Function Method Research Articles

An Online Torque Sharing Function Method Based on Region Division for Reducing Torque Ripple and Copper Losses of Switched Reluctance Motors

An Online Torque Sharing Function Method Based on Region Division for Reducing Torque Ripple and Copper Losses of Switched Reluctance Motors

Applying the monomiality principle to the new family of Apostol Hermite Bernoulli-type polynomials

Abstract In this article, we introduce a new class of polynomials, known as Apostol Hermite Bernoulli-type polynomials, and explore some of their algebraic properties, including summation formulas and their determinant form. The majority of our results are proven using generating function methods. Additionally, we investigate the monomiality principle related to these polynomials and identify the corresponding derivative and multiplicative operators.

Analysis and evaluation of the effectiveness of program codes for particle swarm and ant colony methods for lower semi-continuous functions

In this paper, a comparative analysis of two stochastic methods of global optimization is carried out: the Particle Swarm Optimization method and the Ant Colony Optimization method. The analysis and evaluation of efficiency were carried out using parameters such as the number of calls to the objective function, the rate of convergence, resources, computational efficiency, sensitivity to parameters, and resistance to initial conditions. The article presents the program codes of these methods in the Python environment, designed to calculate the global extremum of semi-continuous functions from below. Well- known test functions were used to construct (by gluing) semi-continuous functions at different values of input parameters.

Stability Analysis Of Two-Position Control System In Interacting Tanks Using Describing Function Method

In a water storage unit consisting of 3 interacting tanks, in its operation there will be problems if manual control is used, because if manual control is not optimal, then when filling water in the three tanks it will cause water overflow, which results in a lot of water being wasted. Two-position control, or "on-off," is a control system that is suitable for use in regulating the water level in the storage unit tank. In a two-position control system, if the frequency of water up and down (Limit Cycle) is large, it will cause an increase in the number of "switching" and "on-off" operations of the switch and solenoid valve per minute, so that the system becomes unstable and will shorten the life of the component. The Describing Function (DF) method is an analysis method that can determine the Limit Cycle frequency based on the width of the water up and down range (hysteresis) of the two-position control system, with the aim of determining the hysteresis parameters that cause the system to be stable.

In silico data-based comparison of the accuracy and error source of various methods for noninvasively estimating central aortic blood pressure

Background and objectivesThe higher clinical significance of central aortic blood pressure (CABP) compared to peripheral blood pressures has been extensively demonstrated. Accordingly, many methods for noninvasively estimating CABP have been proposed. However, there still lacks a systematic comparison of existing methods, especially in terms of how they differ in the ability to tolerate individual differences or measurement errors. The present study was designed to address this gap. MethodsA large-scale ‘virtual subject’ dataset (n = 600) was created using a computational model of the cardiovascular system, and applied to examine several classical CABP estimation methods, including the direct method, generalized transfer function (GTF) method, n-point moving average (NPMA) method, second systolic pressure of periphery (SBP2) method, physical model-based wave analysis (MBWA) method, and suprasystolic cuff-based waveform reconstruction (SCWR) method. The errors of CABP estimation were analyzed and compared among methods with respect to the magnitude/distribution, correlations with physiological/hemodynamic factors, and sensitivities to noninvasive measurement errors. ResultsThe errors of CABP estimation exhibited evident inter-method differences in terms of the mean and standard deviation (SD). Relatively, the estimation errors of the methods adopting pre-trained algorithms (i.e., the GTF and SCWR methods) were overall smaller and less sensitive to variations in physiological/hemodynamic conditions and random errors in noninvasive measurement of brachial arterial blood pressure (used for calibrating peripheral pulse wave). The performances of all the methods worsened following the introduction of random errors to peripheral pulse wave (used for deriving CABP), as characterized by the enlarged SD and/or increased mean of the estimation errors. Notably, the GTF and SCWR methods did not exhibit a better capability of tolerating pulse wave errors in comparison with other methods. ConclusionsClassical noninvasive methods for estimating CABP were found to differ considerably in both the accuracy and error source, which provided theoretical evidence for understanding the specific advantages and disadvantages of each method. Knowledge about the method-specific error source and sensitivities of errors to different physiological/hemodynamic factors may contribute as theoretical references for interpreting clinical observations and exploring factors underlying large estimation errors, or provide guidance for optimizing existing methods or developing new methods.

Solving MADM Problems based on Matrix Games with a New Defuzzification Method for Triangular Intuitionistic Fuzzy Numbers

Abstract: The paper discusses about a new defuzzification method called the Comprehensive Li-Samuel ranking for Triangular Intuitionistic Fuzzy Numbers (TrIFNs) which is improved from the Li-Samuel ranking method associated with membership function and Li-Samuel ranking method associated with non-membership function. The Comprehensive Li-Samuel ranking for TrIFNs is utilised to derive the weights for the Multiple Attribute Decision Making (MADM) problems under TrIFN. The MADM problem is solved based on two-person zero-sum game which is converted into a pair of LPP by using Comprehensive Li-Samuel ranking. The process of transforming decision matrix into a matrix game and deriving decision maker’s and attribute weights from the matrix game are discussed. Numerical illustration is given to justify the viability and effectiveness of the proposed method and comparisons are made with existing ranking methods. The comparison study reveals that the proposed method provides the best maximum optimal solution for the decision problem than the existing methods

Analytical modeling of piezoelectric meta-beams with unidirectional circuit for broadband vibration attenuation

Broadband vibration attenuation is a challenging task in engineering since it is difficult to achieve low-frequency and broadband vibration control simultaneously. To solve this problem, this paper designs a piezoelectric meta-beam with unidirectional electric circuits, exhibiting promising broadband attenuation capabilities. An analytical model in a closed form for achieving the solution of unidirectional vibration transmission of the designed meta-beam is developed based on the state-space transfer function method. The method can analyze the forward and backward vibration transmission of the piezoelectric meta-beam in a unified manner, providing reliable dynamics solutions of the beam. The analytical results indicate that the meta-beam effectively reduces the unidirectional vibration across a broad low-frequency range, which is also verified by the solutions obtained from finite element analyses. The designed meta-beam and the proposed analytical method facilitate a comprehensive investigation into the distinctive unidirectional transmission behavior and superb broadband vibration attenuation performance.

Distributed Adaptive Optimization Algorithm for High-Order Nonlinear Multi-Agent Stochastic Systems with Lévy Noise.

An adaptive neural network output-feedback control strategy is proposed in this paper for the distributed optimization problem (DOP) of high-order nonlinear stochastic multi-agent systems (MASs) driven by Lévy noise. On the basis of the penalty-function method, the consensus constraint is removed and the global objective function (GOF) is reconstructed. The stability of the system is analyzed by combining the generalized Itô's formula with the Lyapunov function method. Moreover, the command filtering mechanism is introduced to solve the "complexity explosion" problem in the process of designing virtual controller, and the filter errors are compensated by introducing compensating signals. The proposed algorithm has been proved that the outputs of all agents converge to the optimal solution of the DOP with bounded errors. The simulation results demonstrate the effectiveness of the proposed approach.

Further Results for Hermite-Based Milne-Thomson Type Fubini Polynomials with Trigonometric Functions

This paper examines generating functions of r-parametric Hermite-based Milne-Thomson polynomials. Using generating function methods, the relationships among these polynomials, Fubini type polynomials, and trigonometric functions are given. Moreover, new formulas are derived by utilizing not only the generating functions of these polynomials but also associated functional equations. These formulas pertain to r-parametric Hermite-based sine-and cosine-Milne-Thomson Fubini polynomials, as well as Stirling type polynomials and numbers. Additionally, by analyzing special cases of newly obtained results, some known formulas are also derived. Furthermore, some identities involving secant and cosecant numbers are derived through the properties of trigonometric functions. Special polynomials and their generating functions are an important tool for solving some problems in many areas such as combinatorics and number theory. By introducing new formulas, this paper significantly enhances these problems-solving abilities in these areas. Consequently, these results have potential to shed light on important applications in mathematics, engineering, and mathematical physics.

Multi-model transfer function approach tuned by PSO for predicting stock market implied volatility explained by uncertainty indexes

This paper studies the forecasting power of uncertainty emanating from the commodities market, energy market, economic policy, and geopolitical threats to the CBOE Volatility Index (VIX). In this study, the relationship between the various uncertainty metrics throughout the period 2012—2022, using a multi-model transfer function technique optimized by particle swarm optimization (PSO) is estimated. Furthermore, we utilize PSO for parameter optimization within the multi-model framework, improving model performance and convergence speed. According to empirical findings, the CBOE Volatility Index reacts nonlinearly to the uncertainty indices. Specifically, the conclusions of the performance metrics show that the OVX index (MAPE: 4.1559%; RMSE: 1.0476% and W: 96.74%) outperforms the geopolitical risk index, the Bloomberg energy index, and the economic policy uncertainty index in predicting the volatility of the US equities market. Although individual models have generated respectful performance, results from the aggregate simulation show that when all predictors are combined, they simultaneously provide better performance indicators (MAVE: 2.7511 %; RMSE: 0.7361%; R2: 98.93%) than when they are estimated separately. In addition, results provide evidence that, when considering non-linear patterns in the data, the multi-model transfer function technique calibrated using PSO demonstrates its outperformance over autoregressive baseline models, traditional econometric models, and deep learning techniques. The effectiveness and accuracy of the multi-model transfer function method tuned by PSO as a forecasting tool are confirmed by the convergence analysis of the cost function. Our methodology innovates by employing a multi-model transfer function technique, which captures the complex and nonlinear relationships between uncertainty indicators and the VIX more comprehensively than traditional single-model approaches. These results are important for traders in terms of hedging as well as portfolio diversification by investing in defensive equities and for policymakers in terms of reliability and preciseness of volatility forecasts.

Distributed Consensus Tracking of Incommensurate Heterogeneous Fractional-Order Multi-Agent Systems Based on Vector Lyapunov Function Method

This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate heterogeneous multi-agent systems are introduced. To cope with incommensurate and heterogeneous situations among followers and the leader, radial basis function neural networks (RBFNNs) and a discontinuous control method are used. Thirdly, the consensus criteria are derived by using the Vector Lyapunov Function method. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical method.

An RBF Method for Time Fractional Jump-Diffusion Option Pricing Model under Temporal Graded Meshes

This paper explores a numerical method for European and American option pricing under time fractional jump-diffusion model in Caputo scene. The pricing problem for European options is formulated using a time fractional partial integro-differential equation, whereas the pricing of American options is described by a linear complementarity problem. For European option, we present nonuniform discretization along time and the radial basis function (RBF) method for spatial discretization. The stability and convergence analysis of the discrete scheme are carried out in the case of European options. For American option, the operator splitting method is adopted which split linear complementary problem into two simple equations. The numerical results confirm the accuracy of the proposed method.

Partially extended oscillation and nonoscillation theorems for half‐linear Hill‐type differential equations with periodic damping

This study addressed the oscillation problems of half‐linear differential equations with periodic damping. The solution space of any linear equation is homogeneous and additive. Generally, by contrast, the solution space of half‐linear differential equations is homogeneous but not additive. Numerous oscillation and nonoscillation theorems have been devised for half‐linear differential equations featuring periodic functions as coefficients. However, in certain cases, such as applying Mathieu‐type differential equations to control engineering, which is a typical example of the Hill equation, some oscillation theorems cannot be applied. In this study, we established oscillation and nonoscillation theorems for half‐linear Hill‐type differential equations with periodic damping. To prove the results, we used the Riccati technique and the composite function method, which focuses on the composite function of the indefinite integral of the coefficients of the target equation and an appropriate multivalued continuously differentiable function. Furthermore, we discuss the special case of the oscillation constant of a damped half‐linear Mathieu equation.

Effect of higher order on constructing the soliton waves to generalized nonlinear Schrödinger equation using improved modified extended tanh function method

Effect of higher order on constructing the soliton waves to generalized nonlinear Schrödinger equation using improved modified extended tanh function method

Fund allocation modeling of compensation subjects for various protection levels of the ecological flow in rivers under runoff variations

Ecological compensation for protecting of river ecological flow (e-flow) is crucial to maintaining the health of river ecosystems; however, determining the fund sharing for ecological compensation can be challenging. To fill this scientific gap, we herein developed a specific framework to determine the fund-sharing of ecological compensation subjects. Such a framework mainly consists of three parts:1) Identifying the subjects who benefit from the consumption and eco-products provided by e-flow protection, and determining the sharing coefficient of the compensation subjects based on the ratio of their economic benefit to the total economic benefit; 2) Evaluating the ecological compensation resulting from the e-flow protection with the help of the production function method; 3) Combining the ecological compensation and compensation sharing coefficient to determine the fund sharing of compensation subjects. We have successfully applied this approach to the Baoji Section of the Weihe River and the Baojixia Yuanshang Irrigation District (BYID). The obtained results revealed that the compensation subjects were Baoji and Xianyang City, and their corresponding fund-sharing coefficients in 2010 in order were 0.71 and 0.29. It was predicted that ecological compensation for e-flow protection would be 209 million yuan in 2010 year, and the corresponding values of capital sharing are 148 million and 61 million yuan. Over the last 23 years (in the time interval of 2000–2022), the share of compensation funds has gradually decreased, indicating an increasing trend with the improvement of the security level. Join us in our mission to protect river ecosystems and maintain a healthy balance by using this approach for ecological compensation.

Plant investigation and the impact on earthen site soil properties in the east city wall of the Sanxingdui site

In southern China, vegetation on exposed earthen sites serves not only to mitigate erosion but also alters their visual appearance, leading to biodeterioration. However, how plants influence the properties of earthen sites is virtually unknown. This study undertook an ecological investigation of the original habitat in the east city wall of the Sanxingdui site, analyzing its soil properties and investigating plant-soil interactions. Research findings indicate that existing plant communities are not conducive to biodiversity nor site presentation. Plants exert a direct influence within a vertical range extending 0–40 cm beneath the site; root content correlates negatively with soil pH value but positively with organic matter content. The herbaceous community (E-2 and E-3) exhibits higher clay content than the arbor community (E-1) within this range. The above conclusions exhibit statistical significance. This study offers a scientific elucidation of the ecological parameters governing plant communities concerning the conservation of earthen sites, and provides an initial influence range of plant communities and biodegradation on the east city wall of the Sanxingdui sites, thereby revealing the technical potential for employing plants as a soft capping for earthen sites in the open air from the function method.

Optimizing the composition of (Ce,La)(Co,Fe)5for permanent magnet applications using density functional theory.

In this work, we calculated physical quantities, including the magnetocrystalline anisotropy constant (Ku) and magnetization (Ms), for disordered (Ce,La)(Co,Fe)5systems. Based on the results, we propose CeCo4.7Fe0.3as the optimum composition for high-performance permanent magnets. The calculations employed the full-potential Korringa-Kohn-Rostoker Green's function method, and dealt with the compositional disorder of the systems within the coherent potential approximation. It was found that the La doping reducesKuat 0 K but increases the Curie temperature (TC), which leads to improvement of the magnetic properties at high temperatures. CeCo4.7Fe0.3had the largest magnetic anisotropy ofKu= 15.14 MJ/m3, which is larger than that of CeCo5(Ku= 14.77 MJ/m3).TCof CeCo4.7Fe0.3estimated by the mean-field approximation was 1005 K, which exceeds that of CeCo5(965 K). Further, our calculations showed that while doping of Fe destabilizes the system, CeCo4.7Fe0.3is stable against decomposition into the simple substances. We also show calculated data that are informative for exploring high-performance permanent magnet materials in this paper.

A New Approach to the Solution of Facility Layout Problems with Filled Function Method

Facility layout problems are generally solved by stochastic methods in the literature. The large number of iterations used in these methods is quite costly in terms of solution time. In this study, in order to get rid of this disadvantage, the facility layout problem was solved using the filled function method, which is known to be very successful in solving global optimization problems. In order to demonstrate the effectiveness of the filled function method, the classical linear facility layout problem was handled in a non-linear manner and the problem was deliberately made more difficult. In order to use the filled function method, the facility layout problem was transformed into an unconstrained and multimodal (including more than one local minima) global optimization problem by using the hyperbolic smoothing technique and the penalty function method. Thus, in this first study in the literature where a deterministic method is combined with the solution of the facility layout problem, it is shown that the non-convex facility layout problem can be solved with the filled function method with very few iterations and short solution times.

Neutral pion polarizabilities from four-point functions in lattice QCD

We report a proof-of-principle lattice QCD simulation of the electric and magnetic polarizabilities for a neutral pion in the four-point function method. The results are based on the same quenched Wilson ensembles on a 243×48 lattice at β=6.0 with pion mass from 1100 to 370 MeV previously used for a charged pion. For electric polarizability, the results are largely consistent with those from the background field method and ChPT. In contrast, there are significant differences for magnetic polarizability among the four-point function method, the background field method, and ChPT. The situation points to the important role of disconnected diagrams for a neutral pion. We elucidate a transparent quark decomposition in the four-point function method that can be used to shed light on the issue.

Mathematical analysis of soliton solutions in space-time fractional Klein-Gordon model with generalized exponential rational function method

In this article, we investigate the space-time Klein-Gordon (KG) model, a significant framework in quantum field theory and quantum mechanics, which also describes phenomena such as wave propagation in crystal dislocations. This model is particularly important in high-energy particle physics. The novelty of this article is to examine the sufficient, useful in optical fibers, and further general soliton solutions of the nonlinear KG model using the generalized exponential rational function method (GERFM), which do not exist in the recent literature. The fractional complex wave transformation is utilized to turn the model into a nonlinear form, and the accuracy of the acquired solutions is confirmed by reintroducing them into the original models using Mathematica. The obtained solutions are expressed in hyperbolic, exponential, rational, and trigonometric forms. We elucidate the fractional effects for specific parameter values, accompanied by illustrative figures. Our results demonstrate that GERFM is effective, powerful, and versatile, providing exact traveling wave solutions for various nonlinear models in engineering and mathematical physics. Our findings reveal that the characteristics of soliton-shaped waves in both three-dimensional and two-dimensional contexts are profoundly influenced by fractional order derivative. This study advances the understanding of nonlinear wave dynamics and offers a robust method for solving complex physical models.