A method is proposed to analyze the 2-adic complexity of generalized cyclotomic binary sequences with period pq. Along with linear complexity, 2-adic complexity serves as an important measure of sequence unpredictability. The method is based on generalized Gaussian periods of various orders using the prime modules p and q. The 2-adic complexity of Ding–Helleseth generalized cyclotomic sequences of orders two, four, and six with high linear complexity is estimated. The analysis shows that these sequences have high 2-adic complexity, which is sufficient to resist attacks using the rational approximation algorithm. Previous results obtained for the sequences of order two are summarized. The proposed method can be applied to a different type of sequences defined using generalized cyclotomic classes of various orders, as well as to investigate the m-adic complexity of both binary and non-binary sequences, such as quaternary sequences.

In recent years, the steady-state flow of viscous fluids has attracted considerable research interest due to its broad engineering applications. This study provides new insights into the classical problem of the theory of the viscous laminar stationary boundary layer of an incompressible Newtonian fluid on a thin flat plate (Blasius problem). A finite-difference solution to the Blasius problem was obtained by the shooting method in combination with the Runge–Kutta numerical scheme of the fourth-order accuracy over a large interval for a very fine mesh. The numerical results were validated against similar known data of calculation tests. The Blasius function f(η) and its first two derivatives were approximated using the third-order B-spline. Excellent agreement with the results of known calculations was demonstrated. A new analytical correlation for the Blasius function, which approximates the results of the calculations in a wide range of the self-similar variable η, was established by the nonlinear least squares method (NLLSM). The values of the function f and its first- and second-order derivatives were compared with known data. The results align with previous solutions. The longitudinal velocity profile in the boundary layer, defined through the derivative f′ of the Blasius function, can serve as the initial velocity profile in the numerical modeling of turbulent flat and three-dimensional flows of an incompressible fluid.

Some parameters of the structural functions method, which is used to construct an approximate solution to the elasticity problem for inhomogeneous solids, were analyzed. The equivalence of two existing approaches to computing structural functions was proved, and the set of known properties of structural functions was expanded. It was demonstrated that the method approximates the displacements in an inhomogeneous body by expressing them as a series involving derivatives of the displacements in a homogeneous (concomitant) body with the same geometry and loading. In practical applications, the series representation of the solution must be replaced by the partial sum of the series. For a specific class of approximate solutions to the concomitant problem, a relationship was established between the number of terms used in the partial sum of the series and the approximation order of the solution to the concomitant problem. Criteria for selecting elastic properties of the concomitant body were discussed.

A language for describing the Common Digital Space of Scientific Knowledge (CDSSK) ontology was proposed. Tailored to the evolving digital knowledge space with its high dynamics in the emergence of new scientific findings and the presence of various types of objects with multilevel attributes and relations, it incorporates the principles of the Ontology WEB Language but focuses on multilevel attributes of objects and named relations of various structures. Based on the analysis of the CDSSK objects, their attributes were classified, as well as the relations between them. Five types of attributes (first- and second-kind simple attributes, first- and second-kind composite attributes, and attributes “as relations”) and three classes of relations (universal, quasi-universal, and specific) were singled out. Within the classes, each relation can be “simple” or composite and falls into one of three distinct kinds. The language uses unified guides and dictionaries in JSON format. Its syntax is built around a system of unique names derived according to fixed mnemonic rules, which uniquely identify the type of the element and its relation to a specific object from the name structure. The language applicability was illustrated with examples.

The analytical solutions for the problems of macroscale flexural-shear and purely transverse-shear buckling modes of test specimens made of fiber-reinforced composites with a [0∘]_s layup (s denoting the number of laminas) were analyzed, as well as the problems of mesoscale transverse-shear buckling modes of their peripheral layers under axial compression. Composite materials characterized by a physically nonlinear relationship only between transverse tangential stresses and the corresponding shear strains were examined. The solutions were obtained using three variants of linearized equations of the equilibrium in a perturbed state: based on the simplest refined S.P. Timoshenko’s model; from a linear approximation of the deflection and a cubic polynomial approximation of the axial displacements in the transverse coordinate with the preliminary satisfaction of the boundary conditions for tangential forces (the first refined version of the theory; Reddy–Nemirovsky model type); and without the preliminary satisfaction of such conditions (the second refined version of the theory). The physical nonlinearity of the material was incorporated in the linearized equations following the Shanley concept by introducing the tangential shear modulus. The theoretical data were compared with the experimental results.

Scientific journals play an important role as a key tool for advancing science and encouraging knowledge exchange during research collaboration. The relationships among them are extremely diverse and cluster together into a complex network of connections. Developing adequate mathematical models of such self-organizing systems is a serious problem that requires in-depth investigation. This article introduces an approach to analyze the journal network based on a new bibliographic graph in which the relationships among journals are defined by shared authorship, i.e., through the binary intersection of author sets. Two levels of journal interaction can be distinguished using consistent source data processing techniques and methods. At the lower level, the relationships among multiple journals are grouped by scientific topics. At the upper level, the interactions between these topics are established. The approach was validated through a pilot study of eLIBRARY.RU data. The findings demonstrate its feasibility and scalability potential.

The problems of hydroelasticity that arise during the mathematical modeling of the nonlinear response of the wall of a narrow channel filled with pulsating viscous liquid were formulated and solved. The plane channel has parallel rigid walls, where the bottom wall with nonlinear elastic supports at the ends undergoes longitudinal vibrations due to its interaction with the opposite vibrating wall through the liquid layer. The liquid dynamics in the channel were analyzed as a pulsating Couette flow with the consideration of the liquid inertia. The movement of the bottom wall of the channel was described using the mass-on-spring model characterized by symmetric stiffness with cubic nonlinearity. With the dissipative properties of the viscous liquid taken into account, the influence of the initial conditions became negligible, making it possible to focus on the formulation of a boundary value problem of mathematical physics for steady-state forced vibrations of the channel wall. Following the asymptotic analysis by the perturbation method, the problem was reduced to a nonlinear ordinary differential equation that generalizes the Duffing equation. The equation was solved by the Krylov–Bogolyubov method, and the nonlinear hydroelastic response of the wall to the primary resonance was determined in the form of its amplitude- and phase-frequency characteristics. The nonlinear hydroelastic response characteristics were expressed as implicit functions and require further numerical investigation. An example of such an investigation was provided, demonstrating that taking into account the liquid inertia and varying thickness of the liquid layer in the channel significantly affects the amplitude of vibrations, resonant frequencies, as well as the range of unstable vibrations with sudden amplitude changes.

Network calculus provides a mathematical framework for determining the delay bounds in network models and, unlike the queueing theory which relies on the distribution functions of random variables, uses simple deterministic parameters describing the characteristics of traffic arrivals and the service device. In this study, network calculus was applied to calculate the upper delay bounds for various types of eCPRI traffic in the fronthaul segment of 4G/5G mobile networks.

Due to the increasing heterogeneity of data models and schemas in the modern world, robust data integration is a high-priority issue. Data integration systems have been extensively deployed across various domains, including astronomy, land use management, and materials science. However, data integration programs can be very complicated. Thus, formal verification of their correctness has emerged as an important task.

In this article, an approach to verify the correctness of data integration in an integrated system of databases on the properties of inorganic substances and materials is considered. The system, developed at the A.A. Baikov Institute of Metallurgy and Materials Science of the Russian Academy of Sciences, employs a two-stage data integration process: during the first stage, the source data marked for deletion, modification, or insertion are converted into an intermediate XML representation; in the second stage, the system invokes the corresponding procedures for XML elements in the target integrated database and updates it accordingly. The data integration programs are implemented by combining an imperative programming language with a declarative language of relational databases. Verification is performed by defining the semantics of the data schemas and data integration programs in a formal specification language and proving the correctness of data integration using automated provers.

A method is proposed for constructing idempotents in a unital algebra 𝒜 using n arbitrary idempotents P₁,...,P_n from this algebra. The properties of the resulting idempotents P = P(P₁,...,P_n) are investigated; for n = 2 and n = 3, explicit forms of the idempotents are obtained: A(P₁,P₂) and B(P₁,P₂,P₃), respectively. It is shown that the mappings

P₂ ↦ A(P₁,P₂), f(P₂) = A(P₁,P₂) and P₃ ↦ B(P₁,P₂,P₃), g(P₃) = B(P₁,P₂,P₃)

preserve the complements ⊥ and are multiplicative on wide classes of idempotent pairs. For a finite trace 𝜑 on a unital C^* -algebra 𝒜, 𝜑(P(P₁,...,P_n)) = 𝜑(P_n). For the projections P₁,...,P_n from the von Neumann algebra 𝒜, the method yields a new projection and enables the construction of some partial isometries.

This article presents the results of an experimental study on the surface morphology, elemental composition, and magnetic properties of Hastelloy C-276 substrates with intermediate Al₂O₃/Y₂O₃/MgO/LaMnO₃ buffer layers and a deposited MgB₂ superconductor. Measurements were carried out at a magnetic field from −5 to 5 T and in the temperature interval from 5 to 15 K, with the annealing temperatures of the tapes in the range from 623 to 923 K. Vacuum annealing had a significant effect on the magnetic characteristics of the substrates, and the specific magnetic moment varied up to 20 % depending on the annealing temperature in the temperature interval from 5 to 15 K.