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Throughout the country's history, replenishing the oil and gas resource base has been a paramount state objective. Due to the state's priority in subsurface exploration, a vast fuel and energy complex was formed in a short period. For several decades now, the West Siberian oil and gas province has been the largest region in terms of hydrocarbon reserves and resources. Over all these years, the Tyumen region, including its autonomous okrugs, has produced 14.3 billion tons of oil out of a total of 27.6 billion tons for the entire country. Gas production amounted to 23.2 trillion cubic meters out of 27.6 trillion cubic meters. The discovery and development of Western Siberia's oil and gas potential is the result of the successful implementation of a large-scale scientific, industrial, and socio-economic project. Currently, the fields of the Khanty-Mansi Autonomous Okrug – Yugra and the Nadym-Pur-Taz region, which have provided the main oil and gas production for several decades, are in a declining trend. The transition to a state-oriented mineral resource policy, based on a long-term subsurface exploration strategy, is necessary. The management system for the oil and gas sector of the economy should legally originate from a state structure endowed with economic functions.

Cross-view geolocalization is the process of establishing correspondence between images of ground objects obtained by surveillance equipment deployed on different platforms, provided that the images generated by the equipment on one platform are geodetically referenced. A cross-view geolocalization method is proposed based on the detection of landmarks e field of view of an unmanned aerial vehicle (UAV) video camera using the YOLOv12 neural network, trained on georeferenced satellite images containing these landmarks. The training set is formed by augmenting the images of the specified landmarks. The results of experiments obtained using a sample from the SUES-200 dataset containing 20 satellite images of various landmarks and 20×50 images of these landmarks obtained by a UAV onboard camera from an altitude of 300 m are presented.

This paper examines the design of algorithms that minimize the localization time of an unknown signal source that manifests itself by generating ultrashort (essentially instantaneous) pulses at random moments. The source being searched for is random in two respects: first, its position within the search interval is unknown, and second, the source generates pulses at random moments. The source is localized using a detector receiver capable of arbitrarily changing its viewing window at any moment in time. Optimal search algorithms are constructed for the case where the a priori probability density function of the source distribution is a two-level piecewise constant function. The optimal parameters of these algorithms are determined, including the expected execution time for each of them. It is proven that an optimal algorithm that takes into account a priori information about the intensity of the source being searched for is always more efficient than an algorithm for which this intensity is unknown.

A method for visualizing translucent objects with subsurface light scattering in real time is proposed. An analytical model is described that takes into account the directivity of the incident light, providing images that are more realistic compared to those generated using known analytical models. A sampling scheme based on the optical properties of the material is considered. A directional dipole using a rendering pipeline on a GPU is presented.

In this article, we introduce a class of nonlinear fractional Lane-Emden equations incorporating Jumarie's fractional derivative with Neumann boundary conditions. To compute approximate numerical solutions, we propose an efficient modification of a variational iteration method (VIM) termed the fractional variational iteration method (FrVIM). Notably, for the limiting case our problem reduces to the classical Lane-Emden equation. We illustrate the effectiveness of our approach through graphical representations of solutions obtained using both Jumarie and Caputo derivatives. Furthermore, we observe that when the order of derivative approaches 1, the fractional solution plots gradually converge to the classical solution, demonstrating the accuracy and reliability of our method.

In this paper, a new fast compressive Fourier collocation algorithm for high-dimensional diffusion equations is constructed. A new algorithm is based on the high-dimensional sparse and fast Fourier transform and the compressive sampling matching pursuit algorithm. The computational complexity of the proposed algorithm is proportional to d², where d is the dimension of PDE domain. The error of the approximate solution is estimated and some numerical experiments are given.

The hyperbolicity preserving numerical solving of equations is a fundamental problem of computational mathematics. In the presence of relativistic effects and a magnetic field, the problem becomes even more complicated. The construction of numerical methods for solving continuum mechanics problems that allow one to control the hyperbolicity of a system of equations in solving the equations is an important problem formulated by Sergey Konstantinovich Godunov. This paper proposes an approach to constructing a Godunov-type scheme using a method of formulating the equations in the form of symmetric hyperbolic systems. An important property of this formalism, in addition to hyperbolicity control, is the use of all waves in solving the Riemann problem, which allows one to reproduce the tangential discontinuities with the quality of the Roe and HLLC schemes. The use of an operator splitting into the pressure forces and the advective transfer in the Riemann problem makes it possible to eliminate the ``sonic point'' problem, which may occur in Roe-type schemes. The scheme is verified by using some classical tests on the breakdown of a discontinuity in one-dimensional and two-dimensional formulations.

Based on the idea of Ogita and Aishima [1] and Ulm's method [2], we designed an inexact Ulm-type method based on matrix multiplication for inverse singular value problems, which avoids the shortcomings of solving a system of linear equations in each iteration of the algorithm in [3]. Thus, it looks more stable and requires less computations. Under the condition that the given singular values are distinct, the algorithm has the quadratic convergence in the sense of root convergence. Moreover, numerical experiments in the last section show that the new method is better than some known algorithms.

This paper presents the results of a dissipation and dispersion analysis of a linearized version of a novel finite difference scheme for the fully nonlinear weakly dispersive shallow water equations. It is a modification of the Rusanov scheme, which is a third-order approximation of the gas dynamics equations. We derive stability conditions, phase change and phase error formulas, and investigate the behavior of the harmonic attenuation coefficient. The study uncovers some previously unknown properties of the Rusanov scheme. Notably, both the original and the modified schemes exhibit high order smallness in the phase error for long waves. Furthermore, we identify the optimal parameter values that ensure monotonicity of the harmonic attenuation coefficient, strong suppression of short-wave harmonics, and small change in their phase.

With the swift advancement of artificial intelligence technology, automatically solving plane geometry problems has emerged as a popular area of research. To improve the automatic solution effect of mathematical plane geometry problems, an efficient deterministic prediction model is constructed by combining the powerful feature extraction ability of transformer, the time series processing ability of long short-term memory network, and the generation ability based on the bidirectional encoder representation of transformer. The outcomes of the ablation experiment show that the model proposed by the research performs the best in regard to accuracy and score, with 92.5% and 0.91%, respectively. The inference time is 0.45 seconds, significantly better than other models. In addition, the accuracy of this model in text relationship extraction, geometric element detection, and graphic annоtation is 97.88%, 93.68%, and 95.36%, which is significantly better than other comparative models. The application effect analysis results show that the proposed model maintains a low average number of steps and the highest accuracy of 96.21% as the number of theorems increases. The model proposed by the research exhibits higher robustness and stability when dealing with problems with different step numbers, providing a new approach for automatically solving plane geometry problems.