Institutul de Matematică şi Informatică "Vladimir Andrunachievici"

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    On Some Solutions of the 3D Navier-Stokes Equations [Articol]
    (2024) Baltag, Iurie
    In this paper, there are determined various solutions of the stationary Navier-Stokes equations, which describe the 3D flow of an incompressible liquid or gas, i.e., solutions containing the components of the velocity of flow – the functions u, v, w and the created pressure P . We mention that in the paper a series of exact solutions are obtained, in which the viscosity coefficient λ participates explicitly.
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    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.
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    Some Applications of Properties of the Extensions of the Ring of Integers [Articol]
    (2024) Teleucă, Marcel; Sali, Larisa
    This article presents some considerations related to the application of ring algebra concepts to solving problems proposed in mathematics competitions. The content can be useful to mathematics teachers and high school students.
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    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).
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    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).
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    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.
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    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.
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    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.
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    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.
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    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.