Lietuvos matematikos rinkinys https://www.journals.vu.lt/LMR <p>The journal publishes articles presenting new and important events in all areas of mathematics.</p> Vilniaus universiteto leidykla / Vilnius University Press lt-LT Lietuvos matematikos rinkinys 0132-2818 <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/informacijos-mokslai/journalpolicy">Journal Policy</a>.&nbsp;</p> Editorial Board and Table of Contents https://www.journals.vu.lt/LMR/article/view/25124 Artūras Štikonas Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-11-29 2021-11-29 62 1 1 Relations between Spectrum Curves of Discrete Sturm-Liouville Problem with Nonlocal Boundary Conditions and Graph Theory. II https://www.journals.vu.lt/LMR/article/view/25128 <p>In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article was devoted to the Sturm--Liouville problem in the case two-points nonlocal boundary conditions.</p> Jonas Vitkauskas Artūras Štikonas Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-12-15 2021-12-15 62 1 8 10.15388/LMR.2021.25128 Supervised linear classification of Gaussian spatio-temporal data https://www.journals.vu.lt/LMR/article/view/25214 <p>In this article we focus on the problem of supervised classifying of the spatio-temporal Gaussian random field observation into one of two classes, specified by different mean parameters. The main distinctive feature of the proposed approach is allowing the class label to depend on spatial location as well as on time moment. It is assumed that the spatio-temporal covariance structure factors into a purely spatial component and a purely temporal component following AR(p) model. In numerical illustrations with simulated data, the influence of the values of spatial and temporal covariance parameters to the derived error rates for several prior probabilities models are studied.</p> Marta Karaliutė Kęstutis Dučinskas Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-12-15 2021-12-15 62 9 15 10.15388/LMR.2021.25214 Logical derivation search with assumption traceability https://www.journals.vu.lt/LMR/article/view/25215 <p>In this paper authors research the problem of traceability of assumptions in logical derivation. The essence of this task is to trace which assumptions from the available knowledge base of assumptions are necessary to derive a certain conclusion. The paper presents a new derivation procedure for propositional logic, which ensures traceability feature. For the derivable conclusion formula derivation procedure also returns the smallest set of assumptions those are enough to get derivation of the conclusion formula. Verification of the procedure were performed using authors implementation.</p> Adomas Birštunas Elena Reivytytė Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-12-15 2021-12-15 62 16 22 10.15388/LMR.2021.25215 Weak approximations of Wright-Fisher equation https://www.journals.vu.lt/LMR/article/view/25217 <p>We construct weak approximations of the Wright-Fisher model and illustrate their accuracy by simulation examples.</p> Gabrielė Mongirdaitė Vigirdas Mackevičius Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-12-15 2021-12-15 62 23 26 10.15388/LMR.2021.25217 COVID-19 reproduction number and non-pharmaceutical interventions in Lithuania https://www.journals.vu.lt/LMR/article/view/25218 <p>Currently the world is threatened by a global COVID-19 pandemic and it has induced crisis creating a lot of disruptions in the healthcare system, social life and economy. In this article we present the analysis of COVID-19 situation in Lithuania and it's municipalities taking into consideration the effect of non-pharmaceutical interventions on the reproduction number. We have analysed the period from 20/03/2020 to 20/06/2021 covering two quarantines applied in Lithuania. We calculated the reproduction number using the incidence data provided by State Data Governance Information System, while the information for applied non-pharmaceutical interventions was extracted from Oxford COVID-19 Government Response Tracker and the COVID-19 website of Government of the Republic of Lithuania. The positive effect of applied non-pharmaceutical interventions on reproduction number was observed when internal movement ban was applied in 16/12/2020 during the second quarantine in Lithuania.</p> Ramunė Vaišnorė Audronė Jakaitienė Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-12-15 2021-12-15 62 27 37 10.15388/LMR.2021.25218 Application of spatial auto-beta models in statistical classification https://www.journals.vu.lt/LMR/article/view/25219 <p>In this paper, spatial data specified by auto-beta models is analysed by considering a supervised classification problem of classifying feature observation into one of two populations. Two classification rules based on conditional Bayes discriminant function (BDF) and linear discriminant function (LDF) are proposed. These classification rules are critically compared by the values of the actual error rates through the simulation study.</p> Eglė Zikarienė Kęstutis Dučinskas Copyright (c) 2021 Lietuvos matematikos rinkinys https://creativecommons.org/licenses/by/4.0 2021-12-15 2021-12-15 62 36 43 10.15388/LMR.2021.25219