The work is a part of software for micro-seismic monitoring data processing.

### Other papers

#### About properties of Cauchy-type integral with a fixed point in the kernel in С1 space

Abstract

The Cauchy-type integral with a fixed point in the kernel is in the as-sumption that fixed point is on the exterior of a circle of RADIUS one. Set fields non-analyticity and the analyticity of the integral. Area non-analyticity naturally splits into two subareas , each of which the integral is calculated ac-cording to a specific formula. Non-analytical functions, which have integral Cauchy type with a fixed point in the kernel satisfies a certain differential equations. Using the method of linear differential operators is link integrals with a fixed point in the kernel with integral Cauchy type.