In this article, an efficient modification of the Picard iteration method for solving the multispecies Lotka-Volterra models (MLVMs) is first proposed. Then the convergence and stability of the modified method are discussed. In order to indicate the efficiency of the modified method, three cases of the MLVMs are given. The obtained results evidence that the developed approach is a useful semi-analytical scheme for the solution of the MLVMs. The modification differs from the classical Picard iteration because only the newly generated local terms of the nonlinear integrand are added at each step; therefore, repeated lower-order calculations are avoided while the same Picard limiting form is preserved.
In this article, we proposed a fast and efficient numerical approach on graded and adaptive meshes for the solution of the multi-term time fractional diffusion equation. The fast L2‑1σ scheme is used for time discretization, which is taken in the Caputo sense, and a compact second-order scheme is used for spatial discretization. Due to the non-local nature of fractional derivatives, this equation often exhibits weak singularities near the initial time. The scheme on the uniform mesh is unable to resolve this issue, leading to reduced accuracy and slow convergence. Because of the dynamic adjustment of meshes based on solution behavior, our approach on graded and adaptive meshes resolves this issue. A rigorous analysis of stability and convergence reveals min{rα_1,2} (0 < α_1 < 1) order in time and second order in space, where r denotes the grading parameter for resolving initial singularity. Five numerical examples are taken to validate the theoretical results.
A new nonlinear mathematical model of the equilibrium of a two-dimensional body with three thin rigid inclusions is investigated. Two rectilinear inclusions are connected by hinge joint and delaminate from the elastic matrix, while the third inclusion may come into contact with the two connected inclusions. To describe the possible contact of the rigid inclusions, a nonlinear pointwise non-penetration condition is used. The prescribed affine structure of infinitesimal rigid displacements for the inclusions allows one to impose an inequality-type constraint. Signorini-type conditions are also specified on the curves corresponding to the delamination cracks. The existence of a solution to a variational equilibrium problem for a composite body is proven.
An inhomogeneous boundary value problem for a stationary magnetohydrodynamics-Boussinesq model with variable leading and lower-order coefficients is investigated. Sufficient conditions on the variable coefficients and other problem data are established, ensuring the global solvability of this problem and the conditional local uniqueness of its solution. Bibl. 35.
This article discusses the issues of analyzing transient processes when a pulsed current is applied to a metal sample in the form of a copper wire to stimulate electroplastic deformation using mathematical modeling. These processes are directly related to the electroplastic effect, which is manifested in a decrease in the resistance of metal to plastic deformation and an increase in its plasticity when passing high-density current pulses under mechanical stress above the yield point. The existing theories about different mechanisms for stimulating electroplastic deformation are described. A mathematical model has been developed that includes the sequential solution of three related problems: electromagnetic, thermal, and mechanical. A step-by-step algorithm has been developed for mathematical modeling of these tasks in the MatLab software package. A sample in the form of a copper wire with a length of 500 mm and a thickness of 1 mm was selected for the study, which is loaded with a “dead” weight of 0.5 kg. Using the geometric parameters of the sample, the physical properties of copper, and the parameters of the current pulse, the final code of the mathematical model was compiled in MatLab. As a result of the simulation, graphs of the average wire temperature, Mises voltage, wire deformation, and current density were obtained. Additionally, the temperature distribution in the wire sections was analyzed, confirming the absence of a skin effect. In conclusion, the conclusions of the work are presented and practical recommendations are proposed for stimulating electroplastic deformation in copper samples. Optimal conditions have also been formulated for the design of new or modernization of existing electric pulse processing plants for metals and alloys.
The paper deals with a 2D water-waves model in a channel. Mathematically, it is simulated by the Zakharov–Kuznetsov equation with a linear transport term posed on a half-strip. The flow is assumed to be generated by a wavemaker. The model is supplemented by homogeneous boundary conditions. Using Bourgain-type spaces adapted to the ZK dispersive structure, anisotropic smoothing and boundary trace estimates, we establish its local well-posedness in L^2 .
We study a shape optimization problem for a stationary linear micropolar fluid. The objective is the squared L2-gap between the microrotation and the local vorticity. This cost measures the deviation of the micropolar model from the limiting Stokes-type regime in which microrotation is aligned with vorticity. The analysis is carried out by transporting the state equation to a fixed reference domain by the Piola transformation. We state the dimensional convention explicitly, prove well-posedness of the state and adjoint systems, derive the weak material derivative in the Piola sense under sufficient data regularity, and obtain a Hadamard boundary representation of the shape derivative under trace regularity assumptions. The resulting boundary density is used in a continuous gradient-flow dynamical system and in a finite-dimensional gradient flow for a fixed set of shape parameters. The numerical section describes the supplied obstacle and pipe-design computations and reports only information visible in the provided source files and output histories.
We consider equations describing two-dimensional unsteady motion of a binary mixture of viscous incompressible fluids. A theorem on the existence and uniqueness of a weak solution to the initial-boundary value problem corresponding to the flow of the mixture in a bounded domain is proved. To prove the existence of a solution, we consider an approximation problem for the Galerkin approximations, establish its solvability and a priori estimates that are independent of the approximation parameter. Then a limit passage with respect to the approximation parameter is performed, and it is shown that the Galerkin approximations converge weakly to a solution of the original problem. The uniqueness of the solution is established using Gronwall’s inequality.
This paper presents a lightweight and high-performance method for 3D spatial object estimation based on monocular vision, designed for autonomous ground vehicle systems. The developed software complex relies on task decomposition: fast 2D object and local feature detection (using YOLOv11s) is combined with classical numerical optimization via the Gauss-Newton method. The architecture is implemented as a directed acyclic graph on the ROS2 platform with a strict relay time synchronization mechanism. The proposed hybrid approach eliminates the need for resource-intensive end-to-end deep learning (DL) models, radically reducing the computational load on the graphics accelerator. Computational experiments on the KITTI dataset demonstrate a phenomenon of metric stability in complex scenes with occlusions (BEV AP 19
Point clouds are widely used for three-dimensional reconstruction, scene analysis, navigation and other applied problems involving spatial data. A characteristic feature of point clouds is the combination of a large number of points, irregular sampling density and the absence of a fixed ordering of elements. These properties increase the computational cost of feature extraction and may lead to redundant processing of geometrically similar points. This paper proposes a mathematically refined principal component analysis (PCA)-weighted sampling module for point-cloud feature extraction. In contrast to approaches that interpret eigenvalues of the covariance matrix directly as point contributions, the proposed formulation estimates the informativeness of each point through the weighted energy of its projections onto principal directions. This makes the sampling criterion point-dependent and gives a clearer mathematical interpretation of the selection procedure. The module can be integrated into a PointNet-style hierarchical feature extraction scheme, where selected points define local regions and a shared neural encoder forms local descriptors. The proposed formulation is intended to reduce redundancy in centroid selection while preserving geometrically informative regions of the original point cloud.
This paper investigates the inverse source identification problem for a fractional differential equation with sequential Caputo derivatives. The primary objective is to determine the unknown source components alongside the classical solution of the boundary-initial value problem. In this problem, we reconstruct a space-dependent source term using an interior observation at a fixed time. Using the method of spectral expansion based on the Fourier series, the exact analytical solutions are constructed. Furthermore, the existence, uniqueness, and uniform convergence of the classical solutions are rigorously established within the framework of Hölder spaces.
The stress state of a transverse rectangular plastic layer in a stretchable heterogeneous plastic strip under plane deformation at a critical moment of loading is studied. The layer consists of a less durable material than the rest of the strip, and the strength parameter at the contact boundary has a jump. The material of the strip, including the layer, is heterogeneous. The strength parameter is determined by the inhomogeneity function, which depends on the distance to the longitudinal axis of symmetry of the strip. As a simplifying condition, it is assumed that the tangential stresses in some neighborhood of the longitudinal axis of symmetry depend linearly on the distance to it. The nature of the distribution of normal stresses at the contact boundary is investigated. Explicit analytical expressions are obtained for the approximate calculation of stresses in the plastic layer and the critical load for some special cases of the heterogeneity function.
A computationally efficient method for enhancing the robustness of monocular simultaneous localization and mapping (SLAM) systems based on the ORB-SLAM3 architecture for operation in dynamic environments is presented. The negative impact of moving objects on epipolar geometry estimation and global scale drift is mathematically formalized. A method for proactive video stream filtering using convolutional neural networks (YOLO-Seg) is proposed, where dynamic objects are identified and excluded from the feature extraction process using binary masks. The necessity of applying morphological mask dilation to compensate for the FAST detector’s aperture is strictly justified. Experiments on the KITTI dataset demonstrate a reduction in the Absolute Trajectory Error (ATE) by 23–31
This paper addresses the problem of a laminated structure consisting of an adhesive layer and two adherents within the framework of simplified strain gradient elasticity (also known as one-parameter gradient elasticity) under antiplane shear. The deformations of both the adhesive layer and the adherents are described by this theory. The shear modulus, scale parameter, and width of the adhesive layer depend on a small parameter δ: the width is proportional to δ, the shear modulus is proportional to δ^-1 , and the scale parameter scales as δ^p with p = 0, 1, 2 . This scaling implies that the adhesive layer behaves as a thin elastic inclusion. By passing to the limit as δ→0 , we derive three new types of limit models featuring imperfect interface conditions that effectively behave as rod-type elastic inclusions, depending on the value of the exponent p.
This article discusses the use of hereditary models of radon volumetric activity (RVA) to describe the dynamics of radon accumulation in a storage chamber, taking into account the memory effects in the process of radon transport. Hereditary RVA models represent a generalization of classical concepts and mathematical models of the RVA process, based on ODEs, to FDEs with Gerasimov-Caputo fractional derivative of variable-order 0<α(t)<1 . The main focus of the article is on the modification of hereditary RVA models to account, among other things, for the parameter τ, which is associated with a certain characteristic time, the time scale of the dynamic process. This is related to the fact that replacing the ordinary derivative in the model equation with a fractional operator cannot go unnoticed in terms of dimensional consistency in such a generalized equation. Therefore, to compensate for the impact of the fractional derivative, a parameter τ≠ 1 is introduced as a certain positive constant with the dimension of time. The aim of the study is to examine the impact of the parameter τ on the simulation results, specifically the amplitude and duration over time of the model curve of the dynamic RVA process. As a result, it is shown that the introduction of the parameter τ≠ 1 into the model equation through the coefficient τ^1-α(t) represents a scaling parameter for the amplitude of the desired solution function of the FDEs. From this, it follows that the introduction of the parameter τ≠ 1 in hereditary RVA models will be sufficient to maintain the equality of the dimensions of the left and right sides of the fractional model equation.
In this work, the inverse problem of reconstructing the squared slowness function in the two-dimensional eikonal equation has been developed and numerically investigated. The inverse problem is reduced to the minimization of a travel-time misfit functional by gradient method and employs the Fast Marching Method for an efficient solution of the direct eikonal problem. A gradient of the functional is calculated by direct and adjoint problems, enabling the computational cost of the gradient comparable to that of a single direct solve. Numerical experiments on synthetic models which parameters are close to the human body with inclusions show that the method can accurately recover the spatial structure and contrast of the slowness distribution under different grid resolutions and source configurations. A comparative analysis of simple gradient and heavy ball method has shown that the use of adaptive relaxation of steps accelerates the convergence of gradient methods, including accelerated gradient methods.
In this paper, we propose an integro-differential model for the spatio-temporal evolution of infectious diseases with asymptomatic transmission. The model consists of a reaction-diffusion system with an integral memory term accounting for the distribution of the incubation period. We first analyze the asymptotic behavior and the properties of the integro-differential model. Then, we prove the local existence of a weak solution of the system by means of the Faedo-Galerkin method and a compactness argument. The model is applied to simulate the geographical evolution of a disease in Lebanon.
Problems of quadcopter (unmanned aerial vehicle) control have been considered in the literature for mathematical models with different classes of controls with various options for phase variables and control parameters. The article presents a derivation of a quadcopter dynamics model with Euler and Krylov angles, in a fixed coordinate system.
This article proposes a novel high-speed reverse converter from the Residue Number System (RNS) to a positional number system. The proposed method is designed for arbitrary RNS moduli sets that include a power-of-two modulus and is based on a Chinese Remainder Theorem with fractional values conversion technique. Hardware simulations demonstrate that our converter outperforms the state-of-the-art designs by 34.70
