Hugo Lemarquand, Mathieu Lugrin, Cédric Content
et al.
Base-flow computations and stability analyses are performed for a hypersonic wind tunnel nozzle at a Mach number of 6. Isothermal and adiabatic wall boundary conditions are investigated, and moderate stagnation conditions are used to provide representative scenarios to study the transition in quiet hypersonic wind tunnel facilities. Under these conditions, the studied nozzle shows a small flow separation at the convergent inlet. Global stability analysis reveals that this recirculation bubble may trigger a classical three-dimensional stationary unstable global mode. Resolvent analysis reveals Görtler, first and second Mack modes affecting the divergent part of the nozzle, along with a Kelvin–Helmholtz instability induced by the bubble. The present study also highlights the key impact of perturbations located in the convergent inlet on the development of instabilities further downstream in the divergent outlet, helping to understand the need and efficacy of a suction lip upstream of the nozzle throat to mitigate instabilities in the divergent section. Detailed knowledge of all these mechanisms is essential for understanding flows in quiet hypersonic wind tunnel nozzles and, consequently, represents a key step towards the optimisation of such nozzles.
Angeliki Bourazana, Alexandros Briasoulis, Christos Kourek
et al.
Over the past decades, coronary revascularization has evolved dramatically with the introduction of bioresorbable scaffolds (BRSs), designed to provide temporary vessel support, elute antiproliferative drugs, and then fully resorb, ideally restoring natural vasomotion and eliminating long-term foreign-body reactions. Early enthusiasm for first-generation polymeric devices, such as the Absorb bioresorbable vascular scaffold, was tempered by increased rates of scaffold thrombosis and late adverse events, largely attributed to thick struts, suboptimal implantation techniques, and unpredictable degradation kinetics. Subsequent developments in polymeric (e.g., MeRes-100, NeoVas) and metallic magnesium-based scaffolds (e.g., Magmaris) have focused on thinner struts, improved radial strength, and refined resorption profiles. Clinical trials and meta-analyses, including ABSORB, AIDA, BIOSOLVE, and BIOSTEMI, reveal that optimized procedural strategies, especially the “PSP” approach (Prepare–Size–Post-dilate) and routine intravascular imaging, substantially reduce thrombosis and restenosis rates, aligning outcomes closer to those of contemporary drug-eluting stents (DESs). Nonetheless, challenges persist regarding inflammatory responses to degradation by-products, mechanical fragility in complex lesions, and patient selection. Ongoing innovations include hybrid polymer–metal designs, stimuli-responsive drug coatings, and AI-assisted imaging for precision implantation. While early-generation BRSs demonstrated both promise and pitfalls, next-generation platforms show steady progress toward achieving the dual goals of transient scaffolding and long-term vessel restoration. The current trajectory suggests that bioresorbable technology, supported by optimized technique and material science, may soon fulfill its original vision; offering safe, effective, and fully resorbable alternatives to permanent metallic stents in coronary artery disease. This review provides an updated synthesis of the design principles, clinical outcomes, and procedural considerations of drug-eluting bioresorbable scaffolds (BRSs). It integrates recent meta-analytic evidence and emerging insights on device mechanics, including the influence of strut thickness on radial strength and the potential role of non-invasive imaging in pre-implantation planning. Special focus is given to magnesium-based scaffolds and future directions in patient selection and implantation strategy.
Diseases of the circulatory (Cardiovascular) system
Purpose of the work is revealing and researching of peculiarities of a motion of a viscous liquid having a free boundary and undergoing periodic in time influences which are characterized by the absence of a predominant direction in space. Methods. The analytic investigation methods of non-linear problems, of boundary problems for the system of Navier– Stokes and continuity equations are used that are the method of perturbations (the method of a small parameter) the method of Fourier (the method of a separation of variables), an averaging, a construction and studying of asymptotic formulas. Results. A new problem on the motion of a viscous liquid is formulated and solved. Asymptotic representations of the found solution are constructed and explored. New hydromechanical effects are revealed. Conclusion. The work is fulfilled in the development of a perspective direction in liquid mechanics that is of researching the dynamics of hydromechanical systems under periodic influences. The obtained results can be used in particular in further investigations of a non-trivial dynamics of hydromechanical systems, under working for the methods of a control of hydromechanical systems.
On August 18, 2023, an outstanding mathematician, a prominent government, political and public figure, a major organizer of science and education in Kazakhstan, the president of the National Engineering Academy of the Republic of Kazakhstan, the president of the Mathematical Society of the Turkic World, laureate of the State Prize of the Republic of Kazakhstan in fields of science, technology and education, Honored Worker of Kazakhstan, Doctor of Technical Sciences, Professor, Academician of the National Academy of Sciences of the Republic of Kazakhstan Bakytzhan Tursynovich Zhumagulov turned 70 years old.
In this paper, in the space L_2(R^2), we study a third-order differential operator with continuous coefficients in R(−∞, +∞). Here, these coefficients can be unlimited functions at infinity. In addition under some restrictions on the coefficients, the bounded invertibility of the given operator is proved and a coercive estimate is obtained, i.e. separability is proved.
This article is devoted to the study of the forcing companions of the Jonsson AP-theories in the enriched signature. It is proved that the forcing companion of the theory does not change when expanding the theories under consideration, which have some properties, by adding new predicate and constant symbols to the language. The model-theoretic results obtained in this paper in general form are supported by examples from differential algebra. An approach in combining a Jonsson and non-Jonsson theories is demonstrated. In this paper, for the first time in the history of Model Theory. This will allow us to further develop the methods of research of Jonsson theories and expand the apparatus for studying incomplete theories.
The classification of inverse problems of dynamics in the class of ordinary differential equations is given in the Galiullin’s monograph. The problem studied in this paper belongs to the main inverse problem of dynamics, but already in the class of second-order stochastic differential equations of the Ito type. Stochastic equations of the Lagrangian structure are constructed according to the given properties of motion under the assumption that the random perturbing forces belong to the class of processes with independent increments. The problem is solved as follows: First, a second-order Ito differential equation is constructed so that the properties of motion are the integral manifold of the constructed stochastic equation. At this stage, the quasi-inversion method, Erugin’s method and Ito’s rule of stochastic differentiation of a complex function are used. Then, by applying the constructed Ito equation, an equivalent stochastic equation of the Lagrangian structure is constructed. The necessary and sufficient conditions for the solvability of the problem of constructing the stochastic equation of the Lagrangian structure are illustrated by the example of the problem of constructing the Lagrange function from a motion property of an artificial Earth satellite under the action of gravitational forces and aerodynamic forces.
In this paper, we obtained several new integral inequalities using fractional Riemann-Liouville integrals for convex s-Godunova-Levin functions in the second sense and for quasi-convex functions. The results were gained by applying the double Hermite-Hadamard inequality, the classical Holder inequalities, the power mean, and weighted Holder inequalities. In particular, the application of the results for several special computing facilities is given. Some applications to special means for arbitrary real numbers: arithmetic mean, logarithmic mean, and generalized log-mean, are provided.
This article deals with the factorization and solution of nonlocal boundary value problems in a Banach space of the abstract form B1 u = A u - S Φ( u )- G Ψ(A0 u) = f, u ∈ D (B1) , where A, A0 are linear abstract operators, S, G are vectors of functions, Φ, Ψ are vectors of linear bounded functionals, and u, f are functions. It is shown that the operator B1 under certain conditions can be factorized into a product of two simpler lower order operators as B 1 = BB0. Then the solvability and the unique solution of the equation B1 u = f easily follow from the solvability conditions and the unique solutions of the equations Bv = f and B0 u = v. The universal technique proposed here is essentially different from other factorization methods in the respect that it involves decomposition of both the equation and boundary conditions and delivers the solution in closed form. The method is implemented to solve ordinary and partial Fredholm integro-differential equations.
M.T. Kosmakova, V.G. Romanovski, D.M. Akhmanova
et al.
The article considers a homogeneous boundary - value problem for the heat equation in the non - cylindrical domain, namely, in an inverted pyramid with a vertex at the origin of coordinates, two faces of which lie in coordinate planes.A solution to the problem is sought in the form of a sum of generalized thermal potentials. There is a need to study the system of two Volterra integral equations of the second kind with singularities of the kernel. It is assumed that densities (heat intensity) depend only on a time variable, i.e. the density in each time section is considered constant. As a result, the system of integral equations is reduced to the homogeneous Volterra integral equation of the second kind. It is shown that this equation is uniquely solvable in the class of continuous functions.
The Helmholtz problem is considered in a probabilistic formulation. By a given stochastic Langevin-Itoˆ equation in an indirect representation, as the equation of the Hamiltonian structure and the equation of the Birkhoffian structure are constructed. The functional that takes a stationary value on solutions of a given stochastic Birkhoff equation, is defined by the method of moment functions. The obtained results are illustrated by two examples: 1) the plane motion of a symmetric satellite in a circular orbit under the action of gravity and aerodynamic forces, and 2) the fluctuation motion of a gyroscope in a gimbal caused by the stochastic fluctuating moment of forces along the suspension axis of the inner ring.
N.К. Shazhdekeeva, G.К. Shambilova, А.N. Мyrzasheva
et al.
Мақалада нақты деректердi пайдалану кезiнде нақты уақыт режимiнде өнiмдi қабаттың коллектор-лық қасиеттерiн дәлiрек анықтауға мүмкiндiк беретiндей сүзгiлеу теориясының керi есебi зерттелдi. Бұл мақсатта ұңғымалар бойынша сұйық дебитiнiң, газ және қабат қысымының уақытқа тәуелдiлi-гiнiң қажеттi шарттары анықталды және нақты мәлiметтер берiлiп, белгiлi бiр кен орнының техноло-гиялық көрсеткiштерi қалпына келтiрiлдi. Тура және керi есептер шығарылды, оларды шешудiң ал-горитмi ұсынылды. Сулы қабаттың облыс шеттерiнде жеткiзу, жеңiлдету және сүзгiлеу-сыйымдылық параметрлерiнiң шарттары қалпына келтiрiлгенде ұңғымалардағы J сәйкессiздiк функционалының азаюы қалпына келтiру және сәйкестендiру есептерiнiң дәйектi шешiмдерiн алудың жеткiлiктi шарты болып табылатындығы көрсетiлдi. Атырау облысы кен орындарында алынған мәлiметтер негiзiнде сандық тәжiрибелер жүргiзiлдi.
Статья посвящена изучению разностной схемы второго порядка точности для решения эллиптикопараболического уравнения с нелокальным граничным условием. Установлена корректность разностной схемы второго порядка точности в пространствах Гёльдера. Получены оценки коэрцитивности в нормах Гёльдера для приближенного решения нелокальной краевой задачи для эллиптикопараболического дифференциального уравнения. Результаты численных экспериментов представлены для поддержки упомянутых выше теоретических утверждений.
M.T. Jenaliyev, S.A. Iskakov, M.I. Ramazanov
et al.
In this paper we consider the first boundary value problem for the loaded equation of heat conduction in a
quarter plane. The loaded term is the trace of the fractional derivative of order ν, 0 ≤ ν ≤ 1 with respect
to the time variable on the line x = t. It is shown that when 0 ≤ ν ≤ 1 and ∀λ ∈C, then the load is a weak
perturbation, that is, the studied problem has a unique solution in the class of bounded functions.
In this paper we define families of classes of functions related to best approximations in harmonic intervals. These families of function classes characterize the order of approximation of functions by trigonometric polynomials with a spectrum from harmonic intervals. The article contains an investigation of various characterizations of the indicated families of function classes, introduces imbedding theorems, and shows the connection between the introduced families of functions classes and the classical Besov spaces. The article is intended for researchers specializing in the theory of approximation and functional analysis, and all those whose interests lie in these areas.
The present paper devoted to problems of Riemannian geometry and planar dynamical systems. In particular we study nondegenerate singular points of normalized Ricci flows on special type of generalized Wallach spaces. Our main goal is to prove the absence of such points. The main idea is based on a special set Ω introduced in [1, 2] for studying general properties of degenerate singular points of Ricci flows. More concretely, for solving the mentioned problem we use the facts that the set (0; 1/2)3 Ո Ω is connected and the set (0; 1/2)3 \ Ω consists of three connected components as it was proved in [3].