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Nowadays, various methods of observation from unmanned aerial vehicles (UAV) are being widely developed. There are many ways of increasing the amount of information retrieved from captured material. Unfortunately, hardware solutions consume a lot of energy, which is unacceptable in UAV applications, as it can have direct impact on the observing time on UAV. Those kinds of problems have been identified during the development phase of stabilizing platform in Polish Research Space Centre in Warsaw. As a result of that fact, energy saving control methods have been implemented, which estimates quality of stabilization process for the observation-tracking device (OTD).

Mathematical model has been designed and validated with real-life experiments for the purpose of optimization of stabilization and control process. Two types of controlling algorithms have been implemented: linear quadratic regulator and proportional derivative method for driving the mechanism. Based on numerical simulations of the mechanical model being controlled by the mentioned driver, it was possible to define membership functions. After the process of defuzzification, the controller predicts quality of stabilization under defined environmental working conditions.

An autonomous energy saving system has been created that can be implemented in many applications, where environmental conditions may change significantly.

To test the proposed fuzzy controller, OTD has been chosen as an example object of application. It is a mechanical platform which houses the optical observation system. It is designed to provide the best working conditions during flight.

That kind of decision-making unit has never been implemented before during observations which were carried out during flying of an object. That innovative controller should bring significant energy consumption savings.

This paper outlines a steady state multi-modal equilibrium transportation model which contains elastic demands and deterministic route-choices. The model may readily be extended to include some stochastic route-choice or mode choice. Capacity constraints and queueing delays are permitted; and signal green-times and prices are explicitly included. The paper shows that, under natural linearity and monotonicity conditions, for fixed control parameters the set of equilibria is the intersection of convex sets. Using this result the paper outlines a method of designing appropriate values for these control parameters; taking account of travellers' choices by supposing that the network is in equilibrium. The method may be applied to non-linear monotone problems by linearising about a current point. An outline justification of the method is given; a rigorous proof of convergence is as yet missing. Thus the method must now be regarded as a heuristic.

In the case of ordered categorical data, the concepts of minimum and maximum inequality are not straightforward. In this chapter, the authors consider the Cowell and Flachaire (2017) indices of inequality. The authors show that the minimum and maximum inequality depend on preliminary choices made before using these indices, on status and the sensitivity parameter. Specifically, maximum inequality can be given by the distribution which is the most concentrated in the top or bottom category, or by the uniform distribution.

A method is derived for estimating a discrete choice model incorporating heteroscedasticities to reflect repeated measurement problems. Heterogeneity of each observation is characterised by a specific scale function and individual heterogeneity is introduced in the random utility choice model. This research proves that the unobserved influences affecting a specific individuals' mode choice are correlated from one of his or her selections to the next repeated questions. This research also suggest a strong evidence of learning effect, implying variances would be decrease as the responses faces repeated questions.

Based on the Jones (1971) model, we construct two dynamic models of international trade in which the rate of time preference is either constant or time-varying. The main purpose is to study whether and under what conditions the results derived in the Jones model still hold in the dynamic framework. It is shown that the results of dynamic models may be similar or different to those obtained in the static model. For example, it is possible that, in both static and dynamic models, an increase in the commodity price raises this commodity's output and the return to the specific factor in this sector. However, the effects on the wage rate may be different due to the factor accumulation impact in the dynamic framework.

To present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.

Programming completely in C++.

Five compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.

The detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.

Distributed photovoltaic (DPV) projects generally have output risks, and the production effort of the supplier is often private information, so the buyer needs to design the optimal procurement contract to maximise its procurement utility.

Based on the principal-agent theory, we design optimal procurement contracts for DPV projects with fixed payments and incentive factors under three situations, i.e. symmetry information, asymmetry information without monitoring and asymmetry information with monitoring. We obtain the optimal production effort and expected utility of the supplier, the expected output and expected utility of the buyer and analyse the value of the information and monitoring.

The results show that under asymmetric information without monitoring, risk-averse suppliers need to take some risk due to output risk, which reduces the optimal production effort of the supplier and the expected output and expected utility of the buyer. Therefore, when the monitoring cost is below a certain threshold value, the buyer can introduce a procurement contract with monitoring to address the asymmetry information. In addition, under asymmetric information without monitoring, the buyer should choose a supplier with a low-risk aversion.

Considering the output risk of DPV projects, we study the optimal procurement contract design for the buyer under asymmetric information. The results provide some theoretical basis and management insights for the buyer to design optimal procurement contracts in different situations.

The purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.

To provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.

In this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.

In this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

Considering the financial service providers’ (FSPs) information asymmetry in evaluating the supplier and their distinct quit probabilities, we want to examine the supplier’s preference of the financing schemes if both the bank and the online platform exist and how the buyer sets the contract terms in the two financing schemes.

We establish a Stackelberg game model to capture the interactions among three parties, i.e. a supplier, a capital-sufficient buyer and an FSP (either a bank or an online platform), within a first-time contract.

In the non-FSPs’ quit case, the buyer’s profit is higher under the bank loan scenario, while the supplier’s profit performs adversely. The supply chain’s profit is heavily dependent on the buyer’s profit difference between the two financing schemes. Moreover, we find that the supplier borrows the money to exactly cover the production cost. The equilibrium solutions of the FSPs’ quit case and of the capital-sufficient supplier’s case are also derived.

First, we assign different risk profiles to different FSPs in our setting so that modeling a previously ignored but practically significant problem. Second, we innovatively take the FSP’s quit probability into account in our model. Third, we elucidate how these factors can influence the relative efficiency of the two types of financing schemes and the settings of the contract, which further complements and extends the current SCF research.