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Capacitive six-axis force/torque (F/T) sensors require various configurations to fulfill diverse performance requirements; however, a systematic method to assess the feasibility of any new configuration is lacking. This study aims to propose three criteria for evaluating the rationality of these configurations, enabling a quick determination of the feasibility of the initial structure of the sensor.

This study used sensitivity isotropy as a performance metric. By examining the signal conversion process from F/T to displacement using the compliance transformation matrix, the authors identified Criterion 1: the symmetry condition. By analyzing the decoupling process of the sensor, the authors discovered Criterion 2: the capacitor arrangement condition. Through the optimization of analog sensors, this study derived Criterion 3: the range and structural parameters conditions. Ultimately, this study designed and fabricated a sensor that fulfills these criteria, thereby demonstrating the feasibility of the approach through its performance.

By analogy with capacitive six-axis F/T sensors that have demonstrated exceptional performance in recent years, the authors have found that they all meet the criteria proposed in this paper. Furthermore, the sensor designed and fabricated in this study achieves an accuracy of 0.64% FS, surpassing both the accuracy and sensitivity of the commercially available high-performance ATI industrial automation (Gamma) sensor. This underscores the feasibility of this study’s criteria.

By following the configuration guidelines presented in this paper, designers can quickly assess whether a new configuration will perform well at the early stages of the design process. This makes it easier to consider other requirements while meeting the basic performance needs, thereby significantly enhancing design efficiency.

Developing countries are characterized by gender wage inequality that can be largely attributed to gender-based disparities in education. Education subsidy can be an effective tool for reducing the inequality in human capital formation. However, the parents’ decision in response to the subsidy is a crucial determinant of gendered inequality in schooling and earnings. The paper aims to examine the effects of gender-neutral and gender-specific education subsidy policies on the gendered differences in schooling and earnings.

A three-sector full employment general equilibrium model is developed, where the amount of schooling of children is determined by the intertemporal utility maximizing behaviour of the parents over two periods.

The results indicate that higher gender-neutral education subsidy may raise the amount of schooling of boys more than girls and aggravate the schooling inequality in a society with traditional gender norms; the effect on earning inequality depends on the relative gendered returns to education and the marginal effects of the subsidy on relative schooling levels. However, gender-specific subsidy policies raise female schooling, thereby narrowing gender-based schooling and are likely to favourably affect the earning inequality.

The paper tries to analyse the linkage between education and labour market within a gender dimension. On the one hand, it tries to explain parental schooling decision due to gender-neutral and gender-specific education subsidies, and on the other, it examines the effects of these two subsidy policies on gendered schooling inequality and gender earnings inequality in a dynamic model.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

The return behavior of customers has a great impact on the e-retail industry and has resulted in the emergence of return-freight insurance (RI). Additionally, customer loss aversion arising from returns affects e-retailers' decisions and manufacturers' profits. Therefore, the main purpose of the authors' study is to determine how e-retailers and manufacturers choose their RI strategy and pricing according to customers' loss aversion.

The authors propose three scenarios: no RI, customer purchase RI and free e-retail RI (FRI). Meanwhile, the authors also model a Stackelberg game between e-retailers and manufacturers for analysis. Then, according to customer return behavior and loss aversion, the authors study the optimal pricing decision and RI premium allocation scheme for e-retailers and manufacturers under different scenarios.

It was found that the loss sensitivity reduces customers' willingness to buy RI, which is not conducive to the development of e-retailers and manufacturers. Additionally, with higher loss sensitivity, e-retailers and manufacturers offer FRI to gain higher profits, which supports the implementation of the FRI strategy.

The authors introduce customers' loss aversion into RI to analyze the optimal pricing decisions and profits of e-retailers and manufacturers, enriching the application of loss aversion theory. In addition, this study analyzes the two-way cost-sharing mechanism between manufacturers and e-retailers to provide FRI, which provides a theoretical basis for RI premium sharing.

The purpose of this study is to (1) improve the spectral features of the second-order uniformly non-oscillatory (UNO) slope limiters, and (2) numerical simulation of the unified-form of generalized fully-coupled saturated thermo-poro-elastic systems in the axisymmetric cylindrical coordinate via cell-adaptive Kurganov-Tadmor (KT) central high-resolution scheme using the UNO limiters.

(1) The spectral features of the UNO limiter are improved by compression-adaptive MINMOD (MM) limiters, achieved by blending different types of MM limiters to achieve less numerical dissipation and dispersion. These blended MM limiters preserve the total variation diminishing (TVD) feature over non-uniform non-centered cells. Also, the spectral features of the central schemes using the UNO limiters are investigated. (2) For the thermo-poro-elastic problem, corresponding first-order hyperbolic system is provided, including flux, source, diffusion and nonlinear terms. Where, there are different interacting components in the source and flux terms. The nonlinear terms are also considered by the Picard-like linearization concept.

Compression-adaptive UNO limiters would be stable over adapted cells with centered and non-centered cells. The benchmarks confirm that both spectral features and numerical accuracy are improved. For the generalized thermo-poro-elastic problem, corresponding responses including the shock waves can properly be captured.

Studying heat effects (e.g. hot fluid or freezing) and explosions on tunnels. Also, the UNO limiters could be used for simulations of various systems of conservation laws.

This study aims to efficiently estimate the extremely small failure probability with high-dimensional inputs and multiple failure domains.

This paper proposed an adaptive stratified mixture importance sampling method. The proposed method first constructs an explicit and regular mixture importance sampling probability density function (M-IS-PDF) by taking the clustering centroids as the density centers. Then by the constructed M-IS-PDF, the proposed method explores the rare multiple failure domains by adaptively stratifying, thereby addressing the issue of estimating extremely small failure probability robustly and efficiently.

Compared with the existing cross-entropy based IS method, the constructed M-IS-PDF not only covers the domains significantly contributing to the failure probability through clustering centroids to reduce the variance of failure probability estimation, but also has no undetermined parameter set to optimize, enhancing the adaptability in high-dimensional problems. Compared with the subset simulation method, the adaptive stratified M-IS-PDF constructed is explicit, regular and easy sampling. It not only has high sampling efficiency but also avoids estimating conditional failure probabilities layer by layer, improving the algorithmic robustness for estimating extremely small failure probability.

Both numerical and engineering examples indicate that, under the similar failure probability estimation accuracy, the proposed method requires significantly smaller sample size and lower computational cost than subset simulation and cross-entropy based IS methods, demonstrating higher efficiency and robustness in addressing intractable reliability analysis problems with high-dimensional inputs, multiple failure domains and rare failure.

The purpose of this paper is to examine the American pricing problem under the assumption that the holder exercises not only when the underlying asset hits the optimal boundary but also when it falls in a properly defined e-optimal set.

The purpose of this paper is to examine the American pricing problem under the assumption that the holder exercises not only when the underlying asset hits the optimal boundary but also when it falls in a properly defined e-optimal set. The put and call versions are examined separately. We derive closed-form formulas for the perpetual case. A numerical algorithm for approximating the e-optimal strip is constructed when the maturity is finite. We adapt the Crank–Nicolson finite difference approach to derive the option price or, more precisely, the interval at which it varies. Some numerical experiments are provided.

We derive closed-form formulas for the perpetual options. A numerical algorithm for approximating the e-optimal strip is constructed when the maturity is finite. We adapt the Crank–Nicolson finite difference approach to derive the option price or, more precisely, the interval in which it varies. Some numerical experiments are provided.

We examine the American pricing problem under the assumption that the holder exercises not only when the underlying asset hits the optimal boundary but also when it falls in a properly defined e-optimal set. This is important to take into account the risk preferences of the investors. Closed-form formulas for the perpetual options are derived. A numerical algorithm for approximating the e-optimal strip is constructed when the maturity is finite. We adapt the Crank–Nicolson finite difference approach to derive the price.

The purpose of this study is to apply the Meshless Local Petrov–Galerkin (MLPG) method to solve the bending problems of linear viscoelastic plates, considering Reissner’s theory.

The weak formulation for the set of equations that govern Reissner’s plate theory is implemented in conjunction with the integral formulation applied to viscoelastic constitutive expressions. A meshless method based on the Moving Least Squares (MLS) approximation is considered in the numerical implementation. The final equation system is assembled by adopting simple and efficient schemes for numerical integration, considering a simplified formulation through centralization of the local interpolation domains and Gaussian quadrature at the same field point. The results obtained are compared with available solutions to demonstrate the efficiency of the proposed formulation.

The hereditary integral approach proved to be the most general way to analyze the viscoelastic problem, especially when applied together with the modified scheme for numerical integration. In addition, the variable changing technique is demonstrated to be an efficient formulation for solving shear-locking effects in thin plate problems.

The differential of the present study is related to the manner in which the properties of linear viscoelastic materials are considered in the formulation. Although most authors consider this point through the application of the correspondence principle, the present study works with a hereditary integral formulation. In addition, the variable changing technique is applied to solve the shear-locking effects, and an alternative approximation technique is considered to speed up the numerical integration process.

The purpose of this study proposes a strategy based on vehicle kinematics, dynamics and fusion estimation. The estimation signal of vehicle driving state is crucial for vehicle driving safety and stability control, and the issue of fault-tolerant reconstruction estimation of vehicle driving state under the failure of yaw rate or lateral acceleration sensors is a significant research topic.

A strategy based on vehicle kinematics, dynamics and fusion estimation is proposed. To address the issue of inaccurate calculation of tire forces because of sensor failure, a method combining adaptive sliding mode observer, genetic algorithm and particle swarm optimization algorithm is proposed to accurately calculate tire forces, and the Square Root Cubature Kalman Filter algorithm is used to reconstruct the estimation of vehicle driving state under sensor failure. To improve the accuracy of fault-tolerant reconstruction estimation of vehicle driving state, an error-weighted multi-method fusion estimation strategy for vehicle driving state is proposed. A fast terminal sliding mode control algorithm is proposed to control the stability of the fault-tolerant reconstruction estimation signal of vehicle driving state.

Simulation results show that the proposed fault-tolerant reconstruction estimation algorithm for vehicle driving state can accurately estimate the actual driving state of the vehicle and stably participate in the vehicle stability control system, achieving fault-tolerant reconstruction estimation and control of vehicle driving state under sensor failure.

The problem of vehicle motion state estimation under yaw velocity sensor fault or lateral acceleration sensor fault is solved, and fault tolerance control under sensor state is realized.

In the present article, sensitivity analysis was studied in the presence of the combined effects of thermal radiation, suction and magnetohydrodynamics (MHD) effects on a Nimonic 80A-Fe_3O4/water hybrid nanofluid across moving a wedge with variable surface temperature and buoyancy effects.

The governing equations were transformed using similarity transformations and solved using MATLAB bvp4c code and response surface methodology (RSM), with quadratic face-centred central composite design being implemented. All results and graphs were formulated after positive outcomes of our results with existing literature.

An increase in magnetic parameter (M) and velocity ratio parameter (R) resulted in an increase in velocity profiles and local Nusselt number, while a reverse trend was observed for temperature profiles. With radiation parameter Rd = 0.8, the local Nusselt number increased by 4.08% as the velocity ratio parameter increased from R = 0.0 to R = 0.5. The Nusselt number was found to be most sensitive to R, while the latter produced negative sensitivity on skin friction coefficient. The skin friction coefficient for the hybrid nanofluid model increased by 35.39% compared to the regular fluid model, with a very low standard deviation value of 10⁻⁴. The Model F-value for Nusselt number model was found to be 939278.49 with a noise ratio of 3618.711. Skin friction coefficient was found to be most sensitive with respect to changes in the parametric values of M.

Nimonic 80A being a super-alloy of nickel-iron-chromium and built in high frequency melting, it can work up to 1500°F and is extensively used in automobile exhaust valves.

The present study finds numerous applications in biotoxicity studies, medical industries, water heaters and the forging of hot exhaust valve heads.

In view of various applications of our present study, there remains a gap in examining the sensitivity analysis of a hybrid nanofluid flow model across a moving permeable wedge using the Tiwari–Das model, which required clinical investigations numerically and statistically.