?
Stability of a Numerov type finite–difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis
Journal of Mathematical Sciences. 2010. Vol. 169. No. 1. P. 84–97.
Zlotnik A., Lapukhina A. V.
We consider an initial-boundary value problem for the one-dimensional nonstationary Schrödinger equation on the half-axis and study a two-level symmetric finite-difference scheme of Numerov type with higher approximation order. This scheme is constructed on a finite mesh, which is uniform with respect to space, with a nonlocal approximate transparent boundary condition of a general form (of Dirichlet-to-Neumann type). We obtain assertions about the stability of the finite-difference scheme in two norms with respect to the initial data and free terms in the equation and in the approximate transparent boundary condition under suitable conditions in the form of inequalities on the operator of approximate transparent boundary condition.
Keywords: устойчивостьThe time-dependent Schrödinger equationapproximate and discrete transparent boundary conditionsприближенные и дискретные прозрачные граничные условияunbounded domainsнеограниченные областинестационарное уравнение Шрёдингераthe Numerov discretization in spaceдискретизация Нумерова по пространству stability
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Maltseva S. V., Голубцов П. В., Барахнин В. Б., Вычислительные технологии 2026 Т. 31 № 1 С. 5–22
The issues of macro-level monitoring of the manufacturing system in the implementation of the concepts of Industry 4.0 and 5.0 based on the study of information flows in manufacturing network structures are considered. The numerical models of three types of network interaction, that taking into account the influence of the number of objects, external influences, ...
Added: February 26, 2026
Мартынова И. А., Дакашева Т. М., В кн.: XLVIII Самарская областная студенческая научная конференция: тезисы докладовТ. 2.: Эко-Вектор, 2022. С. 176–177.
В процессе научно-технического прогресса, а также в связи с последними событиями на мировом пространстве, связанными с пандемией короновируса и другими непредвиденными изменениями, все интенсивнее возрастает потребность специалистов дать названия новым реалиям в своих исследованиях. ...
Added: February 4, 2026
Мартынова И. А., , in: The European Proceedings of Social and Behavioural Sciences: Global Challenges and Prospects of the Modern Economic DevelopmentVol. 106.: European Publisher, 2021. P. 2357–1330.
In the new challenging time, corporate social responsibility has become a central issue for universities to get through the crisis caused by COVID-19. Under the crisis success of universities is directly dependent on their students’ level of satisfaction. The higher their rate of satisfaction is the greater are the chances to succeed. Thus, one of ...
Added: February 4, 2026
Арженовский И. В., Региональная экономика и управление: электронный научный журнал 2021 № 3 (67) Статья 11
At the present stage, regional specializations are being formed in the framework of the next technological wave, which is characterized by digitalization, “green” economy, bio- and nanotechnology, knowledge-based economy, and growing attention to human capital. The changes resulting from the Covid-19 pandemic belong to these characteristics as well. The article analyzes the influence of these ...
Added: January 21, 2026
Konstantin Polyakov, Marina Polyakova, Polyakov A., Procedia Computer Science 2025 Vol. 266 P. 205–212
This study is devoted to the analysis of the relationship between the solution of two different tasks facing the management of a commercial organization - ensuring the efficiency and sustainability of the business. An analysis of publications on this topic shows the existence of contradictory conclusions. The authors hypothesize that there is a strong statistical ...
Added: October 8, 2025
Sorbale A., Stremoukhov D., Shevtsova I., Политическая наука 2025 № 3 С. 36–62
External shocks have a significant impact on the quality of governance and the stability of political systems around the world. The concept of resilience, which until recently was only actively used in natural science research, has become a key focus for political scientists studying the impact of crises on political institutions in various country contexts. ...
Added: September 4, 2025
Котельников А. В., Laboratorium. Журнал социальных исследований (США) 2024 Т. 16 № 2 С. 4–23
The article presents an ethnographic study of the commune Dom (Home), one of about a dozen currently existing communes (“homes”) in Saint Petersburg, Russia, based on cohabitation and management of common household by people who are not related to each other, in large apartments (once communal apartments or dormitories). The residents of the Dom postulate ...
Added: May 20, 2025
Elyashevich I., Чичин Г. Г., Макаров Е. И., Научные исследования и разработки. Экономика фирмы 2025 Т. 14 № 1 С. 91–102
The article is devoted to the issues of the influence of provision of logistics companies with operational resources on their competitiveness. The influence of geopolitical factors on the provision of logistics companies with operational resources is shown. Conclusions are made about the need to integrate global experience and adapt best practices to improve the competitiveness ...
Added: April 10, 2025
Leevik Y., Skaternikova V. A., Vakhrushina A., , in: GSOM ECONOMY AND MANAGEMENT CONFERENCE 2024. Conference bookBook GSOM ECONOMY AND MANAGEMENT CONFERENCE 2024.: St. Petersburg: Saint Petersburg State University, 2024. P. 21–28.
Circular economy (CE) delves into the environmental factor of ESG, creating a more eco-friendly and responsible way to deal with environmental problems. The current study examines the relationships between CE implementation levels and national cultural diversities expressed via 6 Hofstede cultural dimensions. The study is based on data covering 28 European countries and the observation ...
Added: April 1, 2025
Буланова И. С., Dvoinin A., Двойнина В. К., Современная зарубежная психология 2025 Т. 14 № 1 С. 103–113
Recently, the concept of resilience has become very popular in psychological science, which in Russian-language psychology is translated as “zhiznesposobnost” [“viability”] or “ustoichivost” [“stability”]. Despite the fact that this concept has firmly entered the conceptual framework of psychological science, there is still no consensus among researchers on its definition and theoretical load. In the scientific ...
Added: April 1, 2025
Кочкаров А. А., Яцкин Д. В., Кочкаров Р. А., Теоретическая и прикладная экономика 2020 № 1 С. 1–9
This article is dedicated to designing of the transport and logistics systems with built-in resistance to structural failures. The sustainability indicators reflect the impact of the failure of one or several hubs (communication channels) upon working capacity of the already functioning system. In the process of designing the system, the sustainability indicators also provide opportunities ...
Added: March 7, 2025
Lisovskaya I., Гарифзянова А. Р., Мониторинг общественного мнения: Экономические и социальные перемены 2025 № 2 С. 22–44
The article raises the issue of social inclusion of non-resident student youth through different ways of engaging with the university and the city as specific environments with important resources. This article contributes to the field of post-migration research and provides insights into the processes that occur with young people after moving within the country. Social ...
Added: February 21, 2025