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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.

The main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.

This article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.

The proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.

The fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.

The network capacity deployed to manage the busy hour (or peak-hour) traffic remains underused during the nonbusy (off-peak) hours. Transferring some traffic from peak-hour to off-peak hours is likely to improve the utilization of network resources during the off-peak hours. This paper aims to examine whether diverting traffic from peak-hour to off-peak hours is possible by adopting the differential pricing policy.

The peak-load pricing theory suggests that the policy of differential pricing is socially optimal when there is peak demand for a particular duration and then there is off-peak demand. In this study, hourly traffic data from both peak and off-peak periods were collected from the Indian telecom service provider, “Aircel.” The paper analyzed the disparity in traffic between peak and off-peak hours using the nonparametric Tukey’s test. An experiment was also conducted to analyze whether a significant shift in telecom traffic occurs from the peak to the off-peak period when a price discount is applied during the off-peak period.

Statistically significant differences were observed in network traffic between peak-hour and off-peak hours. The network utilization of the telecom service provider Aircel was notably lower, particularly during the off-peak hours. The experiment demonstrated a high degree of price sensitivity among telecom service subscribers. Telecom Regulatory Authority of India (TRAI) has not considered network utilization of telecom service providers as a key performance indicator. Based on the outcomes of the study, this paper recommends that TRAI should adopt a more proactive approach by encouraging telecom service providers to follow the policy of differential pricing to enhance utilization of their network capacity.

To the best of the authors’ knowledge, this is the first paper to explore the issue of pricing as a tool for bringing about more uniform movement of telecom traffic, thereby enhancing network utilization within India’s telecommunications sector.

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.

Spurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment.

In this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box–Jenkins forecasting method is employed to diminish the demand uncertainty.

An appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term.

Applying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box–Jenkins method to reduce uncertainty are the contributions of the present study.

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.