{"title":"New kink-type solution of the equation for artificial axon","authors":"M. A. Knyazev, Т. A. Klimovich","doi":"10.29235/1561-2430-2024-60-1-29-33","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-29-33","url":null,"abstract":"In the paper a (1 + 1)-dimension equation of motion for the artificial axon is considered. The artificial axon is a dynamical structure like a neuron. They are widely used in biophysics, for example, in studying the physiological processes. A topological non-trivial solution of one-kink type for this equation is constructed in an analytical form. The modified direct Hirota method for solving the nonlinear partial derivatives equations is applied. The special cases are considered for different voltages on the contacts of axon. ","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"101 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140754783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Freund – Nambu cosmology with the massless scalar field","authors":"I. G. Dudko, Yu. P. Vyblyi","doi":"10.29235/1561-2430-2024-60-1-43-51","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-43-51","url":null,"abstract":"Within the framework of the generalization of Freund – Nambu scalar-tensor theory of gravity, a massless scalar field is considered, the source of which is the trace of its own energy-momentum tensor. For the cosmological problem, numerical solutions of field equations were obtained, with the help of which the dependencies of the Hubble parameter and the photometric distance to the observed sources on red-shift were constructed. To the consistency of the models with observational data, contours of confidence intervals for model parameters were constructed.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"469 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140750773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fourier series for the multidimensional-matrix functions of the vector variable","authors":"V. S. Mukha","doi":"10.29235/1561-2430-2024-60-1-15-28","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-15-28","url":null,"abstract":"In the article, the theory of the Fourier series on the orthogonal multidimensional-matrix (mdm) polynomials is developed. The known results from the theory of the orthogonal polynomials of the vector variable and the Fourier series are given and the new results are presented. In particular, the known results of the Fourier series theory are extended to the case of the mdm functions, what allows us to solve more general approximation problems. The general case of the approximation of the mdm function of the vector argument by the Fourier series on the orthogonal mdm polynomials is realized programmatically as the program function and its efficiency is confirmed. The analytical expressions for the coefficients of the second degree orthogonal polynomials and Fourier series for possible analytical studies are obtained.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"65 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140751573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Amirkhanov, A. Anisenkov, V. Aulchenko, R. R. Akhmetshin, N. S. Bashtovoy, D. Berkaev, A. Bondar, A. Bragin, D. S. Vasileuskaya, A. O. Gorkovenko, F. Grancagnolo, A. Grebenuk, S. Gribanov, D. Grigoriev, D. Epifanov, A. Erofeev, D. Zhadan, I. Zemlyansky, A. Zubakin, V. Ivanov, F. Ignatov, S. Karpov, V. Kazanin, A. Kirpotin, I. Koop, A. Korobov, A. Kozyrev, E. Kozyrev, P. Krokovny, A. Kuzmin, A. Kuzmenko, Y. Kurochkin, B. D. Kutsenko, I. Logashenko, P. Lukin, K. Mikhailov, V. S. Okhapkin, A. Otboev, Y. Pestov, A. Popov, G. Razuvaev, Yu. A. Rogovsky, A. A. Ruban, N. Ryskulov, A. Ryzhenenkov, A. Semenov, A. Senchenko, A. Sibidanov, E. Solodov, A. Talyshev, V. Titov, S. S. Tolmachev, G. Fedotovich, Y. Shatunov, B. Shwartz, V. Shebalin, D. Shemyakin, D. Shoukavy, L. Epshteyn, Y. Yudin
{"title":"The first measurement of the conversion decay of the omega meson into a neutral pion and an electron-positron pair at the CMD-3 detector","authors":"A. Amirkhanov, A. Anisenkov, V. Aulchenko, R. R. Akhmetshin, N. S. Bashtovoy, D. Berkaev, A. Bondar, A. Bragin, D. S. Vasileuskaya, A. O. Gorkovenko, F. Grancagnolo, A. Grebenuk, S. Gribanov, D. Grigoriev, D. Epifanov, A. Erofeev, D. Zhadan, I. Zemlyansky, A. Zubakin, V. Ivanov, F. Ignatov, S. Karpov, V. Kazanin, A. Kirpotin, I. Koop, A. Korobov, A. Kozyrev, E. Kozyrev, P. Krokovny, A. Kuzmin, A. Kuzmenko, Y. Kurochkin, B. D. Kutsenko, I. Logashenko, P. Lukin, K. Mikhailov, V. S. Okhapkin, A. Otboev, Y. Pestov, A. Popov, G. Razuvaev, Yu. A. Rogovsky, A. A. Ruban, N. Ryskulov, A. Ryzhenenkov, A. Semenov, A. Senchenko, A. Sibidanov, E. Solodov, A. Talyshev, V. Titov, S. S. Tolmachev, G. Fedotovich, Y. Shatunov, B. Shwartz, V. Shebalin, D. Shemyakin, D. Shoukavy, L. Epshteyn, Y. Yudin","doi":"10.29235/1561-2430-2024-60-1-52-71","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-52-71","url":null,"abstract":"The conversion decay w® p0e+e- with the CMD-3 detector on the VEPP-2000 electron-positron collider VEPP-2000 at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences was investigated. The data from the first scan were used in the work, which corresponded to an integral brightness of around 10 pb–1 in the energy range of 660 to 840 MeV in the center of mass system. The 1113 ± 37 signal events were detected. The product of the relative decay probability and ω-meson width G(w® e+e- ) × Br(w® p0e+e- ) = (4, 20 ± 0,12 ± 0, 25) ×10-7 MeV, as well branching ratio Br(w® p0e+e- ) = (6, 78 ± 0,19 ± 0, 40) ×10-4 are measured with better precision than the world average.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"33 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140753059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"In Memory of Lev Mitrofanovich Tomilchik","authors":"Article Editotial","doi":"10.29235/1561-2430-2023-59-4-352","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-352","url":null,"abstract":"<jats:p>.</jats:p>","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"60 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two-photon decay of the pseudoscalar meson in the relativistic quark model","authors":"V. Haurysh, V. V. Andreev","doi":"10.29235/1561-2430-2023-59-4-315-327","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-315-327","url":null,"abstract":"In the relativistic quark model, based on the point form of Poincaré-invariant quantum mechanics, an integral representation of the form-factor of the pseudoscalar P0(π0,η,η′) meson of P0 (qq̅)→γγ decay is obtained taking into account the anomalous magnetic moments of u-, d- and s-quarks. IIn the developed formalism the values of the constituent quark masses and the parameters of the wave functions are calculated using the lepton decay P±(qQ̅ ) → ℓ±νℓ± constant fP± and the pseudoscalar density constant gP±. It is shown that taking into account the gluonium component in η/η′-mesons and using the structure functions of light sector quarks lead to the behavior of the form factors of pseudoscalar π0-, η-, η′-mesons in the area of a small transferred momentum to the lepton pair, which is consistent with the modern experimental data","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analytical calculations of fifth-order electromagnetic corrections to the anomalous magnetic moment of leptons within the Mellin-Barnes representation","authors":"O. Solovtsova, V. Lashkevich, L. Kaptari","doi":"10.29235/1561-2430-2023-59-4-338-351","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-338-351","url":null,"abstract":"We investigate the explicit, analytical expressions for the fifth-order electromagnetic corrections in the fine structure constant α to the anomalous magnetic moment of leptons aL (L = e, μ, τ) from diagrams with insertions of the vacuum polarization operator consisting of pure lepton loops. Our approach is based on the consecutive application of dispersion relations for the polarization operator and the Mellin – Barnes transform for the propagators of massive particles. Exact analytical expressions for the corrections to aL from vacuum polarization by four identical loops are obtained. Asymptotic expansions are found in the limit of both small and large values of the lepton mass ratio (r = mℓ /mL), r≪ 1 and r→∞ The resulting expansions are compared with the corresponding expressions given in the literature.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"4 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical modelling of epidemic processes in the case of the contact stepwise infection pattern","authors":"A. V. Chigarev, M. Zhuravkov, M. Mikhnovich","doi":"10.29235/1561-2430-2023-59-4-291-301","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-291-301","url":null,"abstract":"Herein we consider mathematical models of infection in a population consisting of two types of people: those who transmit infection to others (type 1) and those who do not participate in the spread of infection (type 2). On the basis of the percolation theory and a model of the urn test type, a critical value of the proportion of infected persons in the population is determined, after which the infection process may become explosive. The probabilities of continuous infection and the interruption of its transmission are investigated. On the basis of Feigenbaum logistic mapping for the epidemic process, it is possible to estimate the change in the value of the parameter of the number of contacts and the bifurcations arising in this case, which are modelled in accordance with the scenario of transition to deterministic chaos through the doubling of the cycle period. In modes of stochasticity there are local modes of periodicity, the identification of which, if the model is adequate to the real situation, allows predicting and controlling the epidemic process, translating it or keeping the process in a stable cyclic state.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"11 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The semiclassical approximation of multiple functional integrals","authors":"V. Malyutin, B. Nurjanov","doi":"10.29235/1561-2430-2023-59-4-302-307","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-302-307","url":null,"abstract":"In this paper, we study the semiclassical approximation of multiple functional integrals. The integrals are defined through the Lagrangian and the action. Of all possible trajectories, the greatest contribution to the integral is given by the classical trajectory x̅cl for which the action S takes an extremal value. The classical trajectory is found as a solution of the multidimensional Euler – Lagrange equation. To calculate the functional integrals, the expansion of the action with respect to the classical trajectory is used, which can be interpreted as an expansion in powers of Planck’s constant. The numerical results for the semiclassical approximation of double functional integrals are given.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spherically-symmetric non-static solutions of Einstein’s equations","authors":"Yu. P. Vyblyi, A. A. Leonovich","doi":"10.29235/1561-2430-2023-59-4-308-314","DOIUrl":"https://doi.org/10.29235/1561-2430-2023-59-4-308-314","url":null,"abstract":"In this paper, we considered non-static vacuum spherically symmetric solutions of the Einstein equations and harmonicity conditions in the coordinate system with a non-zero space-time component in the metric. For the case of the weak field, a particular solution of the approximate equations was obtained, which corresponds to a nonstatic source whose boundary moves with a constant speed. For the exact Einstein’s equations we obtained a wave-type solution, determined by two implicitly specified functions, depending on the retarded argument and on the radial coordinate, respectively. The connection between these solutions and the Birkhoff theorem is discussed.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"27 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139535953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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