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Studies the concept of the Cartesian composition of fuzzy finite state machines. Shows that fuzzy finite state machines and their Cartesian composition share many structural properties. Some of these properties are singly generated; retrievability, connectedness, strong connectedness, commutativity, perfection and state independence. Thus a fuzzy finite state machine which is a Cartesian composition of submachines can be studied in terms of smaller machines.

To find martingale theory and methods of parameter vector estimation of multidimensional linear control system in dynamic system.

In parameter vector estimation of dynamic system, due to the limitation of conventional methods, the authors study the iterative formula and consistency of parameter vector estimation using the theory and methods of martingale, and extend its application field.

Some conditions of strongly consistent estimation and iterative formula are obtained. And the consistency of parameter vector estimation in multidimensional linear control system is discussed.

Solved some practical problems of parameter vector estimation in dynamic system.

The paper solve the accuracy problem of parameter vector estimation of multidimensional linear control system in dynamic system and extend parameter vector estimation application field.

This paper aims to propose Bayesian filtering based on solving the Fokker–Planck equation, to improve the accuracy of filtering in non-Gauss case. Nonlinear filtering plays an important role in many science and engineering fields for estimating the state of dynamic system, but the existing filtering algorithms are mainly used for solving the problem of Gauss system.

Under the Bayesian framework, the time update of this filtering is based on solving Fokker–Planck equation, while the measurement update uses the Bayes formula directly. Therefore, this novel algorithm can be applied to nonlinear, non-Gaussian estimation. To reduce the computational complexity due to standard meshing, an adaptive meshing algorithm proposed which includes the coarse meshing, significant domain determination that is generated using extended Kalman filtering and Chebyshev’s inequality theorem, and value assignment for significant domain. Simulations are conducted on a reentry body tracking problem to demonstrate the effectiveness of this novel algorithm.

In this way, finer grid points can be placed in the regions with high conditional probability density, while the grid points with low conditional probability density can be neglected. The simulation results indicate that the novel algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

A novel Bayesian filtering based on solving the Fokker–Planck equation using adaptive meshing is proposed, and the simulations show that algorithm can reduce the computational burden significantly compared to the standard meshing, while achieving similar accuracy.

A novel nonlinear filtering based on solving the Fokker–Planck equation is proposed. The novel algorithm is suitable for non-Gauss system, and can achieve similar accuracy compared to the standard meshing with the significant reduction of computational burden.

To address the various irregularities that occurred during the development of China’s electricity market, particularly the issue of collusive pricing between upstream and downstream firms.

This study constructs a tripartite evolutionary game model involving government regulators, grid operators and power producers to address electricity market pricing chaos. By analyzing the stable strategies within each subject’s evolutionary game, adjustments to the relevant parameters are made to achieve a stable state of strategy selection.

The findings of this study indicate the following: (1) Enhancing the government’s rewards and punishments, increasing speculation and rent-seeking costs for grid operators and modifying tariff sales revenue can promote the integrity of grid operators. (2) Establishing reasonable incentives and penalties can effectively mitigate rent-seeking behaviors resulting from collusive pricing in the power industry. (3) Strengthening the accountability of higher authorities to government regulators and adjusting incentives for grid operators to comply and generators to refrain from rent-seeking behavior can increase the likelihood of rigorous inspections by government regulators.

This study elucidates the impact of factors such as the cost of speculation and sales revenue of grid operators, the cost of rent-seeking by power producers and the strength of rewards and punishments by government departments on the power sector. Adjusting these factors can significantly influence the stability of the three-party evolutionary game, providing valuable insights into the regulatory mechanisms of the power industry.

Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L²_α (K), where K=0,+∞×0,+∞[.

The author has employed the results developed by Titchmarsh, of reference number [1].

In this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform.

To the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

The screen Cauchy–Riemann (SCR)-lightlike submanifold is an important class of submanifolds of semi-Riemannian manifolds. It contains various other classes of submanifolds as its sub-cases. It has been studied under various ambient space. The purpose of this research is to study the geometry of SCR-lightlike submanifolds of metallic semi-Riemannian manifolds.

The article is divided into five sections. The first section is introductory section which represents brief overview of the conducted research of this article. The second section outlines the key results that are utilized throughout the paper. In section three, the definition of SCR-lightlike submanifold is constructed with one non-trivial example. In section four and five, the important results on integrability, totally geodesic foliations and warped product are given.

The SCR-lightlike submanifold is introduced. One non-trivial example is constructed which helps to understand the given structure. The necessary and sufficient conditions for the integrability and to be totally geodesic for various distributions are obtained. The necessary and sufficient conditions for induced connection on totally umbilical SCR-lightlike submanifolds to be a metric connection are discussed. Various results are found on totally umbilical SCR-lightlike submanifolds. Finally, the existence of the warped product lightlike submanifold of the type N^⊥×_λN_T is studied.

SCR-lightlike submanifolds have been explored within ambient manifolds possessing various structures, such as Kaehler, Sasakian and Kenmotsu structures. In this article, we investigate this structure on submanifolds of metallic semi-Riemannian manifolds. This original and authentic research will aid researchers in advancing the study of semi-Riemannian manifolds.

In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditiona l quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the article is to derive a likelihood-ratio test, which to the best of our knowledge is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

We aim to generalize the continuous-time principal–agent problem to incorporate time-inconsistent utility functions, such as those of mean-variance type, which are prevalent in risk management and finance.

We use recent advancements of the Pontryagin maximum principle for forward-backward stochastic differential equations (FBSDEs) to develop a method for characterizing optimal contracts in such models. This approach addresses the challenges posed by the non-applicability of the classical Hamilton–Jacobi–Bellman equation due to time inconsistency.

We provide a framework for deriving optimal contracts in the principal–agent problem under hidden action, specifically tailored for time-inconsistent utilities. This is illustrated through a fully solved example in the linear-quadratic setting, demonstrating the practical applicability of the method.

The work contributes to the existing literature by presenting a novel mathematical approach to a class of continuous time principal–agent problems, particularly under hidden action with time-inconsistent utilities, a scenario not previously addressed. The results offer potential insights for both theoretical development and practical applications in finance and economics.