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The purpose of this paper is to discuss the necessary condition of the relative error between continuous function transformation after inverse transformation and original sequence is not larger than the relative error between transformed sequence and its corresponding simulation sequence.

First, explore the function transformation feature of after inverse transformation the relative error not enlarged, then combine this feature with the function transformation feature of not enlarge the class ratio dispersion, not reduce the smoothness which author have got, and obtain a kind of special transformation that not enlarge class ratio dispersion, not reduce the smoothness and after inverse transformation keep the relative not enlarged. Meanwhile, offer the concrete form of this special function type to monotone increasing continuous function transformation and monotone decreasing continuous function transformation, respectively, and study its properties.

This paper finds the concise and important feature of monotonically increasing function transformation after inverse transformation whether the relative error enlarge or not is at first, the concise and important feature of monotonically decreasing function transformation after inverse transformation relative error not enlarged is. And find that the ideal function transformation which both reduces class ratio dispersion strictly and keeps error of inverse transformation not enlarged is non-exist for monotone increasing function transformation and monotone decreasing function transformation.

Use the necessary condition given by this paper, it may use to judge whether function transformation can keep relative error of inverse transformation not enlarged by easy data calculation before build modeling, therefore, choose the best function transformation. These results tell the authors: the paper cannot treat any functions as the same that whether the relative error of inverse transformation will not enlarge (or not reduced), but the authors should divide them into two parts to discuss that it will be expanded in some range or be reduced in some range. It will affect the future direction of the research, not to find the function transform both satisfies the class ratio dispersion reduced and keep the relative error of inverse transformation not enlarged, but to study which kind of function transform will narrow class ratio dispersion in some range, after the modeling accuracy improvement, but after the inverse transformation the relative error enlarged, and at this time the simulation accuracy is still higher than the simulation accuracy of original data modeling directly. Which kind of function transform will expand class ratio dispersion in some range, after the modeling accuracy diminution, but after the inverse transformation the relative error not enlarged, and now the simulation accuracy is still higher than the simulation accuracy of original data modeling directly, too.

Let peers no longer spend energy in seeking the function transformation which both reduce class ratio dispersion and keep relative error of inverse transformation not enlarged. At the same time, also remind peers that even if a function transformation reduces class ratio dispersion greatly, the data modeling accuracy improves a lot after transformation, but the error of inverse transformation is may quite large, still. Besides, even if function transformation increases class ratio dispersion, the data modeling accuracy is not good after transformation, the ideal situation after inverse transformation would occur, and the possibility cannot be excluded.

The purpose of this paper is to estimate the relative states between the leader and wingman based on vision‐based relative navigation system using extended information filtering (EIF).

For a typical leader‐wingman formation case, the relative navigation equations are introduced. Vision‐based navigation system which consists of an optical sensor and a series of specific light sources is used to capture the line‐of‐sight measurement between the two unmanned aerial vehicles (UAVs). Owing to the limitations on the field of view of the optical sensor, not every specific light source would be visible. And the spatial relative position of the two vehicles could also contributes to the diminution of visibility since some of the light sources are likely to be shielded by the frame and wing. Therefore, the EIF can be applied to the vision‐based relative navigation while every specific light source is regarded and processed as an individual information source. It is demonstrated that the information of visual source could be easily extracted by the simple update equation of information filtering.

The EIF could be used in vision‐based relative navigation system to give an accurate estimation of relative position, velocity and attitude without increasing the amount of calculation or decreasing the estimation accuracy compared to conventional Kalman filtering.

The EIF is first introduced to the vision‐based relative navigation in order to provide relative state between UAVs during formation flight.

To give a closed‐form solution of the relative pose determination problem based on monocular vision during final approach phase of spacecraft Rendzvous and Docking.

Based on the assumption of scaled orthographic projection, the model of perspective projection is simplified by representing the relative attitude using unit quaternion. Then a closed‐form solution is derived. Subsequently, this study correct the approximate solution to compensate the error caused by the assumption of scaled orthographic projection.

Extensive simulation studies were conducted for the validation of the proposed algorithm using Matlab™. When there are no relative attitudes between RVD spacecrafts, target distance for camera=2‐20 m. The simulation results show that the largest relative error of corrected relative position parameters is about 0.12 percent. When distance between RVD spacecrafts exceeds 5 m, the largest error of corrected relative attitude parameters are less than 0.3°. When the distance between spacecrafts are constant, the relative attitude parameters are changed, respectively, the simulition results show the largest relative error of relative position is 1 percent, and largest error of estimated relative attitude is 1.2°, when a relative attitude angle reaches 20°.

The proposed algorithm avoids the multiple results problem in determining the relative position and attitude parameters and the closed‐form solution is simple and effective, is more suitable for on‐board implementation.

The previous literature finds evidence from birth dates of CEOs that the relative-age effect continually influences their career success. The authors look at a significantly larger collection of CEOs and more exact information on school cut-off dates to reexamine the relative-age effect.

The relative-age effect suggests that older individuals within a cohort are more successful. This study investigates if the relative-age effect exists for CEOs in the S&P 1500 by analyzing the distribution of their relative age. The authors utilize an identification strategy that allows to calculate a CEO's relative age in months and enables to resolve known identification problems.

The authors find no support for the existence of the relative-age effect for CEOs either by season of birth or relative age in months. On the whole, the distribution of CEO birth dates is similar to the US population. Additionally, the authors find no evidence of a relative-age effect on firm performance.

Contrary to previous findings, there appears to be no relative-age cohort effect for CEOs of major corporations.

Research shows that CEO characteristics shape firm strategy that in turn affects firm performance. Despite previous work that suggests a relative-age effect, the authors provide a more comprehensive data set and better measurement of relative-age within a cohort. The authors find that the relative-age effect does not continue throughout a CEO's career, and therefore, birth dates are not a characteristic that influences firm strategy and performance.

The purpose of this paper is to propose a fuel‐optimal virtual centre selection method for formation flying maintenance in the J2 perturbed environment.

Based on the relative orbital elements (ROE) theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then the fuel‐optimal virtual centre selection issue for formation flying maintenance are parameterized in terms of ROE. In order to determine the optimal virtual centre, two theories are proposed in terms of ROE.

Numerical simulations demonstrate that the fuel‐optimal virtual centre selection method is valid, and the control of the ROE of each satellite with respect to a virtual optimal centre of the formation is more efficient regarding the fuel consumption than the control of all satellites with respect to a satellite belonging to the formation.

The fuel‐optimal virtual centre selection method is valid for formation flying mission whose member satellite in circular or near circular orbit.

The fuel‐optimal virtual centre selection approach can be used to solve formation flying maintenance problem which involves multiple satellites in the formation.

The paper proposes a fuel‐optimal virtual centre selection method in terms of ROE, and shows that keeping the formation with respect the optimal virtual centre is more fuel efficient.

This study investigates the impact of the increasing proportion of older workers in the workforce by establishing a theoretical framework and estimating the degree of substitutability between them and their younger counterparts.

The first step is to establish a theoretical framework that combines older and younger workers with imperfect substitutability in the production of final goods within an aggregate production function. The author then derives an equation that relates the relative wage, relative supply and elasticity of substitution between the worker types, for use in estimation. Using data from Japan’s Basic Survey on Wage Structure and Population Census from 2010 to 2019 across 47 prefectures, the author estimates the elasticity of substitution between older and younger workers in Japan.

The author finds that workers aged 55 and over and their younger counterparts are gross substitutes, and the estimated elasticity of substitution is in the range of 2.33–2.86. This implies that a 10% increase in the relative number of workers aged 55 and older leads to a fall in their relative wage in the range of 3.5–4.3%. The study estimations suggest that since 2010, there has been a convergence in the relative wage of older workers across Japan’s prefectures.

Understanding the degree of substitutability between older and younger workers is essential for quantitatively assessing the impact of workforce aging, technological advancements and labor policies on the wage distribution. This study estimates the elasticity of substitution between the two worker types based on a theoretical model, and utilizes recent datasets and methodology not adequately addressed in previous literature.

The purpose of this study is to investigate the phenomenon of knowledge transfer between employees and coworkers. That is, when and why employees engage in knowledge seeking or knowledge sabotage when confronted with coworkers with higher relative overqualification.

This study collected survey data from 315 employee-coworker pairs in East China at three-time points.

The results showed that when the cooperative goal interdependence between employee and coworker is high, the perception of coworker’s relative overqualification will cause benign envy of employees, which in turn promote employees to engage in knowledge seeking from coworker. However, when the competitive goal interdependence between employee and coworker is high, the perception of coworker’s relative overqualification will cause malicious envy of employees, which in turn promote employees to engage in knowledge sabotage toward coworker.

This research not only expands the theoretical perspective and outcomes of relative overqualification but also enriches the mechanism of knowledge seeking and knowledge sabotage. Meanwhile, this study also provides practical guidance for enterprises to reduce knowledge sabotage.

This paper aims to report two studies with the purpose of demonstrating and establishing the efficacy of using an alternative method of operationalizing relative brand attitudes based on Cheung's latent congruence model (LCM).

Data are collected concerning brand attitudes related to their product (study 1) and retailer (study 2) preferred and best alternative brands. Structural equation modeling is used to demonstrate and validate the LCM model, as well as to relate relative brand attitudes to satisfaction judgments and loyalty behaviors.

Two separate samples of respondents across two unique marketing settings (product and retailer brands) support the LCM‐based view of relative brand attitude proposed herein. In addition, results suggest that preferred brands are most strongly related to satisfaction with the preferred brand, however, relative brand attitudes are alternatively related to preferred brand loyalty. Thus, relative brand attitudes appear to have both direct and indirect (through satisfaction) influences on brand loyalty.

Practical implications include the availability of a usable method of operationalizing relative brand attitudes in a way that fully utilizes hedonic/utilitarian attitude scale for absolute and relative brand attitudes measures and can control for measurement error. The proposed method thus provides a means to strengthen measurement models associated with relative brand concepts.

The reported studies offer an alternative and practical method of measuring relative brand attitudes in a way that results in practical insights about consumer satisfaction and brand loyalty.

We present, in this study, a method for comparing the relative effectiveness of different non-profit institutions with similar objectives. In addition, we show how this measure of relative effectiveness is related theoretically to their relative efficiency. Relative effectiveness is shown to be a product of the efficacy with which potentially utilizable resources can be converted into usable inputs, and the efficiency with which the inputs are converted to outputs or outcomes. Finally, drawing on developments in data envelopment analysis, we illustrate the new methodology using data from 109 institutions of higher education.

The purpose of this paper is to analyze the frame of a missile formation cooperative control system, and present an optimal keeping controller of a missile formation in the cooperative engagement.

A missile relative motion model is established directly based on the kinematics relationships in the relative coordinated frame, following that is the detailed process of designing an optimal formation controller, which is analyzed through the small disturbance linearized method and transforming control variables method, respectively, these two methods both have themselves properties. The equations and control variables are intuitive during the linearized analysis, but errors brought by the linearized method are unavoidable, which will reduce the control precision. As for the transforming method, the control accuracy is greatly increased although the control form is a little complex, so in this paper the transforming control variable method is mainly researched to design an optimal formation controller. Considering the states of a leader as input perturbation variables, we design an optimal formation controller based on the linear quadric theory, which has quadric optimal performances of the missile flight states and control quantity. In order to obtain a higher accurate solution, the precise integration algorithm is introduced to solve the Riccati Equation that significantly affects the accuracy of an optimal control problem.

The relative motion model established directly in the relative coordinate frame has intuitive physical significance, and the optimal controller based on this relative motion model is capable of restraining the invariable or slowly varying perturbation brought by the velocity of a leader and the input perturbations caused by the maneuver of the leader, at the same time this optimal controller can implement formation reconfiguration and keeping to an expected states rapidly, steadily and exactly; the steady errors can be greatly decreased by analyzing the relative motion model through transforming control variables method compared to the small disturbance linearized operation.

The main frame of a missile formation cooperative engagement system can be found in this paper, which shows a clear structure and relations of each part of this complex system. The relations between each subsystem including the specific input and output variables can also be used to guide and restrict how to design each subsystem. The emphasis of this paper is on designing an optimal formation keeping controller which can overcome slowly varying or invariable perturbations and implement quadric optimal keeping control rapidly, stably and accurately.

This paper provides a new method to analyze the missile relative motion model. The proposed proportional and integral (PI) optimal controller based on this model, and utilizing the Precise Integration Algorithm to solve this optimal controller are also new thoughts for formation control problems.