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This paper investigates the temporal inflow profile that minimises the total cost of travel for a single route. The problem is formulated to consider the case in which the total demand to be serviced is fixed. The approach used here is a direct calculation of the first order variation of total system cost with respect to variations in the inflow profile. Two traffic models are considered; the bottleneck with deterministic queue and the kinematic wave model. For the bottleneck model a known solution is recovered. The wave model proves more difficult and after eliminating the possibility of a smooth inflow profile the restricted case of constant inflow is solved. As the space of possible profiles is finite dimensional in this case, the standard techniques of calculus apply. We establish a pair of equations that are satisfied simultaneously by the optimal inflow and time of first departure.

This paper aims to provide a mathematical modeling and design of H-infinity controller for an autonomous vertical take-off and landing (VTOL) Quad Tiltrotor hybrid unmanned aerial vehicles (UAVs). The variation in the aerodynamics and model dynamics of these aerial vehicles due to its tilting rotors are the key issues and challenges, which attracts the attention of many researchers. They carry parametric uncertainties (such as non-linear friction force, backlash, etc.), which drives the designed controller based on the nominal model to instability or performance degradation. The controller needs to take these factors into consideration and still give good stability and performance. Hence, a robust H-infinity controller is proposed that can handle these uncertainties.

A unique VTOL Quad Tiltrotor hybrid UAV, which operates in three flight modes, is mathematically modeled using Newton–Euler equations of motion. The contribution of the model is its ability to combine high-speed level flight, VTOL and transition between these two phases. The transition involves the tilting of the proprotors from 90° to 0° and vice-versa in 15° intervals. A robust H-infinity control strategy is proposed, evaluated and analyzed through simulation to control the flight dynamics for different modes of operation.

The main contribution of this research is the mathematical modeling of three flight modes (vertical takeoff–forward, transition–cruise-back, transition-vertical landing) of operation by controlling the revolutions per minute and tilt angles, which are independent of each other. An autonomous flight control system using a robust H-infinity controller to stabilize the mode of transition is designed for the Quad Tiltrotor UAV in the presence of uncertainties, noise and disturbances using MATLAB/SIMULINK. This paper focused on improving the disturbance rejection properties of the proposed UAV by designing a robust H-infinity controller for position and orientation trajectory regulation in the presence of uncertainty. The simulation results show that the Tiltrotor achieves transition successfully with disturbances, noise and uncertainties being present.

A novel VTOL Quad Tiltrotor UAV mathematical model is developed with a special tilting rotor mechanism, which combines both aircraft and helicopter flight modes with the transition taking place in between phases using robust H-infinity controller for attitude, altitude and trajectory regulation in the presence of uncertainty.

Using information systems via data mining and cluster analysis technologies, consumers' strategic behaviour can be measured, and their patience levels can be accurately described. This paper investigates the retailer's pricing and ordering policies when facing strategic consumers with different levels of patience and discusses the impacts of consumers' patience levels and proportions on retailers' maximum expected profits.

By cluster analysing transaction data on the number of websites visited, browsing time and purchase decision time, consumers' patience levels can be obtained. The authors formulate a newsvendor model considering customers' different patience levels. Three scenarios are investigated: two segments of consumers with two different levels of patience (Scenario I), multiple segments of consumers with different levels of patience (Scenario II) and a continuum of consumers whose levels of patience follow a continuous distribution (Scenario III). Then, general formulas are deduced for retailers' optimal prices, ordering quantities and profits.

Under Scenario I, if the proportion of less patient consumers is greater (less) than a threshold, the retailer's optimal price is equal to the less (more) patient consumers' reserve price. Under Scenario II, once the proportion of fully strategic consumers exceeds a certain threshold, the retailers' optimal price is equal to the fully strategic consumers' reserve price regardless of consumers' patience levels and proportions. Under Scenario III, the retailer's pricing and ordering policies depend on the distribution of their patience level.

Few studies have considered consumers' different levels of patience when making retailer pricing and ordering decisions. In this paper, strategic consumer behaviour is measured, and consumers' patience levels and proportions are obtained by cluster analysing consumer transaction data recorded by an information system. Three scenarios in which strategic consumers may be heterogeneous and have different patience levels are investigated. The results can guide retailer decision-making.

This paper aims to investigate the underlying process by which a brand’s unit pricing for multiple package sizes influences consumer evaluations by incorporating several mediators and moderators. Two-unit pricing tactics were examined: quantity discounts and surcharges.

Two online experiments were conducted to test the hypotheses. Study 1 examined the mediating role of consumers’ inferred motive for sellers in setting quantity discounts or surcharges in the relationship between the pricing tactics and consumer evaluations. Study 2 incorporated affect as a mediator, and price consciousness and unit price usage as moderators in this relationship.

The mediating role of inferred motive is supported. Motive is related to the sales volume. Furthermore, this mediation effect is more potent when consumers have stronger quantity discount belief. Further, the mediating role of affect is supported. It is more salient when consumers are frequent users of unit prices.

This study compared two pricing tactics and did not include a control condition. The first digit of the unit price for the small package size was different between the pricing tactics.

When applying quantity surcharges to products, it is essential to provide additional information to consumers to preclude the possibility of negative evaluations.

This study makes a significant contribution by offering a deeper understanding of consumer responses to the pricing tactics. In particular, it reveals that pricing tactics trigger both cognitive and affective responses, which then influence evaluations of the pricing tactics. This elicited cognition is associated with deduction about sellers’ brand-size pricing behavior.

In this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.

Theoretical method.

We establish some coincidence points and common fixed point results in partial metric spaces.

Results of this study are new and interesting.

Let E be an elliptic curve with Weierstrass form y2=x3−px, where p is a prime number and let E[m] be its m-torsion subgroup. Let p1=(x1,y1) and p2=(x2,y2) be a basis for E[m], then we prove that ℚ(E[m])=ℚ(x1,x2,ξm,y1) in general. We also find all the generators and degrees of the extensions ℚ(E[m])/ℚ for m=3 and m=4.

This study investigates a production process that requires N kinds of components for the production of a finished product. The producer orders the various kinds of components from different suppliers and receives the orders in lots at the beginning of each production cycle. Similar to situations often encountered in real life, the lead times are random variables with known probability distributions so that a production cycle starts whenever all N kinds of components become available. Each of the lots received at the start of a production run contains both perfect and imperfect quality components. Once all N kinds of components become available, the producer initiates a screening process to detect the imperfect components. The production of the finished product uses only perfect quality components. The imperfect components are removed from inventory whenever the screening process is completed. The percentage of components of perfect quality present in each lot is a random variable with a known probability distribution.

This production process is described and modeled mathematically and the optimal production/ordering policy is derived based on the mathematical model.

The formulated mathematical model resulted in the determination of the optimal policy consisting of the optimal number of finished items ordered to be produce during each production run, the number of components ordered from each supplier, and the reorder point. The derived closed form expression for the optimal lot size depends on the minimum of the number of perfect quality components in a lot, whereas the reorder point is determined based on the maximum lead time.

The modeling approach and results of this study provide practical implications that may be beneficial to both production and supply chain managers as well as researchers.

This modeling approach that incorporates decision-making related to the logistics of acquiring the components and accounts for the probabilistic nature of the lead times and quality of components addresses a gap in the logistics/production literature.

With the advent of the web computing era, the transmission mode of the Internet of Everything has caused an explosion in data volume, which has brought severe challenges to traditional routing protocols. The limitations of the existing routing protocols under the condition of rapid data growth are elaborated, and the routing problem is remodeled as a Markov decision process. this paper aims to solve the problem of high blocking probability due to the increase in data volume by combining deep reinforcement learning. Finally, the correctness of the proposed algorithm in this paper is verified by simulation.

The limitations of the existing routing protocols under the condition of rapid data growth are elaborated and the routing problem is remodeled as a Markov decision process. Based on this, a deep reinforcement learning method is used to select the next-hop router for each data transmission task, thereby minimizing the length of the data transmission path while avoiding data congestion.

Simulation results show that the proposed method can significantly reduce the probability of data congestion and increase network throughput.

This paper proposes an intelligent routing algorithm for the network congestion caused by the explosive growth of data volume in the future of the big data era. With the help of deep reinforcement learning, it is possible to dynamically select the transmission jump router according to the current network state, thereby reducing the probability of congestion and improving network throughput.

Recent models in firm theory assume that problems have to be solved for production to take place and that knowledge is the main input for problem-solving. This paper characterizes the relationship between the predictability of production prcesses and investment in knowledge.

This paper uses a theoretical model of firm theory to study investment in knowledge by a simplified one-layer firm with a stochastic technology, across different market structures, and develops a calibration exercise to illustrate the results.

Firms working closer to the production frontier (those with a larger efficient scale in perfect competition, facing a higher demand in monopoly or more competitive internationally in an open economy) react more in terms of investment in knowledge when problem predictability changes. Investment in knowledge becomes nearly insensitive to such changes for firms with a low output, i.e. those far from the frontier. A calibration exercise suggests that the elasticity of knowledge with respect to the predictability of problems was around 0.59 for the US economy for the period 1980–2020.

These are the first nonambiguous results on the relationship between the predictability of production processes and investment in knowledge and help understanding knowledge acquisition by different firms in distinct competitive environments.

In recent years, the application of robots in different industrial sectors such as nuclear power generation, construction, automobile, firefighting and medicine, etc. is increasing day by day. In large industrial plants generally humans and robots work together to accomplish several tasks and lead to the problem of safety and reliability because any malfunction event of robots may cause human injury or even death. To access the reliability of a robot, sufficient amount of failure data is required which is sometimes very difficult to collect due to rare events of any robot failures. Also, different types of their failure pattern increase the difficulty which finally leads to the problem of uncertainty. To overcome these difficulties, this paper presents a case study by assessing fuzzy fault tree analysis (FFTA) to control robot-related accidents to provide safe working environment to human beings in any industrial plant.

Presented FFTA method uses different fuzzy membership functions to quantify different uncertainty factors and applies alpha-cut coupled weakest t-norm (Tω) based approximate fuzzy arithmetic operations to obtain fuzzy failure probability of robot-human interaction fault event which is the main contribution of the paper.

The result obtained from presented FFTA method is compared with other listing approaches. Critical basic events are also ranked using V-index for making suitable action plan to control robot-related accidents. Study indicates that the presented FFTA is a good alternative method to analyze fault in robot-human interaction for providing safe working environment in an industrial plant.

Existing fuzzy reliability assessment techniques designed for robots mainly use triangular fuzzy numbers (TFNs), triangle vague sets (TVS) or triangle intuitionistic fuzzy sets (IFS) to quantify data uncertainty. Present study overcomes this shortcoming and generalizes the idea of fuzzy reliability assessment for robots by adopting different IFS to control robot-related accidents to provide safe working environment to human. This is the main contribution of the paper.