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We extend the Jones (1971) analysis of the effects of distortions in 2×2 trade models to the case of a two-sector dynamic general equilibrium model of a small open economy with capital accumulation. We do a comparative steady state analysis for the effect of policy changes on factor prices and the capital stock, and examine the dynamics of the system in the neighborhood of the steady state. We also show that the system will have multiple equilibria when value and physical factor intensity rankings of the sectors do not agree.

While steady-state analysis is useful, it does not consider the inherent transient characteristics of repairable systems' behavior, especially in systems that have relatively short life spans, or when their transient behavior is of special concern such as the motivating example used in this paper, military systems. Therefore, a maintenance policy that considers both transient and steady-state availability and aims to achieve the best trade-off between high steady-state availability and rapid stabilization is essential.

This paper studies the transient behavior of system availability under the Kijima Type II virtual age model. While such systems achieve steady-state availability, and it has been proved that deploying preventive maintenance (PM) can significantly improve its steady-state availability, this improvement often comes at the price of longer and increased fluctuating transient behavior, which affects overall system performance. The authors present a methodology that identifies the optimal PM policy that achieves the best trade-off between high steady-state availability and rapid stabilization based on cost-availability analysis.

When the proposed simulation-based optimization and cost analysis methodology is applied to the motivating example, it produces an optimal PM policy that achieves an availability–variability balance between transient and steady-state system behaviors. The optimal PM policy produces a notably lower availability coefficient of variation (by 11.5%), while at the same time suffering a negligible limiting availability loss of only 0.3%. The new optimal PM policy also provides cost savings of about 5% in total maintenance cost. The performed sensitivity analysis shows that the system's optimal maintenance cost is sensitive to the repair time, the shape parameter of the Weibull distribution and the downtime cost, but is robust with respect to changes in the remaining parameters.

Most of the current maintenance models emphasize the steady-state behavior of availability and neglect its transient behavior. For some systems, using steady-state availability as the sole metric for performance is not adequate, especially in systems that have relatively short life spans or when their transient behavior affects the overall performance. However, little work has been done on the transient analysis of such systems. In this paper, the authors aim to fill this gap by emphasizing such systems and applications where transient behavior is of critical importance to efficiently optimize system performance. The authors use military systems as a motivating example.

The advent of the new retail era witnessed the consumers’ demand shift from on the traditional product quality to on the full supply chain service quality, and product service and service manufacturing is gradually taking shape. The purpose of this paper is to propose whether there is a “quality bridge” in the dynamic evolution process of retail service supply chain (RSSC) and discuss the system role, steady-state characteristics and dynamic evolution mechanism of service quality in this dynamic evolution process.

This paper proposes the dissipation system structure of the RSSC under the steady-state quality constraint, constructs a Markov chain model (MCM) for the evolution of the service quality of RSSC, and tests the objective existence of the steady-state distribution of the service quality by taking Chinese HJ retail enterprises as samples.

The research value of this study is summarized as follows. The research finds that the evolution of service quality of RSSC is a dynamic and non-linear growth process, which has significant characteristics of complex adaptability and steady-state convergence. The study finds that the quality evolution process of the RSSC is a steady-state convergence process, and there is a steady-state distribution of quality in its co-evolution, in which different process input levels have a significant positive impact on the stable level of quality state. The study finds that the steady state of quality plays a crucial role in the collaborative evolution of the RSSC, that is, when the service quality reaches a certain steady state distribution, the operating efficiency and profit level of the whole chain will show an “explosive” growth trend.

Quality bridge, an original concept in this paper, represents the role of quality steady-state in the operation of RSSC. Based on Markov chain and system simulation tools, this paper verifies the existence of steady-state service quality and its positive effect on the co-evolution and sustainable development of RSSC. When the service quality reaches a certain steady distribution, the operating efficiency and income level of the whole chain will show n trend of explosive growth.

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.

The purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important.

In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated with the Newton method to accelerate the convergence.

The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient state is very low, it is preferable to use the classical approach, namely, the time-stepping FEM.

The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources.

In the context of the use of the time-stepping FEM, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and directly gives the steady state.

The proposed approach will permit to model and study the electromagnetic systems in the steady state, and particularly the transformers. Because of the gain in computing time, the use of optimisation techniques will be facilitated.

The novelty of this study is the proposal of the waveform relaxation–Newton method to directly obtain the steady state when applied to the three-phase transformer.

The purpose of this paper is to present the Galerkin method for analysis of steady-state processes in periodically time-varying circuits.

A converter circuit working on a time-varying load is often controlled by different signals. In the case of incommensurable frequencies, one can find a steady-state process only via calculation of a transient process. As the obtained results will not be periodical, one must repeat this procedure to calculate the steady-state process on a different time interval. The proposed methodology is based on the expansion of ordinary differential equations with one time variable into a domain of two independent variables of time. In this case, the steady-state process will be periodical. This process is calculated by the use of the Galerkin method with bases and weight functions in the form of the double Fourier series.

Expansion of differential equations and use of the Galerkin method enable discovery of the steady-state processes in converter circuits. Steady-state processes in the circuits of buck and boost converters are calculated and results are compared with numerical and generalized state-space averaging methods.

The Galerkin method is used to find a steady-state process in a converter circuit with a time-varying load. Processes in such a load depend on two incommensurable signals. The state-space averaging method is generalized for extended differential equations. A balance of active power for extended equations is shown.

This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models.

Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only.

An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain.

Reduction of software and hardware requirements for determining steady-states of electromagnetic.

A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form.

Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models.