The study of Ricci flows on (pseudo-) Riemannian manifolds has been the subject of work by many mathematicians. Among the key test cases are Lie groups equipped with a left-invariant Riemannian or Lorentzian metric and the Levi-Civita connection. Previously, Ricci flows on three-dimensional unimodular Lie groups with a left-invariant Riemannian metric and the Levi-Civita connection were investigated in the works of D. Knopf and K. McLeod. In the authors’ papers, this problem was addressed on three-dimensional Lie groups with a left-invariant Riemannian metric within the class of semisymmetric equiaffine connections. This study examines the behavior of the Ricci flow on three-dimensional unimodular Lie groups endowed with a left-invariant Lorentzian metric and the Levi-Civita connection. In J. Milnor’s coordinates, the original Ricci flow equation transforms into a system of differential equations involving the structure constants of Lie algebras. Solutions have been investigated for each of the possible types of pseudo-orthogonal bases in Lie algebras.
Anti-de Sitter spaces are well known in Einstein’s general theory of relativity and are of interest to physicists and mathematicians. For example, in the study of 1-symmetric Lorentzian manifolds by Kahen and Wallach, it turned out that anti-de Sitter spaces, along with Kahen-Wallach spaces, are an important example of 1-symmetric spaces and play a significant role in research in Lorentzian geometry. Previously, E.D. Rodionov and D.N. Oskorbin studied Ricci solitons and their relationship to Killing fields on generalized Kahen-Wallach spaces, as well as conformal Killing vector fields on 1-symmetric Lorentzian manifolds. Furthermore, conformal Killing vector fields on 2-symmetric indecomposable Lorentzian manifolds were studied. It was established that the conformal factor of the conformal analog of the Killing equation on these manifolds depends on the behavior of the Weyl tensor. In the case where the Weyl tensor is zero, nontrivial examples of conformal Killing vector fields with a variable conformal factor were constructed using Airy functions. In this paper, conformal Killing vector fields on anti-de Sitter space are investigated. The equation of a conformal Killing vector field in a special coordinate system is reduced to a system of differential equations, and a general solution is found.
The article analyzes algorithms for the fast-optimized dynamic search for point Poisson sources that generate ultrashort (instantaneous) delta pulses at random instants. A key distinguishing feature of the algorithms proposed in this article is that the authors developed and applied (and implemented on a specialized cluster) acceleration methods based on parallel computations to calculate the cumbersome multidimensional integral expressions that arise during the solution of the problem. An example of a software calculation of the parameters of an optimal search algorithm for several localized pulsed objects with a given localization accuracy is provided. The optimal number of scanning stages for minimizing the average localization time is calculated. The search strategies described in this paper are focused on localizing sources with a uniform distribution density, but the conducted research opens up further prospects for developing fast-optimized localization algorithms for random signal sources with arbitrary distribution densities.
The review summarizes the results of publishing activities of the "Izvestiya of Altai State University" journal for the 30-year period from 1996 to 2026 in the field of physical research. The presented data demonstrate the significant contribution of the journal to the development of physical knowledge, unification of researchers from various universities and scientific organizations, support of young researchers, holding significant scientific events, and training highly qualified personnel, primarily for Siberian regions. The paper identifies and describes specific strands of modern physical research that have been most thoroughly presented in the journal’s papers, including condensed matter physics, theoretical physics and space physics, and the physics of nanosystems and nanotechnology. There are also several essential examples of significant scientific results in the field of physics, reflected on the pages of the journal over the 30-year period of its publication.
The paper proposes a mathematical model of carbon dioxide disposal in a non-isothermal viscoelastic porous medium. Following the two-dimensional approach and considering the smallness of the solid phase velocity, the initial system of equations is reduced to the problem of finding the effective pressure and porosity of the medium. Thermal effects caused by gas injection are introduced into the model by the equation for the temperature of the medium. The study investigates scenarios of carbon dioxide injection into a layer with low initial porosity and analyzes the effect of temperature on gas distribution and pore space dynamics. It is shown that zones of increased mechanical stress critical for longterm storage integrity can be identified using the heat transfer. The sensitivity of the proposed model to parameter variations (thermal conductivity of the medium, injection rate) is investigated through a series of computational experiments. The obtained experimental results help identify optimal injection parameters to minimize heat losses and ensure the stability of the geological structure. The results of the study demonstrate that considering the temperature effects improves the prediction of storage layer dynamics during long-term storage of CO2.
