Institutul de Matematică şi Informatică "Vladimir Andrunachievici"

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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.
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).
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.
Alternative Clifford-like algebras [Articol]
(2024) Smith, Jonathan-D
The real, complex, and quaternion division algebras may be constructed as Clifford algebras. However, while the octonions and split octonions share many features with Clifford algebras, such as an involutary anti-automorphism, their nonassociativity prevents their realization as Clifford algebras. We now introduce Kingdon algebras: alternative Clifford-like algebras over vector spaces which are equipped with a symmetric bilinear form, such that the octonions and split octonions arise as Kingdon algebras. In the process, they acquire 2-graded (superalgebra) structure. A comparable construction yields 3-graded algebras over spaces equipped with an alternating trilinear form.
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.
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.
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.
Factor-Group of a Topological Group and Factor-Ring of a Topological Ring and Completeness Issues [Articol]
(2024) Arnautov, V. I.; Ermacova, G. N.
The connection between the completeness of topological groups and topological rings and the completeness of their factor groups and factor rings, respectively, are discussed in this article.
Finiteness for Sets with Atoms [Articol]
(2024) Andrei, Alexandru; Ciobanu, Gabriel
We present various definitions for finite sets in the framework of finitely supported sets. We compare these definitions and emphasize their independence.
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.
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.
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.
International Conference dedicated to the 60th anniversary of the foundation of Vladimir Andrunachievici Institute of Mathematics and Computer Science, MSU: Proceedings IMCS-60, October 10-13, 2024 [Conferință]
(2024)
The Vladimir Andrunachievici Institute of Mathematics and Computer Science (VA IMCS) is approaching its 60th anniversary, underscoring its enduring status as a premier research institution in pure and applied mathematics and computer science. Established by the esteemed mathematician Vladimir Andrunachievici, VA IMCS has achieved recognition for its significant scientific contributions and pioneering research schools in algebraic rings, differential equations, quasigroups, functional analysis, and mathematical logic.Over six decades, the VA IMCS has been a beacon, a guide of knowledge, and a renowned center of excellence. About 80 national and international research projects have been realized; more than 400 PhDs and habilitated doctors theses have been defended.The institute publishes three prestigious journals: The Bulletin of the Academy of Sciences of the Republic of Moldova. Mathematics,Computer Science Journal of Moldova, and Quasigroups and Related Systems. These three journals make a valuable contribution to the promotion and international recognition of the scientific results obtained by the institute’s researchers, ensuring their visibility and facilitating their participation in various international projects.In celebration of its 60th anniversary, VA IMCS hosted the International Conference, promoting collaboration between academia, research institutions on critical issues in mathematics and computer science and their socio-economic applications. The conference proceedings feature 86 papers spanning Pure Mathematics, Applied Mathematics,and Computer Science, focusing on practical solutions for both national and global challenges.The anniversary conference, the Proceedings of which we are bringing to your attention, presented a summary of the Institute’s achievements and opened new ways for collaboration.
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.
List of Normal 3-Isohedral Spherical Tilings for Group Series 2 ∗ n [Articol]
(2024) Zamorzaeva, Elizaveta
Tilings of the 2-dimensional sphere with disks which fall into 3 transitivity classes under the group action are studied. For isometry group series 2 * n, n = 1, 2, …, we list all normal by Grünbaum and Shephard 3-isohedral spherical tilings.
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.
On a Method of Prolongation of Quasigroups [Articol]
(2024) Cuznețov, Elena
We consider a method of prolongation of finite quasigroups using two transversals, which intersect exactly in one cell, and study the recursive 1-differentiability of such prolongations.
On Geodesic Points of 6-Dimensional Hermitian Submanifolds of Cayley Algebra [Articol]
(2024) Banaru, Mihail; Banaru, Galina
Six-dimensional Hermitian submanifolds of Cayley algebra defined by means of three-fold vector cross products are considered. It is proved that the Weyl tensor of a 6-dimensional Hermitian submanifold of Cayley algebra vanishes at a geodesic point if and only if the scalar curvature at this point also vanishes.
On Self-Orthogonal n-ary Quasigroups [Articol]
(2024) Syrbu, Parascovia; Rotari, Tatiana
We consider self-orthogonal finite n-ary quasigroups and give some estimations of their spectrum in the present work. A method of construction of self-orthogonal n-quasigroups, using self-orthogonal quasigroups of lower arity, is given. In particular, it is shown that there exist: 1) self-orthogonal 2k-ary quasigroups of every order q > 3; q ≠ 6, where k ≥ 1; 2) self-orthogonal pk quasigroups of prime order p, for every p ≥ 3 and every k ≥ 1; 3) self-orthogonal 2n-quasigroups of order q, for every q > 3; q ≠ 6 and n + 1 ≢ 0 (mod q).