This paper introduces an effective and simple approach to analyze functionally graded triply periodic minimal surface (FG-TPMS) nanoplates, taking advantage of a novel nonlocal strain gradient ...nonlinear analysis. TPMS has recently gained attention as an extraordinary solution for constructing structures, drawing inspiration from natural architectures. It offers remarkable features, including high interconnectivity porous architectures, smooth surfaces, and the ability to achieve mathematically controllable geometry features. However, the extensive potential and benefits of TPMS structures have not been fully explored in current research. Hence, this study aims to address this limitation and unlock new possibilities for FG-TPMS nanoplates. Three patterns of FG-TPMS nanoplates, namely Primitive (P), Gyroid (G), and I-gragh and Wrapped Package-graph (IWP), are utilized in this investigation. The proposed model effectively incorporates the nonlocal,strain gradient and nonlinear effects into nanoplate structures. It enables a comprehensive understanding of the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate by fine-tuning the nonlocal and strain gradient parameters. This research offers promising prospects for future design and optimization, providing a robust approach to address the intricate nonlinear behavior observed in FG-TPMS nanoplates.
To address the problem of efficient task for the fully-actuated aerial manipulation system, the flight platform control scheme based on neural networks embedding is proposed. We embed the neural ...networks controllers (NNC) into some base controllers, which are Lyapunov stable for their system. Due to the learning and optimizing capability of NNC, the derivative controllers allow to improve control performance by updating the parameters of NNC under Lyapunov stability condition. The backstepping technology based on the mixture basis functions that approximates unknown system dynamics and the improved disturbance observer is designed for the base controller of platform attitude. And the linear active disturbance rejection controller (LADRC) is utilized as the base controller of platform position. Considering safety and cost, we made some virtual experiments in CoppeliaSim a software which offers high accuracy physical engine. The results of virtual experiments prove that compared with some state-of-the-art technologies the methods proposed are advanced in tracking errors performance due to NNC.
•A method of design for ball Said-Ball (BSB) curve is proposed.•The geometrical properties and algorithms of BSB curve are investigated.•The conditions for G1 and G2 continuity of BSB curves are ...obtained.•An extension method of BSB curve with minimum energy is presented.•A novel BSB rotation surface with thickness is constructed.
The representation method of curves and surfaces is an essential tool in industrial design, while a ball curve with adjustable thickness has its advantages in representing freedom tubular objects. By combing the Said-Ball basic functions and the control balls, this paper constructs the ball Said-Ball (BSB, for short) curve and discusses the related geometrical properties and algorithms. Then, the G1 and G2 continuity conditions between two adjacent BSB curves are discussed. Furthermore, on the premise of G2 continuity, an extension method of the BSB curve with minimum energy is studied. For this method, the GaussNewton-NL2SOL algorithm is used to obtain the best scale parameters of the center curve. Meanwhile, the optimal parameters of the radius function are also determined by solving the extreme. Finally, the construction of the BSB rotation surface with different continuity is given. The provided modeling examples show that the BSB curve with thickness is more suitable and valuable in the design for the modeling of objects, on the premise of maintaining excellent geometric properties.
Pan-sharpening methods allow the transfer of higher resolution panchromatic images to multispectral ones concerning the same scene. Different approaches are available in the literature, and only a ...part of these approaches is included in remote sensing software for automatic application. In addition, the quality of the results supplied by a specific method varies according to the characteristics of the scene; for consequence, different algorithms must be compared to find the best performing one. Nevertheless, pan-sharpening methods can be applied using GIS basic functions in the absence of specific pan-sharpening tools, but this operation is expensive and time-consuming. This paper aims to explain the approach implemented in Quantum GIS (QGIS) for automatic pan-sharpening of Pléiades images. The experiments are carried out on data concerning the Greek island named Lesbo. In total, 14 different pan-sharpening methods are applied to reduce pixel dimensions of the four multispectral bands from 2 m to 0.5 m. The automatic procedure involves basic functions already included in GIS software; it also permits the evaluation of the quality of the resulting images supplying the values of appropriate indices. The results demonstrate that the approach provides the user with the highest performing method every time, so the best possible fused products are obtained with minimal effort in a reduced timeframe.
This paper begins a new approach to the
r
-trace formula, without removing the nontempered contribution to the spectral side. We first establish an invariant trace formula whose discrete spectral ...terms are weighted by automorphic
L
-functions. This involves extending the results of Finis, Lapid, and Müller on the continuity of the coarse expansion of Arthur’s noninvariant trace formula to the refined expansion, and then to the invariant trace formula, while incorporating the use of basic functions at unramified places.
The tremor injury is one of the common symptoms of Parkinson's disease. The patients suffering from Parkinson's disease have difficulty in controlling their movements owing to tremor. The intensity ...of the disease can be determined through specifying the range of intensity values of involuntary tremor in Parkinson patients. The level of disease in patients is determined through an empirical range of 0-5. In the early stages of Parkinson, resting tremor can be very mild and intermittent. So, diagnosing the levels of disease is difficult but important since it has only medication therapy. The aim of this study is to quantify the intensity of tremor by the analysis of electromyogram signal. The solution proposed in this paper is to employ a polynomial function model to estimate the Unified Parkinson's Disease Rating Scale (UPDRS) value. The algorithm of Fast Orthogonal Search (FOS), which is based on identification of orthogonal basic functions, was utilized for model identification. In fact, some linear and nonlinear features extracted from wrist surface electromyogram signal were considered as the input of the model identified by FOS, and the model output was the UPDRS value. In this research, the proposed model was designed based on two different structures which have been called the single structure and parallel structure. The efficiency of designed models with different structures was evaluated. The evaluation results using K-fold cross validation approach showed that the proposed model with a parallel structure could determine the tremor severity of the Parkinson's diseasewith accuracy of 99.25% ±0.41, sensitivity of 97.17% ±1.9 and specificity of 99.72% ±0.18.
A novel step‐by‐step linearization high‐order Extended Kalman filter SH‐EKF is designed for a class of nonlinear systems composed of linear functions and the product of several separable basic ...functions. The basic functions in the state and measurement models are defined as latent variables; the state and measurement models are equivalently formulated into pseudo‐linear models based on the combination of the original variable and the latent variables; latent variables are regarded as new variables, and a dynamic linear model between each latent variable and other latent variables with original state is established; the measurement model is rewritten into the first‐order linear product form between the current state and each latent variable; latent variables are solved by Kalman filter step by step, and a stepwise linearized high‐order extended Kalman filter is designed. Illustration examples are presented to demonstrate the effectiveness of the new algorithm.
In this paper, we introduce a functional method to investigate how betas change over time in factor models. Based on the China A-share data, we drop the constant beta assumption in the CAPM and ...multi-factor models to estimate the time-varying betas directly from the functional data regression. The empirical results show that exposures to all risk factors have certain time-varying patterns in the Chinese A-share stock market.
•Functional data analysis constructs functional data to extract information.•Functional asset pricing model allows time-varying betas.•Exposures to all risk factors have time-varying patterns in the Chinese stock market.
In this paper, a method has been proposed to finding a numerical function for the Riccati differential equations of non integer order (FRDEs), in which trigonometric basic functions are used. First, ...by defining trigonometric basic functions, we define the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the numerical function is defined as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get a numerical solution function with discrete derivatives of the solution function, we have determined the numerical solution function which satisfies the FRDEs. In the end, the algorithm of the method is elaborated with several examples. Numerical results obtained show that the proposed algorithm gives very good numerical solutions. In one example, we have presented an absolute error comparison of some numerical methods.
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