The paper considers a class of nonlinear differential equations which are not solvable in quadratures in general case. The author’s technology for solving such equations contains six problems. In this article, the solution to one of these probl...
This paper presents the final stage in the study of the analytical approximate solution to a class of nonlinear differential equations unsolvable in quadrature in the general case in the neighborhood of a perturbed value of a moving singular point. A...
This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the...
The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the que...
Earlier, the authors formulated and proved interval and point criteria for the existence of moving singular points of a third-degree nonlinear differential equation with a polynomial seventh-degree right-hand side for a real domain. For the complex d...
The paper deals with the results of a study of a third-order nonlinear differential equation with moving singular points and critical poles. So far, this type of equation cannot be solved in quadratures. The development of the author’s approach...
Ozone density at cold-point mesopause (O3-CPM) can provide information on long-term atmospheric trends. Compared to ground-level ozone, O3-CPM is not only adversely affected by chemical substances emitted from human activities but is also regulated b...
In previous studies, the authors formulated precise criteria for finding moving singular points of one class of nonlinear differential equations with a second degree polynomial right-hand side for a real domain. In this paper, the authors generalize...
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact that it depen...
Although parallel mechanisms are used in various fields, their application is often limited by singularities and a restricted workspace. Kinematic redundancy is a promising approach for mitigating these issues while also extending the functionality o...
This article reports an experimental work that unveils some interesting yet unknown phenomena underneath all smooth nonlinear maps. The findings are based on the fact that, generalizing the conventional gradient dynamics, the right singular vectors o...
A method for studying properties of the Earth’s surface tremor, measured by means of GPS, is proposed. The following tremor characteristics are considered: the entropy of wavelet coefficients, the Donoho–Johnston wavelet index, and two es...
The paper considers the specifics of nonlinear differential equations that have applications in different areas. Earlier, the authors proved the existence and uniqueness theorem for a solution to a class of non-linear differential equations in a neig...
This paper proposes a modified nonsingular fast terminal sliding mode (NFTSM) guidance law to solve the problem of ground moving target tracking for fixed-wing unmanned aerial vehicle (UAV) in a planar environment. Firstly, the loitering algorithm is...
This paper presents and investigates a new three-rotation (3R) parallel compliant mechanism that uses compliant rods to achieve three rotations. The mechanism is designed for use in pointing devices or as a spatial parallel manipulator. The mobility...
The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On th...
This study investigated whether Vincent van Gogh became increasingly self-focused—and thus vulnerable to depression—towards the end of his life, through a quantitative analysis of his written pronoun use over time. A change-point analysis was conduct...
We consider the two- and n-body problems on the two-dimensional conformal sphere
In this study, we constructed a 3D range-only (RO) localization algorithm based on improved unscented Kalman filtering (UKF). The algorithm can determine the location of unknown UWB nodes in a 3D environment through a moving node with low computation...
The recent technology advancements in miniaturizing the primary components of spacecraft allow the classic CubeSats to be considered as a valid option in the design of a deep space scientific mission, not just to support a main typical interplanetary...
The transport process is an important part of the research of fluid dynamics, especially when it comes to tracer advection in the atmosphere or ocean dynamics. In this paper, a series of high-order semi-Lagrangian methods for the transport process on...
Revealing singular quantum phenomena in various non-Hermitian systems is a hot topic in condensed matter physics research, with the bulk-boundary correspondence being one of the core issues in non-Hermitian topological states. In addition, the spin-o...
Due to the fixed size of the structure or the possibility of only simple manual adjustment, the traditional toilet wheelchair cannot easily be adapted to the size of the user or the toilet. In this paper, a planar two-degree-of-freedom parallel mecha...
This paper proposes an approach to derive the Jacobian matrix of a hybrid mechanism by applying a velocity operator to the transformation matrix. This Jacobian matrix is capable of deducing hybrid singularities, which cannot be identified by using th...
The angular position measurement of an array antenna based on a wireless signal has high accuracy in an indoor no-occlusion environment. However, due to the high complexity of indoor environments, signal occlusion, multipath, and other interfering fa...
In this paper, a new modified particle swarm optimization, m-PSO, is proposed, in which the novelty consists of proposing a fitness-based particle swarm optimization algorithm, PSO, which adapts the particles’ behavior rather than the PSO param...
One of the main challenges that face the reliable use of photovoltaic solar systems in hot arid regions is the prevailing high temperatures during the day. To overcome this issue, Phase Change Materials (PCM) are used for passive cooling providing di...