Founded in 1961. Publishes articles presenting new and important events in all areas of mathematics.
Vilniaus universiteto leidykla / Vilnius University Press
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This article [1] has been retracted by the editor due to incomplete authorship confirmation procedures at the time of publication. The retraction does not reflect concerns regarding the scientific content of the article. [1] https://doi.org/10.15388/LMR.2025.44495
Copyright (c) 2025 Artūras Štikonas https://creativecommons.org/licenses/by/4.0
Comparison of relevant credit risk assessment algorithms
Assessing credit risk is essential when making financial decisions, especially investing in debt securities. As the bond market is the largest securities market in the world, a great demand exists for tools to assess issuer creditworthiness. Furthermore, information describing the probability of default is also useful in other areas, such as risk management. In the era of machine learning and big data, new techniques have emerged that allow for automated risk assessment based on large amounts of data. Traditional creditworthiness assessment methods may be inaccurate, as the investor could be biased or misinterpret available information. A review and comparison of modern tools that would allow intelligent processing of large amounts of information will help assess the issuer's credit risk as objectively as possible.
Copyright (c) 2025 Simas Rimašauskas | Igoris Belovas | Rolandas Gricius https://creativecommons.org/licenses/by/4.0
Retracted: Digit staircases and a general identity for multiplication by (b-1)
Multiples of nine in base 10 form a staircase pattern: the tens digit increases, the ones digit decreases, and their sum is always nine. We establish a general identity showing that in any base~b, multiplication by (b – 1) produces the same phenomenon. Examples across numeral systems illustrate its link to digital roots and modular arithmetic, while its pedagogical and historical significance highlights how an elementary curiosity fits within number theory and mathematics education.
Copyright (c) 2025 Raven Quilestino-Olario | Maricor Jane R. Alzola | Maria Bianca C. Galicia | JR I. Lantaca | Kayshe Joy F. Pelingon https://creativecommons.org/licenses/by/4.0
Stability analysis of an implicit and explicit numerical method for Volterra integro-differential equations with kernel K(x,y(t),t)
We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate test equation to study the stability of both algorithms. We prove that the implicit method is unconditionally stable in the third quadrant. We determine the stability region in the third quadrant for the explicit method numerically. The explicit method has a bounded region close to the origin. We perform several calculations to demonstrate our results.
Copyright (c) 2025 Justin Steven Calder Prentice https://creativecommons.org/licenses/by/4.0
Short proof of the fundamental theorem of algebra
High school students may be introduced not only to important mathematical statements, such as the fundamental theorem of algebra, but also to their proofs. This famous theorem has various proofs, and its proofs have various modifications. The article discusses one such proof that is accessible to students.
Copyright (c) 2025 Aivaras Novikas | Juozas Juvencijus Mačys https://creativecommons.org/licenses/by/4.0
Loop-check free sequent calculi for unary fragment of temporal logic
This paper explores the construction of an efficient sequent calculus for a selected fragment of porpositional linear temporal logic (PLTL), extending the ideas of classical calculi discussed in [1], and builds upon previous investigations into the issue of loops in PLTL. Unary fragment of PLTL is identified in which formulas can contain at most one outermost ☐ (``always'') operator. Fragments are typically analyzed with the aim of defining more efficient calculi for formulas belonging to the fragment, especially when such an approach is not feasible for the full logic (such a strategy is employed in [3,4]). New or-type rule (⊦ ☐L*) is introduced by the authors. Authors propose newly developed sequent calculus PLTL – F1 for this fragment, which eliminates the need for loop axioms while improving derivation efficiency. Furthermore, the authors also introduce a totally loop-check free sequent calculus PLTL – F3. Elimination of loops was achieved by proving restrictions on the applications of the (⊦ ☐) and (∘) rules.
Copyright (c) 2025 Lukas Maksimiak | Adomas Birštunas https://creativecommons.org/licenses/by/4.0
Scalable watermarking for identifying large numbers of viewers
The study aims to introduce a scalable watermarking model that could be used to design a fast watermarking tool that is invisible and robust enough to identify the content source–viewer. This tool would enable adequate digital copyright protection at scale. To this end, a survey of watermarking methods that could embed unique viewer information in real-time has been carried out. The model can reliably scale frequency-domain watermarking techniques for mass application.
Copyright (c) 2025 Deivis Zolba https://creativecommons.org/licenses/by/4.0
A brief overview of the Poincare conjecture
The Poincar'e conjecture – a problem formulated 120 years ago by the French mathematician Henri Poincar'e, and solved at the beginning of this century by G. Perelman – has been one of the major issues of modern mathematics. It simply states that any three-dimensional space which is closed and without holes can be deformed into a three-dimensional sphere. The purpose of this article is to briefly review what we know today about the Poincar'e conjecture and its related problems in dimension 3.
Copyright (c) 2025 Daniele Ettore Otera https://creativecommons.org/licenses/by/4.0
Examples of incorrect mathematics in Lithuanian textbooks
The article discusses the cases of incorrect mathematics in textbooks. For example, instead of defining of a mathematical concept, textbooks explain mathematical symbols and terms. In other cases, false or non-trivial facts are used to justify or prove statements as if they were self-evident. We also provide examples of logical reasoning errors. We explain some cases of incorrect mathematics in textbooks by the problematic nature of mathematics syllabus. Other cases of incorrect mathematics arises from the different treatment of the same topics in different textbooks. In all the cases discussed, we offer alternative correct solutions.
Copyright (c) 2025 Rimas Norvaiša https://creativecommons.org/licenses/by/4.0
People understood the concept of a curve intuitively in ancient times. By observing the trajectory of a thrown stone, the curvature of riverbanks, the contours of leaves of plants and flowers, people gradually developed the concept of curve. The paper attempts to discuss such curves, which have led mathematicians to take a deeper look at the concept of curve and to study the properties of curves more seriously. The authors use the term ``remarkable curves'' for those curves of third and fourth order that give rise to circles (generating circles). The equations of such curves in Cartesian coordinates can be derived using elementary geometry methods, usually using the similarity of triangles. The authors believe that the ideas presented in this article will help mathematics teachers to encourage students to take a more serious interest in the very interesting science of mathematics.
Copyright (c) 2025 Edmundas Mazėtis | Grigorijus Melničenko https://creativecommons.org/licenses/by/4.0
23 years ago, R. Kudžma in the journal Alfa plius omega [7] argued that the TEV textbook [14] presents the inverse function and its graph incorrectly. The head of the textbook's author group, V. Stakėnas [15], replied that this was not incorrect, but a traditional approach. The discussion did not develop. The separation of the function f : x ↦ f(x), o y = f(x) and the equation y = f(x) notations proposed in this article may help resolve the seemingly irreconcilable views on the inverse function and its graph. The idea is also developed that the graph of the function f in the original coordinate system Oxy is also the graph of the inverse function in Oyx coordinate system.
Copyright (c) 2025 Ričardas Juozas Kudžma https://creativecommons.org/licenses/by/4.0
Comparison of team and individual results of the young mathematicians competition
The article presents a comparative analysis of the team and individual results of the 11th–12th grade students who participated in the Young Mathematicians Competition held between 2022 and 2025, taking into account the solvability of tasks.
Copyright (c) 2025 Karolina Kanišauskienė https://creativecommons.org/licenses/by/4.0
Testing of the hypotheses of the renewal process under local asymptotic normality
The paper deals with a statistical experiment induced by a renewal process with a continuous compensator. Given the local asymptotic normality of probability measures, the asymptotically locally most powerful criteria for testing the simple hypothesis with the complex parametric alternative are found. It is also shown how these hypotheses are practically tested with specific data.
Copyright (c) 2025 Vaidotas Kanišauskas https://creativecommons.org/licenses/by/4.0
Copyright (c) 2025 Vita Verikaitė | Henrikas Jasiūnas https://creativecommons.org/licenses/by/4.0
Analysis and forecasting of admission indicators of the faculties of Vilnius University (2000–2026)
The study investigates the general admission indicators of Vilnius University and its faculties during the 2000–2026 academic years. AR, ARIMA, and exponential smoothing models are applied for data analysis and forecasting. Using correlation analysis, the study aims to assess the impact of demographic factors and determine whether their influence on admission results is statistically significant.
Copyright (c) 2025 Martynas Jokubaitis | Igoris Belovas https://creativecommons.org/licenses/by/4.0
From the contemporary history of VU Faculty of Mathematics and Informatics: the development of admission to mathematical studies (1991–2024)
The study examines the trends in student admissions to undergraduate mathematics and informatics programs at the Faculty of Mathematics (1991–1999) and the Faculty of Mathematics and Informatics (1999–2024) of Vilnius University. The review is based on data drawn from primary sources.
Copyright (c) 2025 Igoris Belovas https://creativecommons.org/licenses/by/4.0
From the history of VU Faculty of Mathematics and Informatics: the development of admission to mathematical studies
Based on primary source data, the paper examines the development of admissions to mathematical studies at Vilnius University's Faculty of Physics and Mathematics (1945–1965), Faculty of Mathematics and Mechanics (1966–1977), and Faculty of Mathematics (1978–1990).
Bootstrap approximation for probabilities of large deviations
Copyright (c) 1997 Leonas Saulis https://creativecommons.org/licenses/by/4.0
On A-decomposition of probability measures in Hilbert spaces
Copyright (c) 1997 Feliksas Mišeikis https://creativecommons.org/licenses/by/4.0
Copyright (c) 1997 Remigijus Leipus | Alfredas Račkauskas https://creativecommons.org/licenses/by/4.0
On the asymptotics of the nearly non-stationary AR(1) models
Copyright (c) 1997 Kęstutis Kubilius https://creativecommons.org/licenses/by/4.0
The approximation of accuracy to the χn2 distribution function
The approximation of accuracy of distribution function of the sum independent and indentically distributed random variables to the χn2 distribution function is considered.
Copyright (c) 1997 Antanas Karoblis https://creativecommons.org/licenses/by/4.0
The estimate of convergence rate of the density of maximum of multivariate random variables
In this paper the asymptotic of the density of the maximum of the independent identically distri­buted multivariate random variables is investigated. The nonuniform estimate of the convergence rate is obtained.
Copyright (c) 1997 Arvydas Jokimaitis https://creativecommons.org/licenses/by/4.0
Copyright (c) 1997 Vydas Čekanavičius https://creativecommons.org/licenses/by/4.0
On the transference theorem on a max-scheme
The generalized transference theorem named after B. V. Gnedenko has been proved. Illustrative examples are presented.
Copyright (c) 1997 Algimantas Aksomaitis https://creativecommons.org/licenses/by/4.0
Finite automata based processing of two-dimensional images
Finite automata theory based methodics for the compression of two-dimensional gray-scale images is presented. Variable block-size segmentation procedure as well as techniques for the improve­ment of similarity of non-overlapping parts of the image are applied. Compression effect is attained by producing an image modeling finite automaton with minimal number of states.
Copyright (c) 1997 Jonas Valantinas https://creativecommons.org/licenses/by/4.0
On numerical modelling of stochastic systems
The paper considers a method to construct numerical models of non-markovian stochastic systems. The idea is to approximate a general distribution function of positive random value by mixture of exponential stages. The example is given.
Copyright (c) 2025 Eimutis Valakevičius https://creativecommons.org/licenses/by/4.0
Models of finite elements in solution of temperature fields' problems
The paper deals with ways of modelling the junction zones of thin walled branched structures by finite elements in solving temperature fields' problems. An adjoint spatial finite element with a rectangular basis is suggested for discretization. Coordinate transformation and temperature phenomena re-calculation formulas have been ob­tained. They allow to build a grid of finite elements of the investigated object by using angular as well as middle of the sides of a prism points. The numerical examples are presented. Present solutions are compared with available control solutions.
Copyright (c) 1997 Sigita Turskienė https://creativecommons.org/licenses/by/4.0