2. Articole

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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.
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.
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.
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).
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.
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.
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.
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.

2. Articole

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