The technique of recovery of causative sources in case of strong interference of gravity fields using the continuous wavelet transform

The technique of processing gravimetric data is offered in this study. Offered technique based on wavelet transform with so-called «native» wavelet basis functions. Distinctive feature of the technique is a close relationship with both direct and inverse problems of gravimetry. It was shown that the peculiarity allows to quite simply and quickly location of causative sources even under of strong interference of gravity fields. Keywords: gravimetry; wavelet transform; anomaly; inverse problem.

Improving the accuracy of designing a delta robot for 3D printing

Currently, there is a need in the industry for design changes to existing installations, such as conveyor lines, various machine tools, 3D printers, and so on. Designing delta robots for 3D printers reveals the advantages of using delta robots as working parts of printers compared to traditional designs. In this article, the direct and inverse problems of the kinematics of the delta robot are solved in a geometric way. Also, dependencies for the search for angular velocities and accelerations of the input links were obtained, which allows in the future to design more accurate working bodies of 3D printers. The research was carried out through mathematical modeling.

Approach for the COVID-19 Epidemic Source Localization in Russia Based on Mathematical Modeling

The paper presents the results of statistical data from open sources on the development of the COVID-19 epidemic processing and a study сarried out to determine the place and time of its beginning in Russia. An overview of the existing models of the processes of the epidemic development and methods for solving direct and inverse problems of its analysis is given. A model for the development of the COVID-19 epidemic via a transport network of nine Russian cities is proposed: Moscow, St. Petersburg, Nizhny Novgorod, Rostov-on-Don, Krasnodar, Yekaterinburg, Novosibirsk, Khabarovsk and Vladivostok. The cities are selected both by geographic location and by the number of population. The model consists of twenty seven differential equations. An algorithm for reverse analysis of the epidemic model has been developed. The initial data for solving the problem were the data on the population, the intensity of process transitions from one state to another, as well as data on the infection rate of the population at given time moments. The paper also provides the results of a detailed analysis of the solution approaches to modeling the development of epidemics by type of model (basic SEIR model, SIRD model, adaptive behavioral model, modified SEIR models), and by country (in Poland, France, Spain, Greece and others) and an overview of the applications that can be solved using epidemic spread modeling. Additional environmental parameters that affect the modeling of the spread of epidemics and can be taken into account to improve the accuracy of the results are considered. Based on the results of the modeling, the most likely source cities of the epidemic beginning in Russia, as well as the moment of its beginning, have been identified. The reliability of the estimates obtained is largely determined by the reliability of the statistics used on the development of COVID-19 and the available data on transportation network, which are in the public domain.

The structure and features of the software for geophysical geometrical 3D inversions

The structure and features of a software package for 3D inversion of geophysical data are considered. The presented software package is focused on solving direct and inverse problems of electrical exploration and engineering geophysics. In addition to the parameters that determine physical properties of the medium, the software package allows you to restore the geometry parameters of the geophysical model, namely layer reliefs and boundaries of three-dimensional inclusions. The inclusions can be in the form of arbitrary hexagons or prisms with a polygonal base. The software package consists of four main subsystems: an interface, subsystems for solving direct and inverse problems, and a client-server part for performing calculations on remote computing nodes. The graphical interface consists of geophysicist-oriented pre- and postprocessor modules that allow you to describe the problem and present the results of its solution in user-friendly terms. To solve direct problems, the finite element method and the technology for dividing the field into normal and anomalous components are used. At the same time, special methods of discretization of the computational domain are used, which make it possible to take into account both the complex three-dimensional structure of the environment and the presence of man-made objects (wells) in the computational domain. To increase the efficiency of solving direct problems, nonconforming grids with cells in the form of arbitrary hexahedrons are used. Methods for efficient calculation of derivatives (with respect to these parameters) necessary for solving inverse problems by the Gauss-Newton method are also described for the geometry parameters. The main idea for efficient derivatives computation is to identify the effect of changing the value of the parameter (used to compute the value of the generalized derivative) on the problem. The main actions performed by the subsystem for solving inverse problems and the features associated with the processing of geometry parameters are described.

Incomplete Information And Columns-Based Intelligent Systems

The paper considers columns-based intelligent systems that work under conditions of incomplete information, that is, input patterns are represented by their sub-patterns. The definition of direct and inverse problems under incomplete information is given. The solution of these problems is shown using the method of element-wise comparison of patterns and the intersection method. A relation between system’s ability to work under incomplete information and prediction is shown.

Problem of Determining a Multidimensional Kernel in One Parabolic Integro–differential Equation

The multidimensional parabolic integro-differential equation with the time-convolution in- tegral on the right side is considered. The direct problem is represented by the Cauchy problem for this equation. In this paper it is studied the inverse problem consisting in finding of a time and spatial dependent kernel of the integrated member on known in a hyperplane xn = 0 for t > 0 to the solution of direct problem. With use of the resolvent of kernel this problem is reduced to the investigation of more convenient inverse problem. The last problem is replaced with the equivalent system of the integral equations with respect to unknown functions and on the bases of contractive mapping principle it is proved the unique solvability to the direct and inverse problems