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This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.

The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.

The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).

The authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.

The authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.

Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.

It uncovers subjects' intelligent interactively trading behaviors.

The purpose of this study is to develop an efficient model to solve the electromagnetic forward problem using a novel semi-analytical approach to compute the electromagnetic fields because of the presence of a scatterer.

The proposed model involves a novel formulation of a complete orthonormal set of radiating/nonradiating polarization currents. Furthermore, an integral equation-based representation is derived, and the appropriate boundary conditions are imposed to get the scattered electromagnetic field. An error term is introduced to evaluate the obtained results.

The proposed model was tested using several examples at different frequencies. The results of this study show that the novel representation exhibits fast convergence behavior and achieves highly accurate results, when compared to the results provided by the transmission line method.

The derived formulations presented in this study are significant in the electromagnetic forward modelling field because of the meaningful physical representation they provide. This is an important aspect that leads to precise calculation of electromagnetic fields for various applications.

In eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the generic analytical model for evaluating corrosion in layered conductor using ferrite-cored probe has not yet been developed. The purpose of this paper is to propose and verify the analytical model of an E-cored probe for evaluating corrosion in layered conductive materials.

A cylindrical coordinate system is adopted and the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived first, and then the expansion coefficients of the solution are obtained by matching the boundary and interface conditions between the regions and the subregions. Finally the closed-form expression of the impedance of the multi-turn coil is derived by using the truncated region eigenfunction expansion (TREE) method, and the impedance calculation is carried out in Mathematica. In the frequency range of 100 Hz to 10 kHz, the impedance changes of the E-cored coil and air-cored coil due to the layered conductor containing corrosion are calculated, respectively, and the influences of corrosion on the coil impedance change are investigated.

An analytical model for the detection and evaluating of corrosion in layered conductive materials using E-cored probe is proposed. The model can quickly and accurately calculate the impedance change of E-cored coil due to corrosion in layered conductor. The correctness of the analytical model is verified by finite element method and experiments.

An accurate theoretical model of E-cored probe for evaluating corrosion of multilayer conductor is presented. The analytical model can be used to detect the inhomogeneity of layered conductor, design ferrite-cored probe or directly evaluate the corrosion defects of layered conductors.

The boundary integral method (BIM) is very attractive to practicing engineers as it reduces the dimensionality of the problem by one, thereby making the procedure computationally inexpensive compared to its peers. The principal feature of this technique is the limitation of all its computations to only the boundaries of the domain. Although the procedure is well developed for the Laplace equation, the Poisson equation offers some computational challenges. Nevertheless, the literature provides a couple of solution methods. This paper revisits an alternate approach that has not gained much traction within the community. The purpose of this paper is to address the main bottleneck of that approach in an effort to popularize it and critically evaluate the errors introduced into the solution by that method.

The primary intent in the paper is to work on the particular solution of the Poisson equation by representing the source term through a Fourier series. The evaluation of the Fourier coefficients requires a rectangular domain even though the original domain can be of any arbitrary shape. The boundary conditions for the homogeneous solution gets modified by the projection of the particular solution on the original boundaries. The paper also develops a new Gauss quadrature procedure to compute the integrals appearing in the Fourier coefficients in case they cannot be analytically evaluated.

The current endeavor has developed two different representations of the source terms. A comprehensive set of benchmark exercises has successfully demonstrated the effectiveness of both the methods, especially the second one. A subsequent detailed analysis has identified the errors emanating from an inadequate number of boundary nodes and Fourier modes, a high difference in sizes between the particular solution and the original domains and the used Gauss quadrature integration procedures. Adequate mitigation procedures were successful in suppressing each of the above errors and in improving the solution accuracy to any desired level. A comparative study with the finite difference method revealed that the BIM was as accurate as the FDM but was computationally more efficient for problems of real-life scale. A later exercise minutely analyzed the heat transfer physics for a fin after validating the simulation results with the analytical solution that was separately derived. The final set of simulations demonstrated the applicability of the method to complicated geometries.

First, the newly developed Gauss quadrature integration procedure can efficiently compute the integrals during evaluation of the Fourier coefficients; the current literature lacks such a tool, thereby deterring researchers to adopt this category of methods. Second, to the best of the author’s knowledge, such a comprehensive error analysis of the solution method within the BIM framework for the Poisson equation does not currently exist in the literature. This particular exercise should go a long way in increasing the confidence of the research community to venture into this category of methods for the solution of the Poisson equation.

Financial performance has been paid attention at an unprecedented level, which can be confirmed as a fact that the quantitative expansion of financial performance evaluation work. The purpose of this study is to propose a more appropriate model for financial performance evaluation under the unbalanced development.

This paper introduces the differentiation criteria to eliminate the deviation caused by the same principle for multiple performance evaluation objects whose development are unbalanced; Then the generalized grey number is adopted to describe the value of performance evaluation index; and the information entropy weight is used to obtain the index weight to reduce the artificial judgment error; Finally, the generalized grey information entropy weight TOPSIS evaluation model is constructed.

Empirical research shows that in the new evaluation model, the differentiated possibility function effectively eliminates the deviation caused by the same principle, the application of information entropy weight reduces the human judgment error, and the value of generalized grey number further enhances the closeness of the results. Moreover, it is also found that in different scenarios, an adaptive performance evaluation model should be selected to match scientifically reasonable results.

The proposed model offers a solution for financial performance evaluation considering unbalanced development among cities. It can be realized by determining the differentiation possibility function matrix, and then the information entropy weight TOPSIS evaluation model can be constructed. This model reflects the actual situation, improves the performance evaluation accuracy, and can be used under similar conditions.

The calculation of electromagnetic fields can involve many degrees of freedom (DOFs) to achieve accurate results. The DOFs are directly related to the computational effort of the simulation. The effort is decreased by using the proper generalized decomposition (PGD) and proper orthogonalized decomposition (POD). The purpose of this study is to combine the advantages of both methods. Therefore, a hybrid enrichment strategy is proposed and applied to different electromagnetic formulations.

The POD is an a-priori method, which exploits the solution space by decomposing reference solutions of the field problem. The disadvantage of this method is given by the unknown number of solutions necessary to reconstruct an accurate field representation. The PGD is an a-priori approach, which does not rely on reference solutions, but require much more computational effort than the POD. A hybrid enrichment strategy is proposed, based on building a small POD model and using it as a starting point of the PGD enrichment process.

The hybrid enrichment process is able to accurately approximate the reference system with a smaller computational effort compared to POD and PGD models. The hybrid enrichment process can be combined with the magneto-dynamic T-Ω formulation and the magnetic vector potential formulation to solve eddy current or non-linear problems.

The PGD enrichment process is improved by exploiting a POD. A linear eddy current problem and a non-linear electrical machine simulation are analyzed in terms of accuracy and computational effort. Further the PGD-AV formulation is derived and compared to the PGD-T-Ω reduced order model.

The present work involves analytical and experimental investigation of sloshing in a two-dimensional rectangular tank including the effect of porous baffles to control and/or reduce the wave motion in the sloshing tank. The purpose of this study is to assess the analytical solutions of the drag coefficient effect on porous baffles performance to track free surface motion variation in the sloshing tank by comparison with experimental shake table tests under a range of sway excitation.

The linear second-order ordinary differential equations for liquid sloshing in the rectangular tank were solved using Newmark’s beta method and obtained the analytical solutions for liquid sloshing with dual vertical porous baffles of full submergence depths in a sway-oscillated rectangular tank following the methodology similar to Warnitchai and Pinkaew (1998) and Tait (2008).

The porous baffles significantly reduce wave elevation in the varying filled levels of the tank compared to the baffle-free tank under the range of excitation frequencies. It is observed that the Reynolds number-dependent drag coefficient for porous baffles in the tank can significantly reduce the sloshing elevations and is found to be effective to achieve higher damping compared to the porosity-dependent drag coefficient for porous baffles in the sloshing tank. The analytical model’s response to free surface elevation variations in the sloshing tank was compared with the experiment’s test results. The analytical results matched with shake table test results with a quantitative difference near the first resonant frequency.

The scope of the study is limited to porous baffles performance under range sway motion and three different filling levels in the tank. The porous baffle performance includes Reynolds number dependent drag coefficient to explore the damping effect in the sloshing tank.

The porous baffles with low-level porosities in the sloshing tank have many engineering applications where the first resonant mode of sloshing in the tank is more important. The porous baffle drag coefficient is an important parameter to study the baffle’s damping effect in sloshing tanks. Hence, obtained analytical solution for liquid sloshing in the rectangular tank with Reynolds number as well as porosity-dependent drag coefficient (model 1) and porosity-dependent drag coefficient porous baffles (model 2) performance is discussed. The model’s test results were validated using a series of shake table sloshing experiments for three fill levels in the tank with sway motion at various excitation frequencies covering the first four sloshing resonant modes.

This work presents a new two-step iterative technique for solving absolute value equations. The developed technique is valuable and effective for solving the absolute value equation. Various examples are given to demonstrate the accuracy and efficacy of the suggested technique.

In this paper, we present a new two-step iterative technique for solving absolute value equations. This technique is very straightforward, and due to the simplicity of this approach, it can be used to solve large systems with great effectiveness. Moreover, under certain assumptions, we examine the convergence of the proposed method using various theorems. Numerical outcomes are conducted to present the feasibility of the proposed technique.

This paper gives numerical experiments on how to solve a system of absolute value equations.

Nowadays, two-step approaches are very popular for solving equations (1). For solving AVEs, Liu in Shams (2021), Ning and Zhou (2015) demonstrated two-step iterative approaches. Moosaei et al. (2015) introduced a novel approach that utilizes a generalized Newton’s approach and Simpson’s rule to solve AVEs. Zainali and Lotfi (2018) presented a two-step Newton technique for AVEs that converges linearly. Feng and Liu (2016) have proposed minimization approaches for AVEs and presented their convergence under specific circumstances. Khan et al. (2023), suggested a nonlinear CSCS-like technique and a Picard-CSCS approach. Based on the benefits and drawbacks of the previously mentioned methods, we will provide a two-step iterative approach to efficiently solve equation (1). The numerical results show that our proposed technique converges rapidly and provides a more accurate solution.