2. Articole

Permanent URI for this collectionhttps://msuir.usm.md/handle/123456789/13372

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T-QUASIGROUPS WITH STEIN 2-ND AND 3-RD IDENTITY
(2023) Shcherbacov, Victor; Radilova, Irina; Radilov, Petr
In this paper we prolong research of T-quasigroups with Stein 2-rd (𝑥𝑦 · 𝑥 = 𝑦 · 𝑥𝑦) and Stein 3-rd (𝑥𝑦 · 𝑦𝑥 = 𝑦) identities [9].
DISCOVERING THE MYSTERIES OF PI NUMBER USING AR TECHNOLOGIES
(2023) Titchiev, Inga; Caftanatov, Olesea; Talambuta, Dan
The integration of Augmented Reality (AR) in education requires a strategic approach in order to ensure effectiveness in the learning process. AR technologies are constantly evolving, offering new possibilities for educational content, making it an evolving and innovative tool for educators. Exploring the mathematical world of Pi through AR can be an engaging and interactive experience for learners. This article presents the approach used in the development of an Augmented Reality application intended for Pi learning.
PROFESSOR ALEXANDRU SUBĂ ON HIS 70TH BIRTHDAY
(CEP al Universității Pedagogice de Stat „Ion Creangă”, 2023) Cozma, Dumitru; Popa, Mihail
ON STABILITY OF SOME EXAMPLES OF TERNARY DIFFERENTIAL CRITICAL SYSTEMS WITH QUADRATIC NONLINEARITIES
(2023) Neagu, Natalia; Popa, Mihail
Starting with Example 1 of A.M. Lyaponov’s thesis [1] (§32), which represents a ternary differential system with quadratic nonlinearities, examples of differential systems of the generalized Darboux type were constructed in the critical case. The stability conditions of the unperturbed motion described by these systems were determined
QUARTIC DIFFERENTIAL SYSTEMS WITH A NON-DEGENERATE MONODROMIC CRITICAL POINT AND MULTIPLE LINE AT INFINITY
(2023) Subă, Alexandru; Vacaraş, Olga
The quartic differential systems with a non-degenerate monodromic critical point and non-degenerate infinity are considered. We showthat in this family the maximal multiplicity of the line at infinity is seven. Modulo the affine transformation and time rescaling the classes of systems with the line of infinity of multiplicity two, three, . . . , seven are determined. In the cases when the quartic systems have the line at infinity of maximal multiplicity the problem of the center is solved.
ÎMBUNĂTĂȚIREA CALITĂȚII EXPERIENȚELOR DE REALITATE AUGMENTATĂ ÎN CONTEXTUL DEZVOLTĂRII APLICAȚIILOR
(CEP USM, 2024) Țițchiev, Inga; Caftanatov, Olesea; Talambuța, Dan
In this article, we present solutions to enhance augmented experiences based on our two years of developing educational applications. Thus, the purpose of this work is to present the challenges, problems and solutions regarding the improvement of augmented experiences. These were detected including by testing the developed application by the students and providing feedback. The solutions will increase the efficiency and quality of the learning process.
Some Types of LCA Groups with Local Ring of Continuous Endomorphisms [Articol]
(2024) Popa, Valeriu
We describe the structure of some locally compact abelian (LCA) groups whose ring of continuous endomorphisms is local.
About Quadratic Functional Equations on Quasigroups [Articol]
(2024) Sokhatsky, Fedir; Krainichuk, Halyna
Functional equations over binary quasigroups are under consideration. An equation is called: quadratic, if each individual variable has either two appearances or none; cancellable, if a variable has two appearances and another none in a proper subterm; reducible, if it is equivalent to a system of equations such that every of which has less number of individual variables than the given one. Only the functional equations of unipotency, commutativity, associativity and mediality are noncancellable, and the irreducible ones are the same except the mediality. The criteria for the parastrophic equivalency of the equations up to the noncancellable equations were found.
Combinatorial Symmetry of Twisty Puzzles and Twist Axes of Order 4, 6, 8, 9, 10 and 11 [Articol]
(2024) Popa, Alexandru
This paper introduces the notion of conbinatorial symmetry of twisty puzzles, presents geometric principles of searching for twisty puzzles with sun mechanism. Additionally, some geometrical and combinatorial properties of such puzzles and their polyhedra are discussed.
About Multiple Prolongations of Latin Cubes [Articol]
(2024) Sokhatsky, Fedir; Moroz, Daria
We propose an algorithm of prolongation of a Latin cube with k new elements (k ≥ 1).
High Dimensional Inference – a Literature Review [Articol]
(2024) Lopotenco, Alexandru; Teleuca, Marcel
High dimensional inference has been a crucial topic in statistical learning, especially with the rise of data that has a lot of features yet is difficult to gather. We analyze regressions on data in large dimensions p that are much greater than the samples available, n. The usual method in constructing confidence intervals used for OLS is not useful when p » n since asymptotic normality fails. We survey literature that comes up with new method of constructing these intervals.
Combined Encryption Algorithm Using a Generalization of the Markovski Algorithm [Articol]
(2024) Malyutina, Nadezhda; Shcherbacov, Victor
This article is devoted to the construction of a generalization of a cryptographic algorithm based on the use of quasigroups of a special type. Here is a more detailed description of the algorithm proposed in [1]. An example is given to illustrate the operation of the developed algorithm. Our task was to show the effectiveness and advantages of using quasigroups of a special type in cryptology.
About AC-Groupoids [Articol]
(2024) Izbas, Vladimir; Izbas, Ana-Maria
The concept of a right (left) AC-groupoid over an arbitrary group is defined and studied. Necessary and sufficient conditions which transform a right (left) AC-groupoid into a quasigroup are given. The AC-groupoids form a wide class of special groupoids and quasigroups that have a transitive subset of automorphisms.
On the Volumes of Polyhedra which Tile the Hyperbolic Space Face-to-Face and Solid-Transitively [Articol]
(2024) Gutsul, Ion
We constructed five countable series of bounded and unbounded polyhedra of the same volume in H3.
Invariant Transformations of Loop Transversals in Loops. 1. The Case of Isomorphism [Articol]
(2024) Kuznetsov, Eugene
A special class of invariant transformations of loop transversals in loops is investigated. The considered transformations correspond to arbitrary isomorphisms of transversal operations in loops. Isomorphisms of loop transversal operations with the same unit 1 are investigated.
Invariant Transformations of Loop Transversals in Loops. 2. The Case of Isotopy [Articol]
(2024) Kuznetsov, Eugene
A special class of invariant transformations of loop transversals in loops is investigated. Transformations from this class correspond to arbitrary isotopies of transversal operations in loops. Isotopies of loop transversal operations with the same unit 1 are investigated.
Semisymmetric Quasigroups [Articol]
(2024) Didurik, Natalia N.; Shcherbacov, Victor A.
A quasigroup satisfying the identity x(yx) = y is called semisymmetric. In this article, the isotopy of semisimmetric quasigroups is studied. A condition is found when a loop, isotopic to a semisymmetric quasigroup, is a semisymmetric loop.
Model-assisted Adaptive Designs for Dose-ranging Clinical Trials [Articol]
(2024) Dragalin, Vladimir
The overall goal of dose-ranging studies is to establish the existence, nature, and extent of dose effect. Recently, a great effort has been made to investigate and develop designs and methods for efficient learning about dose response and more accurate and faster decision making on dose. The focus is on adaptive modelassisted optimal designs of experiments modeling safety, efficacy, or both efficacy and safety endpoints. The proposed dose allocation rules are based on a combination of D- and c-optimality criteria in optimal design of experiments.
Some Hash Functions Based on Quasigroups [Articol]
(2024) Cernov, Vladimir; Shcherbacov, Victor
In this paper, we consider the construction of hash functions based on finite quasigroups.
Groupoids and Quasigroups Obeying Certain Laws [Articol]
(2024) Chiriac, Liubomir; Josu, Natalia; Lupashco, Natalia; Pîrlog, Artiom
In this paper we study under which conditions the binary topological groupoid with some algebraic properties can be ”transformed” into a topological quasigroup with the same algebraic properties.