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A new, highly constrained guidance law is proposed against a maneuvering target while satisfying both impact angle and terminal acceleration constraints. Here, the impact angle constraint is addressed by solving an optimal guidance problem in which the target’s maneuvering acceleration is time-varying. To deal with the terminal acceleration constraint, the closed-form solutions of the new guidance are needed. Thus, a novel engagement system based on the guidance considering the target maneuvers is put forward by choosing two angles associated with the relative velocity vector and line of sight (LOS) as the state variables, and then the system is linearized using small angle assumptions, which yields a special linear time-varying (LTV) system that can be solved analytically by the spectral-decomposition-based method. For the general case where the closing speed, which is the speed of approach of the missile and target, is allowed to change with time arbitrarily, the solutions obtained are semi-analytical. In particular, when the closing speed changes linearly with time, the completely closed-form solutions are derived successfully. By analyzing the generalized solutions, the stability domain of the guidance coefficients is obtained, in which the maneuvering acceleration of the missile can converge to zero finally. Here, the key to investigating the stability domain is to find the limits of some complicated integral terms of the generalized solutions by skillfully using the squeeze theorem. The advantages of the proposed guidance are demonstrated by conducting trajectory simulations.

The paper aims to establish diverse soliton solutions for the integrable Kuralay equations and to explore the integrable motion of space curves induced by these equations. The solitons arising from the integrable Kuralay equations are examined through qualitative studies. They are considered highly significant for understanding various phenomena in fields such as nonlinear optics, optical fibers, and ferromagnetic materials. This model is analyzed using the new generalized exponential rational function method and the new extended hyperbolic function method. With symbolic computations, the new extended hyperbolic function generates closed-form solutions to the integrable Kuralay equations, expressed in hyperbolic, trigonometric, and exponential forms. In contrast, the new extended hyperbolic function method provides hyperbolic, trigonometric, polynomial, and exponential solutions. The model is found to exhibit soliton solutions like periodic oscillating nonlinear waves, kink-wave profiles, multiple soliton profiles, singular solution, mixed singular solution, mixed hyperbolic solution, periodic pattern with anti-troughs and anti-peaked crests, mixed periodic, mixed complex solitary shock solution, mixed shock singular solution, mixed trigonometric solution, and periodic solution. These solutions are novel and have not been previously reported in the open literature. Using symbolic computation by Mathematica 11.3 or Maple , these newly derived soliton solutions are verified by substituting them back into the associated system.

Artificial intelligence technology is widely used in the field of wireless sensor networks (WSN). Due to its inexplicability, the interference factors in the process of WSN object localization cannot be effectively eliminated. In this paper, an explainable-AI-based two-stage solution is proposed for WSN object localization. In this solution, mobile transceivers are used to enlarge the positioning range and eliminate the blind area for object localization. The motion parameters of transceivers are considered to be unavailable, and the localization problem is highly nonlinear with respect to the unknown parameters. To address this, an explainable AI model is proposed to solve the localization problem. Since the relationship among the variables is difficult to fully include in the first-stage traditional model, we develop a two-stage explainable AI solution for this localization problem. The two-stage solution is actually a comprehensive consideration of the relationship between variables. The solution can continue to use the constraints unused in the first-stage during the second-stage, thereby improving the performance of the solution. Therefore, the two-stage solution has stronger robustness compared to the closed-form solution. Experimental results show that the performance of both the two-stage solution and the traditional solution will be affected by numerical changes in unknown parameters. However, the two-stage solution performs better than the traditional solution, especially with a small number of mobile transceivers and sensors or in the presence of high noise. Furthermore, we have also verified the feasibility of the proposed explainable-AI-based two-stage solution.

In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.

This paper shows how fused decomposition modeling (FDM), as a three-dimensional (3D) printing technology, can engineer lightweight porous foams with controllable density. The tactic is based on the 3D printing of Poly Lactic Acid filaments with a chemical blowing agent, as well as experiments to explore how FDM parameters can control material density. Foam porosity is investigated in terms of fabrication parameters such as printing temperature and flow rate, which affect the size of bubbles produced during the layer-by-layer fabrication process. It is experimentally shown that printing temperature and flow rate have significant effects on the bubbles’ size, micro-scale material connections, stiffness and strength. An analytical equation is introduced to accurately simulate the experimental results on flow rate, density, and mechanical properties in terms of printing temperature. Due to the absence of a similar concept, mathematical model and results in the specialized literature, this paper is likely to advance the state-of-the-art lightweight foams with controllable porosity and density fabricated by FDM 3D printing technology.

This paper presents a simple and fast closed-form solution approach for two-dimensional (2D) target localization using range difference (RD) measurements. The formulation of the localization problem is derived using a pentagram array. The target position is determined using passive radar measurements (RDs) between the target and the (N+1=10) receivers’ locations. The method facilitates the problem of target position and can be used as a counter-parallel method for spherical interpolation (SI) and spherical intersection (SX) methods in time difference of arrival (TDOA) and radar systems. The performance of the method is examined in 2D target localization using numerical analysis under the distribution of receivers in the pentagram array. The simulations are conducted using four different far-distance targets and comparatively large-area distributed receivers. The RD measurements were distorted by two different values of Gaussian errors based on ionosphedriec time delays of 20 and 50 nsec owing to the different receivers’ positions. The findings highly verified the validity of the method for addressing the problem of target localization. Additionally, a theoretical accuracy study of the method is given, which solely relies on the RD measurements.

This study proposes a dedicated closed-form solution and satellite phasing rules for designing a geosynchronous orbit (GSO) constellation. Trajectories of GSO satellites have a characteristic figure-eight shape because their rotation speed is the same as that of the Earth. The GSO has the advantage of providing good coverage performance for local areas. Recently, several countries have begun developing local navigation systems based on the GSO. Various GSO constellation designs are available for an effective regional navigation performance analysis; however, no dedicated GSO constellation solution exists. This study provides a solution for such constellations and proves its practicability through a comparative analysis and evaluation of the geometric dilution-of-precision performance for several cases.

The mechanical and durability properties of ultra-high-performance fiber-reinforced concrete (UHPFRC) are superior to conventional concrete. However, the available stress-strain models of UHPFRC are relatively complicated and cannot be applied to the analytical analysis of loaded beams for the ultimate and serviceability limit states. In this paper, a piecewise linear axial stress-strain relationship is proposed. The stress-strain relationship is further simplified as a rectangular stress block, and the stress of concrete during the whole loading process is accordingly evaluated. The development of the beam hinge at the midspan is described in detail, and it is then incorporated into the concrete stress blocks to derive an analytical approach and a closed-form solution for modeling the whole loading process of UHPFRC beams. Through comparisons with experimental results collected from the literature, it is validated that the proposed approaches can reasonably predict the whole loading process, including the ultimate strength, flexural rigidity, and ductility of UHPFRC beams, which only require material properties without any experimental calibration. Keywords: analytical approach; closed-form solution; flexural load; stress block; ultra-high-performance fiber-reinforced concrete (UHPFRC) beam.

Clustering algorithms are usually iterative procedures. In particular, when the clustering algorithm aims to optimise an objective function like in k-means clustering or Gaussian mixture models, iterative heuristics are required due to the high non-linearity of the objective function. This implies higher computational costs and the risk of finding only a local optimum and not the global optimum of the objective function. In this paper, we demonstrate that in the case of one-dimensional clustering with one main and one noise cluster, one can formulate an objective function, which permits a closed-form solution with no need for an iteration scheme and the guarantee of finding the global optimum. We demonstrate how such an algorithm can be applied in the context of laboratory medicine as a method to estimate reference intervals that represent the range of “normal” values.

The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Monge–Ampère type equations is given, in which their unusual qualitative features are noted. For the first time, the Lie group analysis of the considered highly nonlinear PDE with three independent variables is carried out. An eleven-parameter transformation is found that preserves the form of the equation. Some one-dimensional reductions allowing to obtain self-similar and other invariant solutions that satisfy ordinary differential equations are described. A large number of new additive, multiplicative, generalized, and functional separable solutions are obtained. Special attention is paid to the construction of exact closed-form solutions, including solutions in elementary functions (in total, more than 30 solutions in elementary functions were obtained). Two-dimensional symmetry and non-symmetry reductions leading to simpler partial differential equations with two independent variables are considered (including stationary Monge–Ampère type equations, linear and nonlinear heat type equations, and nonlinear filtration equations). The obtained results and exact solutions can be used to evaluate the accuracy and analyze the adequacy of numerical methods for solving initial boundary value problems described by highly nonlinear partial differential equations.