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This paper presents two mathematical models to perform probabilistic safety analysis in maintenance environment. Both models assume system operating in safe and unsafe environments. Model I represents a repairable system with three states: working normally, working in unsafe mode, and failed safely. Model II represents a repairable system with four states: working normally, working in unsafe mode due to human error, working in unsafe mode due to hardware failure, and failed safely. Equations for state probabilities, system availabilities, reliability, and mean time to failure are developed.

To develop a theory of concepts that solves the combination problem, i.e. to deliver a description of the combination of concepts. We also investigate the so‐called “pet fish problem” in concept research.

The set of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators and context and properties are orthogonal projections.

The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination problem is proposed. Using the tensor product, a natural product in Hilbert space mathematics, a procedure for describing combined concepts is elaborated. This procedure also provides a solution to the pet‐fish problem, and it allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented.

The combination problem is considered to be one of the crucial unsolved problems in concept research. Also the pet‐fish problem has not been solved by earlier attempts of modeling.

The purpose of this paper is to introduce new non‐classical implementations of neural networks (NNs). The developed implementations are performed in the quantum, nano, and optical domains to perform the required neural computing. The various implementations of the new NNs utilizing the introduced architectures are presented, and their extensions for the utilization in the non‐classical neural‐systolic networks are also introduced.

The introduced neural circuits utilize recent findings in the quantum, nano, and optical fields to implement the functionality of the basic NN. This includes the techniques of many‐valued quantum computing (MVQC), carbon nanotubes (CNT), and linear optics. The extensions of implementations to non‐classical neural‐systolic networks using the introduced neural‐systolic architectures are also presented.

Novel NN implementations are introduced in this paper. NN implementation using the general scheme of MVQC is presented. The proposed method uses the many‐valued quantum orthonormal computational basis states to implement such computations. Physical implementation of quantum computing (QC) is performed by controlling the potential to yield specific wavefunction as a result of solving the Schrödinger equation that governs the dynamics in the quantum domain. The CNT‐based implementation of logic NNs is also introduced. New implementations of logic NNs are also introduced that utilize new linear optical circuits which use coherent light beams to perform the functionality of the basic logic multiplexer by utilizing the properties of frequency, polarization, and incident angle. The implementations of non‐classical neural‐systolic networks using the introduced quantum, nano, and optical neural architectures are also presented.

The introduced NN implementations form new important directions in the NN realizations using the newly emerging technologies. Since the new quantum and optical implementations have the advantages of very high‐speed and low‐power consumption, and the nano implementation exists in very compact space where CNT‐based field effect transistor switches reliably using much less power than a silicon‐based device, the introduced implementations for non‐classical neural computation are new and interesting for the design in future technologies that require the optimal design specifications of super‐high speed, minimum power consumption, and minimum size, such as in low‐power control of autonomous robots, adiabatic low‐power very‐large‐scale integration circuit design for signal processing applications, QC, and nanotechnology.

The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form.

It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system.

The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system).

Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.

Focuses on steady state modelling of basic unipolar non‐isolated PWM AC line matrix‐reactance choppers (MRC). Their single‐phase topologies are similar to well‐known basic DC/DC converter ones. The MRC are built up through the adaptation of DC/DC converter topologies, which are based on the substitution of self‐commutated unidirectional switches by bi‐directional ones.

Presents an approach to modelling of the MRC with averaging operator different to the one used in averaged modelling of the DC/DC converters. There is running averaging of each switching period in the proposed approach. Following this, there is a demonstration of the solutions convergence of the state space and averaged state space equations for infinitive switching frequency.

The running averaging of each switching period should be used if averaged state space method is applied to the analysis of presented choppers. A circuit averaged model build‐up procedure of the presented choppers is the same as for the DC/DC ones.

Presents a quantitative assessment of accuracy for the averaged models of the presented MRC for finite switching frequency.

Understanding the performance and flight envelope of a damaged aircraft is a preliminary requirement to recover the aircraft after damage. This paper aims to provide a comprehensive understanding of wing damage effect on airplane performance, local stability, and flying quality of each trim state inside the achievable flight envelope.

This paper demonstrates the use of attainable equilibrium points which are referred as trim states in order to estimate a damaged airplane manoeuvring flight envelope using a numerical computation method.

Wing damaged airplane manoeuvring flight envelope is estimated for different portions of the wing tip loss. Local stability at each trim condition inside the estimated flight envelope is analysed, and also motion flight modes and flying quality sensitivity to the wing damage are explored.

Local stability and flying quality analysis at each trim condition inside the flight envelope which demonstrate the effect of damage provides a criterion to prioritize the choice of trimmed flight condition as motion primitives for the airplane post‐damage flight and safe landing.

This paper aims to present the development and performance evaluation of an attitude and rate estimation algorithm using an extended Kalman filter structure based on a body‐referenced representation of the state.

The algorithm requires only geomagnetic field data and can be used as a low‐cost alternative or as a back‐up estimator in the case of attitude sensor failures. The satellite rate is estimated as a part of the filter state and thus no gyroscope is necessary. The assessment of the algorithm performance is realized through a Monte Carlo simulation using a low‐Earth orbit, nadir‐pointing satellite.

Given some attitude and rate error requirements, the range of admissible initial errors on the filter state and the effect of un‐modelled disturbance torque are determined, along with the achievable attitude and rate accuracies.

Because the simulation set‐up is clearly stated, the results of this evaluation can be used as a benchmark for other estimation algorithms.

The necessary assumptions and approximations used to derive the filter equations are explicitly pointed out for the benefit of the readers. Well‐defined filter initial conditions are used in an extensive series of tests resulting into a unique set of findings.

The purpose of this paper is to study the combined effect of human error, common‐cause failure, redundancy, and maintenance policies on the performance of a system composed of three‐state devices.

Generalized expressions for time‐dependent and steady state availability of a generalized maintainable three‐state device parallel system subjected to human errors and common‐cause failures are developed in the paper under two maintenance policies: Type I repair policy (i.e. only the completely failed system is repaired); and Type II repair policy (i.e. both partially and completely failed system is repaired). The Markov method is used to develop general and special case expressions for state probabilities, and system time‐dependent and steady state availabilities.

In the case of three‐state devices, it is demonstrated that by increasing the number of redundant devices in parallel do not necessarily lead to the improvement in the system availability. In fact, the availability of the system depends significantly on the dominant failure mode of the devices (i.e. short‐mode or open‐mode). When comparing the effect of maintenance policies on the system availability, it is observed that the Type II repair policy does not lead to an improvement in the system availability. Furthermore, it is observed that both human error and common‐cause failure independently lead to lower system availability.

This study will help maintenance engineers and reliability practitioners to become aware of the combined impact of redundancy, human error, common‐cause failure, and maintenance policies on the performance of the three‐state device systems. Consequently, they will make better maintenance related decisions in organizations such as oil refineries and power stations that use three state devices quite extensively.

Most of the past models have independently studied the effects of redundancy, human error, and common‐cause failure on maintainable system made up of three‐state devices. This effort is one of the first attempts to study the combined effects of all these factors in a parallel system composed of three state devices.

The purpose of this paper is to allocate marketing budgets in complex environments, where data are scarce and management judgment is available. In this research, marketing budgets are allocated, to maximize customer equity as a long-term profitability measure.

The researchers provide a model for allocation of marketing budgets based on both decision calculus and econometric models and combine it with the concept of Markov chain model to cope with data scarcity. Dynamic programming is used to find the optimal solution.

The authors examine the model in telecommunication industry. Applicability of the model is supported by an illustrative example. To allocate marketing budgets, researchers consider three strategies for each period: do nothing, retention-focused strategy and acquisition-focused strategy. The results show the applicability and effectiveness of the model to find the best strategy.

As the suggested approach is based on management judgment, it is useful in situations, as the authors have experts or experienced managers to achieve reliable data. In situations which the authors do not have access to experienced managers, the results may be unreliable.

The suggested approach is useful in situations of data scarcity, where experienced managers are accessible. The researchers have focused on telecommunication industry cases; however, the model is useful in other industries like the insurance industry.

The main contribution of the research lies in the suggestion of a new approach to allocate marketing budgets in data scarcity situations in multi-period planning horizons. The researchers use both decision calculus and econometric tools to find the transition matrices of marketing plans.

EDMC represents extended dynamic matrix control, which can be applied to nonlinear process control. In this method, control inputs are determined based on a linear model that approximates the process and is updated during each sampling interval. Since nonlinear relation still exists between the prediction error and the control input, numerical (iterative) methods are used to solve the optimization problem defined in the method. For nonlinear processes with high variation and/or sign changes in their steady‐state gain, iterative methods do not converge properly to an acceptable solution for some desired outputs or external disturbances. To eliminate the problem, we augment the process with its steady‐state gain inverse (or pseudo inverse whenever required) such that the steady‐state gain for the new augmented system is constant or contains slow variations. In the case of unstable processes, the method may be applied after stabilizing the process using a proper state or output feedback. Effectiveness of the method has been examined using computer simulations of some benchmark processes. Some of the obtained results are presented in this paper.