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That part of human behaviour which is not rigidly determined by external constraints can be considered as a sequence of more or less free choices. One can talk of a choice only if it is one of several alternatives, and of a free choice only in so far as it is not determined by conditions over which the individuals have no control. Moreover, we recognise an alternative only if it is actually elected by at least a fraction of a population. This leads to the concept of statistical freedom. Postulates are formulated which must be satisfied by any numerical measures of statistical freedom, and certain mathematical expressions are proposed which are shown to conform to these postulates. Statistical freedom has two fundamental features, which appear as factors in its numerical measure: diversity and independence. The measures of diversity and independence are derived in the first place front a certain model of society, but once they are obtained, the model is discarded, and the statistical coefficients are justified by their mathematical properties. Safeguards against arbitrary manipulation of statistical material are discussed, and the potential use of the new measures is illustrated by application to the problem of choice of profession.

The objective of this paper is to demonstrate how to use the Elton, Gruber, and Padberg [1978] model to construct optimal portfolios and to facilitate the use of this paradigm by providing an example of how the technique is used. The EGP model uses the risk‐adjusted, excess return for an asset to determine the optimal portfolio for a given risk‐free rate of return. This paper shows exactly how to calculate the optimal portfolio and provides a True Basic@ program to do so. The data used are constructed from Capital International Indexes taken from various issues of Barrons from March 1978 to December 1986.

Keeping satellite position within close tolerances is key for the utilization of satellite formations for space missions. The presence of perturbation forces makes control inevitable if such mission objective is to be realised. Various approaches have been used to obtain feedback controller parameters for satellites in a formation; this paper aims to approach the problem of estimating the optimal feedback parameter for a leader–follower pair of satellites in a small eccentric orbit using nature-based search algorithms.

The chaotic artificial bee colony algorithm is a variant of the basic artificial bee colony algorithm. The algorithm mimics the behaviour of bees in their search for food sources. This paper uses the algorithm in optimizing feedback controller parameters for a satellite formation control problem. The problem is formulated to optimize the controller parameters while minimizing a fuel- and state-dependent cost function. The dynamical model of the satellite is based on Gauss variational equations with J2 perturbation. Detailed implementation of the procedure is provided, and experimental results of using the algorithm are also presented to show feasibility of the method.

The experimental results indicate the feasibility of this approach, clearly showing the effective control of the transients that arise because of J2 perturbation.

This paper applied a swarm intelligence approach to the problem of estimating optimal feedback control parameter for a pair of satellites in a formation.

Light, when constructed in terms of the elementary quanta of light, may be viewed in particle‐like or wave‐like terms. The elementary quanta of light, when placed in motion through space/time at a speed of a constancy of c forms a light path through the space or reference frame viewed. The light path formed is curved, as space/time is curved. The curvilinear light path formed is a function of the gravitational potential within the viewed frame of reference. The linear description of this light path, termed the geodesic (Riemannian), does not describe the curvilinear light path, but rather the chord of the curvilinear path described by the inscribed arc. This linear description of the light path is the manner in which we describe the coordinate system involved, and is the same manner in which we determine the “speed of light”. The arc length of the light path, compared to the lesser value as described by the chord length, allows for a displacement to be determined, if both measures are applied to a linear measure. A displacement of linear coordinates then occurs, with this displacement a result of the gravitational potential occurring within the frame viewed. This displacement, derived via observation and predictions of the quantum model, resolves Maxwell as well as Newton. The theory concludes that the Special Theory of Relativity, suitably modified to account for gravitational displacement within one particular frame, derives a precise relative model of gravitation within the special frame. This model satisfies Newton, as the model arrives at an exact description of the three‐body problem.

The purpose of this paper is to consider relative navigation – a vital technology to satellites formation flying, and to propose a new concept for relative navigation determination along with a technical approach for its practical implementation.

The determination of relative orbit is considered with the relative distance elevation and azimuth measurements about formation flying while the primary satellite is in a circle or ellipse orbit. This measurement is obtained by laser range finder and the estimations of the intersatellite relative position and velocity are obtained by utilizing the unscented Kalman filter instead of extended Kalman filter.

The simulation results show that the error of the relative position and velocity can be estimated with the order of cm and mm/s, respectively, under the effect of J2, converge faster than EKF, and then demonstrate that the approach is feasible.

The paper proposes a new concept for relative navigation determination and describes a technical approach for its practical implementation.

The purpose of this paper is to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

Based on the concept of fractionated spacecraft, orbit design requirements for cluster flight in the case of fractionated spacecraft are proposed, and categorized into three requirements: stabilization requirement, passive safety requirement, and the maximum inter‐satellite distance requirement. These design requirements are then reformulated in terms of relative eccentricity and inclination vectors (E/I vectors) using a relative motion model based on relative orbital elements (ROEs). By using ROEs theory, the cluster flight orbit design issue is modelled as the distribution of relative E/I vectors for each member satellite in the cluster, and solved by combining three different heuristic search methods and one nonlinear programming (NLP) method.

The simulation results show that the NLP method is valid and efficient in solving the cluster flight orbit design problem and that for some cluster flight scenarios, the heuristic search methods can be adopted to give feasible solutions without the NLP method.

The cluster flight scenario in this paper is limited because the cluster should be in the near‐circular low earth orbit (LEO), and the relative distance between the member satellites should be small enough to satisfy the relative motion linearization assumption.

The cluster flight orbit design method proposed in this paper can be applied by fractionated spacecraft mission designers to propose potential cluster flight orbit solutions.

In this paper, the relative E/I vectors method is adopted to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

The nature of the relation between complex stress creep under conditions of relaxation and complex stress creep under conditions of steady stress was investigated. The required relation has been examined for an RR59 aluminium alloy at 200 deg. C. and for a magnesium (2 per cent aluminium) alloy at 50 deg. C. For RR59 aluminium alloy at 200 deg. C. and for magnesium (2 per cent aluminium) alloy at 50 deg. C., a reasonably close prediction of the course of relaxation complex stress time curves is given by the mechanical age hardening theory of creep on the basis of steady complex stress creep data. Other mechanical theories tend to predict for a specific relaxed stress a relaxation time in excess of that noted in experiment.

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.

The purpose of this paper is to present an implementation of a soft‐computing (SC) based navigation approach on a bi‐steerable mobile robot, Robucar. This approach must provide Robucar with capability to acquire the obstacle avoidance, target localization, decision‐making and action behaviors after learning and adaptation. This approach uses three neural networks (NN) and fuzzy logic (FL) controller to achieve the desired task. The NNs corresponding to the obstacle avoidance and target localization are trained using the back‐propagation algorithm and the last one is based on the reinforcement learning paradigm while the FL controller uses the Mamdani search and match algorithm. Simulation and experimental results are presented, showing the effectiveness of the overall navigation control system.

In this paper, an interesting navigation approach is applied to a car‐like robot, Robucar, with addition of an action behavior to deal with the generation of smooth motions. Indeed, this approach is based on four basic behaviors; three of them are fused under a neural paradigm using Gradient Back‐Propagation (GBP) and reinforcement learning (RL) algorithms and the last behavior uses a FL controller. It uses a set of suggested rules to describe the control policy to achieve the action behavior.

In the implemented SC‐based navigation, the intelligent behaviors necessary to the navigation are acquired by learning using GBP algorithm and adaptation using FL. The proposed approach provides Robucar with more autonomy, intelligence and real‐time processing capabilities. Indeed, the proposed NNs and FLC are able to remedy problems of analytical approaches, missing or incorrect environment knowledge and uncertainties which can lead to undesirable effects as the rough velocity changes. The simulation and experimental results display the ability of the proposed SC‐based navigation approach to provide Robucar with capability to intelligently navigate in a priori unknown environment, illustrating the robustness and adaptation capabilities of the approach.

This work can be extended to consider mobile obstacles with a velocity higher than the velocity of the robot.

This paper presents a learning approach to navigating a bi‐steerable mobile robot in an unknown environment using GBP and RL paradigms.

Motivated by the growing importance of the expected shortfall in banking and finance, this study aims to compare the performance of popular non-parametric estimators of the expected shortfall (i.e. different variants of historical, outlier-adjusted and kernel methods) to each other, selected parametric benchmarks and estimates based on the idea of forecast combination.

Within a multidimensional simulation setup (spanned by different distributional settings, sample sizes and confidence levels), the authors rank the estimators based on classic error measures, as well as an innovative performance profile technique, which the authors adapt from the mathematical programming literature.

The rich set of results supports academics and practitioners in the search for an answer to the question of which estimators are preferable under which circumstances. This is because no estimator or combination of estimators ranks first in all considered settings.

To the best of their knowledge, the authors are the first to provide a structured simulation-based comparison of non-parametric expected shortfall estimators, study the effects of estimator averaging and apply the mentioned profiling technique in risk management.