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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.

In the construction of charging piles, traditional gas stations possess significant advantages in terms of regional and financial resources. The transformation of gas stations into “refueling+charging” integrated gas stations relies on charging pile manufacturers and government, involving coordination issues with them. This paper aims to propose a joint coordination contract based on the principles of cost-sharing and revenue-sharing. The objective is to achieve systemic coordination among integrated gas stations, charging pile manufacturers, and the government, optimizing the planning of the quantity of charging piles and charging prices.

We have constructed an operational system model based on the Stackelberg game between charging pile manufacturers, integrated gas stations, and government. We have analyzed the optimal quantity of charging piles and charging prices under the impact of government subsidy policies in both decentralized and centralized operation scenarios. Additionally, we have proposed a joint coordination contract based on cost-sharing and revenue-sharing to coordinate this tripartite operational system.

The study reveals that, under simple cooperative contracts, the optimal decision does not yield maximum profits for the operational system due to the “double-marginal effect”. However, under the impact of the joint coordination contract, which combines cost-sharing and revenue-sharing as proposed in this paper, gas stations will consider the charging pile manufacturer’s costs and government subsidies when determining the optimal quantity and price. This not only achieves system coordination but also results in Pareto improvement in the benefits of all system members by adjusting contract parameters.

The value of this research lies in its insights into operational strategies for the construction of charging piles for electric vehicles. By analyzing optimal decisions under different contract arrangements, the study provides guidance to relevant stakeholders, enabling the operational system to achieve greater efficiency and coordination and realize more extensive Pareto improvements. Furthermore, it extends the application of coordination contract theory in the context of charging pile construction and operations.

Three-way decision (3WD) and probabilistic rough sets (PRSs) are theoretical tools capable of simulating humans' multi-level and multi-perspective thinking modes in the field of decision-making. They are proposed to assist decision-makers in better managing incomplete or imprecise information under conditions of uncertainty or fuzziness. However, it is easy to cause decision losses and the personal thresholds of decision-makers cannot be taken into account. To solve this problem, this paper combines picture fuzzy (PF) multi-granularity (MG) with 3WD and establishes the notion of PF MG 3WD.

An effective incomplete model based on PF MG 3WD is designed in this paper. First, the form of PF MG incomplete information systems (IISs) is established to reasonably record the uncertain information. On this basis, the PF conditional probability is established by using PF similarity relations, and the concept of adjustable PF MG PRSs is proposed by using the PF conditional probability to fuse data. Then, a comprehensive PF multi-attribute group decision-making (MAGDM) scheme is formed by the adjustable PF MG PRSs and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Finally, an actual breast cancer data set is used to reveal the validity of the constructed method.

The experimental results confirm the effectiveness of PF MG 3WD in predicting breast cancer. Compared with existing models, PF MG 3WD has better robustness and generalization performance. This is mainly due to the incomplete PF MG 3WD proposed in this paper, which effectively reduces the influence of unreasonable outliers and threshold settings.

The model employs the VIKOR method for optimal granularity selections, which takes into account both group utility maximization and individual regret minimization, while incorporating decision-makers' subjective preferences as well. This ensures that the experiment maintains higher exclusion stability and reliability, enhancing the robustness of the decision results.

This study examined the reciprocal influence of demand learning and preference matching in the context of store brand customization. The demand-learning effect refers to the collection of market demand information through production, based on pre-order demands, enabling retailers to accurately predict and allocate product quantities, thus improving inventory management. The preference-matching effect involves engaging consumers in the production and design processes of store brands to align fully with their preferences, thereby increasing the purchase impact of store brand products and promoting consumption.

We employ game-theoretic models to analyze a two-echelon supply chain consisting of a manufacturer and a retailer. The retailer offers both national brands, manufactured by the supplier and in-house store brands. To enhance their competitive edge, the retailer can adopt a customized strategy targeting the store brand to attract a wider consumer base.

The analysis reveals that, under low commission fees, the manufacturer consistently opts for high production quantities, irrespective of the level of demand uncertainty. However, when the perceived value of a store brand is low and demand uncertainty is either low or high, the retailer should choose a minimal or zero production quantity. The decision-making process is influenced by the customization process, wherein the effects of demand learning and preference matching occasionally mutually reinforce each other. Specifically, when the perceived value of a store brand is low, or the product cost is high, along with high customization costs, the interplay between demand learning and preference matching becomes mutually inhibiting. Consequently, the significance of store brand customization diminishes.

This study enhances the current body of knowledge by providing a deeper understanding of the theoretical value of store brand customization. In addition, it offers valuable decision-making support to enterprises by assisting them in selecting appropriate inventory and customization strategies.

The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.

First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.

Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.

This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

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.