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Buffer operators can be utilized to improve the smooth degree of the raw data sequence, and to increase the simulation accuracy of the model. The purpose of this paper is to analyze the cause of increase in the simulation accuracy of the buffer operator.

This paper probed into the modeling mechanism of several typical buffer operators such as the arithmetic buffer operators, the buffer operators with monotonic function and weighted buffer operators. The paper also gives an example of the buffer operator sequence.

The results indicate that after applying an infinite buffer operator, whether the authors adopt a weakening buffer operator or a strengthen buffer operator, the raw sequence can be changed into a constant sequence. Because the discrete GM(1,1) model can completely simulate constant sequence, the simulation accuracy is 100 percent. Because the discrete GM(1,1) model is the accurate form of the GM(1,1) model, after applying an infinite buffer operator, the GM(1,1) model can have a very high simulation accuracy. The buffer operator model can increase the simulation accuracy of both the GM(1,1) model and the discrete GM(1,1) model.

The paper analyses the cause of increasing simulation accuracy of the buffer operator model. The paper may indicate that possible results can be studied in the future. All the buffer operator models have similar properties. After applying an infinite buffer operator, the raw sequence can be changed into a constant sequence. A fixed-point axiom may be the basic cause.

Describes how the USA and UK have established many and varied tough new provisions in the fight against crime, and corruption in particular. Traces the long history of corruption and attempts to suppress it, and defines the terms bribery and corruption. Looks at the US legislation against corruption, focusing on the Racketeer Influenced and Corrupt Organizations Act (RICO) 1970 and the Foreign Corrupt Practices Act (FCPA) 1977, also the Financial Institutions Reform, Recovery and Enforcement Act (FIRREA) 1989 and most recently the PATRIOT Act 2001, which covers corruption as part of a wider response to the terrorist attacks on the USA. Moves onto UK legislation since 1889, including the OECD Convention, the Anti‐Terrorism, Crime and Security Act 2001, the draft Corruption Bill, and legislation enacted against money laundering and to seize the proceeds of crime.

The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation.

This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state.

Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used.

The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large.

The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

The purpose of this paper is to present the terms of sequence operators and grey data mining.

The definitions of basic terms about sequence operators and grey data mining are presented one by one.

The reader could know the basic explanation about the important terms about sequence operators and grey data mining from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardize all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

The purpose of this paper is to solve the challenging problem of automatic carrier landing with the presence of environmental disturbances. Therefore, a global fast terminal sliding mode control (GFTSMC) method is proposed for automatic carrier landing system (ACLS) to achieve safe carrier landing control.

First, the framework of ACLS is established, which includes flight glide path model, guidance model, approach power compensation system and flight controller model. Subsequently, the carrier deck motion model and carrier air-wake model are presented to simulate the environmental disturbances. Then, the detailed design steps of GFTSMC are provided. The stability analysis of the controller is proved by Lyapunov theorems and LaSalle’s invariance principle. Furthermore, the arrival time analysis is carried out, which proves the controller has fixed time convergence ability.

The numerical simulations are conducted. The simulation results reveal that the proposed method can guarantee a finite convergence time and safe carrier landing under various conditions. And the superiority of the proposed method is further demonstrated by comparative simulations and Monte Carlo tests.

The GFTSMC method proposed in this paper can achieve precise and safe carrier landing with environmental disturbances, which has important referential significance to the improvement of ACLS controller designs.

The study aims to optimize truck routes by minimizing social and economic costs. It introduces a strategy involving diverse drones and their potential for reusing at DNs based on flight range. In HTDRP-DC, trucks can select and transport various drones to LDs to reduce deprivation time. This study estimates the nonlinear deprivation cost function using a linear two-piece-wise function, leading to MILP formulations. A heuristic-based Benders Decomposition approach is implemented to address medium and large instances. Valid inequalities and a heuristic method enhance convergence boundaries, ensuring an efficient solution methodology.

Research has yet to address critical factors in disaster logistics: minimizing the social and economic costs simultaneously and using drones in relief distribution; deprivation as a social cost measures the human suffering from a shortage of relief supplies. The proposed hybrid truck-drone routing problem minimizing deprivation cost (HTDRP-DC) involves distributing relief supplies to dispersed demand nodes with undamaged (LDs) or damaged (DNs) access roads, utilizing multiple trucks and diverse drones. A Benders Decomposition approach is enhanced by accelerating techniques.

Incorporating deprivation and economic costs results in selecting optimal routes, effectively reducing the time required to assist affected areas. Additionally, employing various drone types and their reuse in damaged nodes reduces deprivation time and associated deprivation costs. The study employs valid inequalities and the heuristic method to solve the master problem, substantially reducing computational time and iterations compared to GAMS and classical Benders Decomposition Algorithm. The proposed heuristic-based Benders Decomposition approach is applied to a disaster in Tehran, demonstrating efficient solutions for the HTDRP-DC regarding computational time and convergence rate.

Current research introduces an HTDRP-DC problem that addresses minimizing deprivation costs considering the vehicle’s arrival time as the deprivation time, offering a unique solution to optimize route selection in relief distribution. Furthermore, integrating heuristic methods and valid inequalities into the Benders Decomposition approach enhances its effectiveness in solving complex routing challenges in disaster scenarios.

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 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.