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The paper studies the quantum action for the five-dimensional real $\phi^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed., Comment: LaTeX, 20 pages, 5 figures. Firstly appeared in Russian, April 9, 2024, see https://www.pdmi.ras.ru/preprint/2024/24-05.html

This paper presents the experience of developing and utilizing computer simulations for student laboratory assignments in atomic physics, specifically focusing on emission atomic spectra. The fundamental component of each laboratory assignment is a computer simulator of a spectrograph, which displays atomic line spectra on the monitor screen. The simulator operates by converting the wavelength of radiation into an RGB triplet. Calibration of the spectrograph is conducted using the atomic spectrum of mercury. The configuration of setup parameters and experimental conditions is unique to each student conducting the laboratory assignment using the simulator. Individualized parameters, stored in Google Sheets, are transferred to the HTML template of the laboratory assignment via the Google Apps Scripts service. This individualization of simulator parameters serves to encourage students to engage in independent work., Comment: 17 pages, in Russian, 9 figures

The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not empty. As an example, an explicit function is presented. It is proved by explicit construction that there are functions satisfying the criterion in a stronger formulation., Comment: LaTeX, 8 pages, 1 figure. Firstly appeared in Russian, March 5, 2024. Compared to the Russian version, some comments and minor corrections have been added. The forgotten imaginary unit in the Fourier transform has also been restored. See https://www.pdmi.ras.ru/preprint/2024/24-04.html

The paper presents various modifications of the Frank-Wolfe algorithm in the equilibrium traffic assignment problem. The Beckman model is used as a model for experiments. In this article, first of all, attention is paid to the choice of the direction of the basic step of the Frank-Wolfe algorithm. Algorithms will be presented: Conjugate Frank-Wolfe (CFW), Bi -conjugate Frank-Wolfe (BFW), Fukushima Frank-Wolfe (FFW). Each modification corresponds to different approaches to the choice of this direction. Some of these modifications are described in previous works of the authors. In this article, following algorithms will be proposed: N-conjugate Frank-Wolfe (NFW), Weighted Fukushima Frank-Wolfe (WFFW). These algorithms are some ideological continuation of the BFW and FFW algorithms. Thus, if the first algorithm used at each iteration the last two directions of the previous iterations to select the next direction conjugate to them, then the proposed algorithm NFW is using more than N previous directions. In the case of Fukushima Frank-Wolfe, the average of several previous directions is taken as the next direction. According to this algorithm, a modification WFFW is proposed, which uses a exponential smoothing from previous directions. Experiments with various modifications were carried out on several datasets representing urban structures and taken from publicly available sources. The relative gap value was taken as the quality metric. The experimental results showed the advantage of algorithms using the previous directions for step selection over the classic Frank-Wolfe algorithm. In addition, an improvement in efficiency was revealed when using more than two conjugate directions. For example, on various datasets, the modification 3FW showed the best convergence. In addition, the proposed modification WFFW often overtook FFW and CFW, although performed worse than NFW., Comment: 14 pages, in Russian language, 8 figures

The paper tests the validity of the critique of the fiscal theory of the price level. A stochastic general equilibrium model with continuous time is constructed. An active fiscal policy and a passive monetary policy have been set. Monetary policy manages the interest rate through the Taylor rule. The stochastic default factor in the special form is introduced. A complete definite system of equations is obtained for the detection of equilibrium. It is asserted that the peculiarities of the approach to modeling are of critical importance for verifying the presence of certain hypotheses and formulating conclusions. The results of this work are in support of the fiscal theory of the price level., Comment: Master Thesis, in Russian. Supervisor: Sergey E. Pekarski

The paper studies the quantum action for the four-dimensional real $\phi^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $\beta$-function is presented. Consistency with previously known results is shown., Comment: LaTeX, 71 pages, 8 figures. Firstly appeared in Russian, February 6, 2024, see https://www.pdmi.ras.ru/preprint/2024/pr2024.html