Fixed Period Of Time Research Articles

Optimal Flexibility Dispatching of Multi-Pumped Hydro Storage Stations Considering the Uncertainty of Renewable Energy

With the continuous increase in the penetration rate of renewable energy, the randomness and flexibility demand in the power system continues to increase. The main grid side of the power system vigorously develops pumped hydro storage (PHS) resources. However, the current PHS station scheduling method of a fixed time period and fixed power has lost a certain flexibility supply. In this paper, an optimal dispatching model of multi-pumped hydro storage stations is proposed to supply flexibility for different regions of the state grid in east China. Firstly, the credible predictable power (CPP) of renewable energy is calculated and the definition of flexibility demand of a power system is given. The calculation model for flexibility demand is established. Secondly, considering the regional allocation constraint in the state grid in east China, a non-centralized model of multi-PHS within the dispatch scope is established. In the model, the constraints of storage capacity of different hydropower conversion coefficients of each PHS station is considered. The flexibility supply model of PHS stations to each region of the state grid in east China is established to realize reasonable flexibility allocation. Then, by combining the PHS station models and the flexibility demand calculation model, the optimal dispatching model for the flexibility supply of multi-PHS stations is established. Finally, based on the network dispatching example, the effectiveness and superiority of the proposed strategy are verified by a case study.

Operant ethanol self-administration behaviors do not predict sex differences in continuous access home cage drinking

Understanding sex differences in disease prevalence is critical to public health, particularly in the context of alcohol use disorder (AUD). The goal of this study was to understand sex differences in ethanol drinking behavior and define the precise conditions under which sex differences emerge. Consistent with prior work, C57BL/6J females drank more than males under continuous access two-bottle choice conditions. However, using ethanol self-administration - where an operant response results in access to an ethanol sipper for a fixed time period - we found no sex differences in operant response rates or ethanol consumption (volume per body weight consumed, as well as lick behavior). This remained true across a wide range of parameters including acquisition, when the ethanol sipper access period was manipulated, and when the concentration of the ethanol available was scaled. The only sex differences observed were in total ethanol consumption, which was explained by differences in body weight between males and females, rather than by sex differences in motivation to drink. Using dimensionality reduction approaches, we found that drinking behavior in the operant context did not cluster by sex, but rather clustered by high and low drinking phenotypes. Interestingly, these high and low drinking phenotypes in the operant context showed no correlation with those same categorizations in the home cage context within the same animals. These data underscore the complexity of sex differences in ethanol consumption, highlighting the important role that drinking conditions/context plays in the expression of these differences.

Generalized Early Stopping in Evolutionary Direct Policy Search

Lengthy evaluation times are common in many optimization problems such as direct policy search tasks, especially when they involve conducting evaluations in the physical world, e.g. in robotics applications. Often when evaluating solution over a fixed time period it becomes clear that the objective value will not increase with additional computation time (for example when a two wheeled robot continuously spins on the spot). In such cases, it makes sense to stop the evaluation early to save computation time. However, most approaches to stop the evaluation are problem specific and need to be specifically designed for the task at hand. Therefore, we propose an early stopping method for direct policy search. The proposed method only looks at the objective value at each time step and requires no problem specific knowledge. We test the introduced stopping criterion in five direct policy search environments drawn from games, robotics and classic control domains, and show that it can save up to \(75\%\) of the computation time. We also compare it with problem specific stopping criteria and show that it performs comparably, while being more generally applicable.

Compound Conway-Maxwell Poisson Gamma Distribution: Properties and Estimation

The distribution of a random sum of random events is called a compound distribution. It involves a counting (discrete) distribution to model the number of occurrences of the random event in a fixed time period and a continuous distribution to model the outcome of the random event. It has applications in the fields of actuarial sciences, meteorology etc. For example, in modelling insurance loss amounts through compound distributions, the number of claims and the claim amounts are used to calculate the total claim amount of a portfolio. The number of claims is modelled through a discrete distribution and the claim amounts are modelled through continuous distributions. Generally, Poisson distribution is used in compound models as the discrete distribution and such models are known as compound Poisson models. However, the equi-dispersion property of the Poisson distribution hinders its application in scenarios where the underlying count data is either over- or under-dispersed. In this paper, a two-parameter Poisson distribution, namely, Conway-Maxwell Poisson (CMP) distribution, which handles both over- and under-dispersed data, is considered as the counting distribution, and the corresponding compound CMP distribution is developed. Some mathematical properties of the distribution are derived and a methodology to estimate the parameters using the likelihood approach is proposed. A numerical illustration of the proposed methodology is given through a simulation study. An application of the compound CMP model is illustrated through transportation security administration (TSA) insurance claim data. Also, the estimation of the risk measures associated with the TSA claim data is discussed.

Role of multiplicity in examination oriented teaching destroying mathematics quality education

Today the teacher does not focus on knowledge oriented but on result oriented teaching of mathematics in which s(he) focuses on the probable topics that may be asked in mid and end term examinations, so that maximum students can get good grades. Feedback from students and student centric teaching has bounded a teacher to complete the curriculum within a fixed time period and the students’ examination centric study has compelled the teachers to focus on examination oriented teaching. The concept of multiplicity plays an important role in it. Introducing its concepts in definitions, properties, named theorems and examples, we get the concept of recent trends of examination oriented teaching of mathematics. In the paper it has been shown that how the role of multiplicity is applied and how it has been destroying mathematics quality education.

A new statistical methodology using the sine function: Control chart with an application to survival times data.

Statistical methodologies have a wider range of practical applications in every applied sector including education, reliability, management, hydrology, and healthcare sciences. Among the mentioned sectors, the implementation of statistical models in health sectors is very crucial. In the recent era, researchers have shown a deep interest in using the trigonometric function to develop new statistical methodologies. In this article, we propose a new statistical methodology using the trigonometric function, namely, a new trigonometric sine-G family of distribution. A subcase (special member) of the new trigonometric sine-G method called a new trigonometric sine-Weibull distribution is studied. The estimators of the new trigonometric sine-Weibull distribution are derived. A simulation study of the new trigonometric sine-Weibull distribution is also provided. The applicability of the new trigonometric sine-Weibull distribution is shown by considering a data set taken from the biomedical sector. Furthermore, we introduce an attribute control chart for the lifetime of an entity that follows the new trigonometric sine-Weibull distribution in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested chart is investigated using the average run length. A comparative study and real example are given for the proposed control chart. Based on our study of the existing literature, we did not find any published work on the development of a control chart using new probability distributions that are developed based on the trigonometric function. This surprising gap is a key and interesting motivation of this research.

Peak Demand Minimization via Sliced Strip Packing

We study the Non-preemptive Peak Demand Minimization (NPDM) problem, where we are given a set of jobs, specified by their processing times and energy requirements. The goal is to schedule all jobs within a fixed time period such that the peak load (the maximum total energy requirement at any time) is minimized. This problem has recently received significant attention due to its relevance in smart-grids. Theoretically, the problem is related to the classical strip packing problem (SP). In SP, a given set of axis-aligned rectangles must be packed into a fixed-width strip, such that the height of the strip is minimized. NPDM can be modeled as strip packing with slicing and stacking constraint: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions where two slices of the same rectangle are intersected by the same vertical line. Non-preemption enforces the slices to be placed in contiguous horizontal locations (but may be placed at different vertical locations). We obtain a (5/3+varepsilon )-approximation algorithm for the problem. We also provide an asymptotic efficient polynomial-time approximation scheme (AEPTAS) which generates a schedule for almost all jobs with energy consumption (1+varepsilon ) {textrm{OPT}}. The remaining jobs fit into a thin container of height 1. This AEPTAS is used as a subroutine to acquire the (5/3+varepsilon )-approximation algorithm. The previous best result for NPDM was a 2.7-approximation based on FFDH (Ranjan et al., in: 2015 IEEE symposium on computers and communication (ISCC), pp 758–763, IEEE, 2015). One of our key ideas is providing several new lower bounds on the optimal solution of a geometric packing, which could be useful in other related problems. These lower bounds help us to obtain approximative solutions based on Steinberg’s algorithm in many cases. In addition, we show how to split schedules generated by the AEPTAS into few segments and to rearrange the corresponding jobs to insert the thin container mentioned above, such that it does not exceed the bound of (5/3+varepsilon ) {textrm{OPT}}.

Real-world changes in costs over time among patients in the United States with hereditary angioedema on long-term prophylaxis with lanadelumab

AimsInvestigate trends in paid lanadelumab costs over time in a population of patients persistent for 18 months, and to understand overall hereditary angioedema (HAE) treatment cost trends, including costs of acute medication/short-term prophylaxis and supportive care. Lastly, we sought to describe the proportion of lanadelumab patients with evidence of down titration via changes in total paid amounts for lanadelumab in a fixed time period.MethodsPatients were identified in the Merative MarketScan Databases who had ≥1 claim for lanadelumab during 1/1/2018-6/30/2022 (index), a ≤ 60-d gap in days of supply over 18 months, and were enrolled for ≥6 months pre-index and 18 months post-index. Lanadelumab and HAE-specific costs were assessed during follow-up months 0–6, 7–12, and 13–18. Down titration was defined as a ≥ 25% decrease in lanadelumab costs from months 0–6 to months 7–12 or 13–18. Outcomes were compared between time periods using paired t-tests and McNemar’s test.ResultsFifty-four lanadelumab users were included; 25 (46%) had evidence of down titration. Lanadelumab costs decreased from $316,724 to $269,861 to $246,919 in months 0–6, 7–12, and 13–18, respectively (p < .01); total HAE treatment costs decreased from $377,076 to $329,855 to $286,074 in months 0–6, 7–12, and 13–18, respectively (p < .01).LimitationsPersistence was determined via days of supply on medication claims; use of the medication was not confirmed. Down titration was based on costs; the lanadelumab regimen could not be assessed. Results may not be generalizable to uninsured patients or those without commercial or Medicare insurance.ConclusionsPatients on long-term prophylaxis with lanadelumab experienced a significant reduction (24%) in HAE treatment costs over 18 months, driven by lower costs of acute medications and lanadelumab down titration. Down titration among appropriate patients with controlled HAE may lead to substantial savings in healthcare costs.

Long-term opioid treatment and endocrine measures in chronic non-cancer pain patients.

The prevalence of chronic non-cancer pain (CNCP) has increased dramatically the past decades, which combined with indiscriminate use of prescribed opioids has become a public health problem. Endocrine dysfunction may be a complication of long-term opioid treatment (L-TOT), but the evidence is limited. This study aimed at investigating the associations between L-TOT and endocrine measures in CNCP patients. Cortisol (spot and after stimulation), thyrotropin (TSH), thyroxin (T4), insulin-like growth factor 1 (IGF-1), prolactin (PRL), 17-hydroxyprogesterone, androstenedione, dehydroepiandrosterone (DHEAS), sex hormone-binding globulin (SHBG), total testosterone (TT) and free testosterone (fT) were measured. Group comparisons were done between CNCP patients in L-TOT and controls as well as between patients on high- or low-dose morphine equivalents. Eighty-two CNCP patients (38 in L-TOT and 44 controls not receiving opioids) were included. Low TT (p = 0.004) and fT concentrations (p < 0.001), high SHBG (p = 0.042), low DEAS (p = 0.017) and low IGF-1 (p = 0.003) in men were found when comparing those in L-TOT to controls and high PRL (p = 0.018), low IGF-1 standard deviation score (SDS) (p = 0.006) along with a lesser, but normal cortisol response to stimulation (p = 0.016; p = 0.012) were found when comparing L-TOT to controls. Finally, a correlation between low IGF-1 levels and high opioid dose was observed (p < 0.001). Our study not only supports previous findings but even more interestingly disclosed new associations. We recommend future studies to investigate endocrine effects of opioids in larger, longitudinal studies. In the meanwhile, we recommend monitoring endocrine function in CNCP patients when prescribing L-TOT. This clinical study found associations between L-TOT, androgens, growth hormone and prolactin in patients with CNCP compared to controls. The results support previous studies as well as add new knowledge to the field, including an association between high opioid dose and low growth hormone levels. Compared to existing research this study has strict inclusion/exclusion criteria, a fixed time period for blood sample collection, and adjustments for potential confounders, which has not been done before.

Comparison of Academic Results during Conventional and Online Modes of Learning: A Case Study of Two Groups of Saudi University Students

The COVID-19 outbreak disrupted all aspects of people’s lives, including pedagogy and instruction at universities, where its impact was felt globally, and the Kingdom of Saudi Arabia is no exception. This paper discusses and compares the academic results during the conventional mode of learning (spring semester of 2019) and during the online mode of learning (spring semester of 2020), which was throughout the pandemic period. Specifically, the study considers two Saudi groups of fifty students who were enrolled in the Department of Health Information Management and Technology at the University of Hafr Al-batin in the eastern region of Saudi Arabia. The students’ accumulative marks in six first-year courses in two semesters were analyzed and compared by calculating the passing/failure percentages, descriptive statistics (mean, median, mode, standard deviation, variance, maximum, minimum, and range), and the p-value of an inferential t-test. Additionally, the students filled out a six-category survey about their experiences and level of satisfaction with online learning compared to the regular learning mode. It was concluded that more students passed with higher grades in the year 2020 in five theoretical courses. Differently, it was deduced that practical courses such as computer applications had similar passing averages in the two years; the course required students to submit continuous assignments and projects in a fixed time period. Additionally, the participants revealed in their filled online survey that they preferred many features of the remote learning mode and the online assessment methodology. They inclined toward online learning for its flexibility and effectiveness, even though they confessed to having less interaction and focus during online sessions. Thus, the results imply to authorities in the Ministry of Higher Education to carefully and gradually embed online teaching for selected subjects with exam validation measures such as time strict limits, question banks, randomizations, and other security features.

Investigation of novel ligand targeting bromodomain-containing protein 4 (BRD4) for cancer drug discovery: complete pharmacophore approach

The Bromodomain (BRD4) and extra-terminal (BET) protein family are reversible; lysine-acetylated epigenetic readers identified as key important epigenetic regulators for protein recognition in posttranslational modifications for targeting cancer for its role in super-enhancers and transcription of oncogene expression in cancer and other forms of cancer and various diseases. Firstly, JQ-1a small potent BET inhibitors, targeting BET proteins were currently in clinical trials to ablate cancer. The identified compounds were taken from the library of preexisting therapeutically potent molecules. The objective of the present study is to identify the potential small molecule inhibitors against BRD4 through in-silico approach for the treatment of cancer. In present study, designed an in-silico screening of small molecules through ligand-based pharmacophore studies against bromodomain-containing protein 4 (BRD-4) protein and used for virtual screening through Database and their binding affinity and interaction of identified molecules were predicted through molecular docking, molecular dynamics simulations for 12 fixed time period, Molecular mechanics (MMGBSA) binding free energy calculations, ADME with drug-likeness properties including violations of lipinski's rule of 5, Jorgensens rule of 3 and other parameters were studied. The docking results indicate from the reported database screened molecules were validated with docking score −7.92 to −4.27Kcal/mol for BRD4-BD1 and the best model identified 21 hits. Among these two drugs were filtered and scrutinized for their ability based on binding modes and common interaction, MMGBSA of the highest affinity −54.53 Kcal/mol of BRD4-BD1 and ADME properties of selected molecules were predicted for its various parameters, dynamics studies evaluating its binding stability using Maestro software. In Conclusion, two BRD4 inhibitors were found to bind strongly in the similar binding sites as JQ-1, highlighting the role of BRD4-BD1. These compounds were identified as promising new options for regulating epigenetics and understanding the structural needs of BRD4 protein, further research in these areas could lead to the development of more effective and targeted cancer drugs.Communicated by Ramaswamy H. Sarma

Care coordination for healthcare referrals under a shared‐savings program

Accountable care organizations (ACOs) are responsible for the quality and cost of care of specified patient populations, including the cost of referrals. Motivated by this environment, we study care coordination for healthcare referrals. We consider an ACO that refers an uncertain number of patients from its attributed population to a preferred external provider for specialized health services. ACOs are typically paid under the Medicare Shared Savings Program (MSSP). Under the MSSP, the payer sets a spending benchmark for the beneficiary population during a fixed time period and shares any gains (losses) relative to it with the ACO. During the billing period, all services delivered to the attributed population by the ACO and external providers continue to be reimbursed under fee‐for‐service. Gains (losses) are determined at the end of the period by comparing the actual spending, which includes all care expenses (regular visits, referrals, and failed treatments) incurred by the payer in the period to the predefined benchmark. In this environment, the ACO and external providers—the latter not compensated under the MSSP—lack incentives to invest enough in care coordination initiatives. We study financial incentive mechanisms between the ACO and its preferred external provider to achieve integrated care coordination in referral markets under the MSSP. We show that traditional fee‐for‐service and capitation agreements do not provide sufficient incentives for care coordination in referral markets. However, a risk‐ and cost‐sharing mechanism can induce integrated care coordination efforts while satisfying the ACO and provider's participation constraints. We characterize a family of such mechanisms and numerically study the variability of the ACO and the external provider's profit. We demonstrate that this type of agreement can be used not only to induce integrated care coordination but can also result in a Pareto improvement in profit variability. We also illustrate the impact of the different MSSP risk tracks parameters on the performance of this care coordination mechanism, including their effect on the quality of care and the payer's mean spending.

Теоретичната инверсия на Асен Игнатов – основания и следствия

The article’s task is to generally clarify the grounds for the theoretical reversal in Asen Ignatov’s concepts by diachronically pointing out the main theoretical changes in them. At the same time, synchronic analysis is related to indicating general attitudes, ideological and political frameworks, and actions during the fixed time period. This would allow us to go beyond the personal reasons for such a transition, and to build a more complete picture of this inversion respectively, both in theoretical and socio-political terms. The article seeks to reveal what the consequences are of perceiving the dogmatic limitation of Marxism in socialist countries, as well as Ignatov’s position on this. In this way, the synergistic action of the various factors studied would expand the possibility of a truer understanding of the events in Ignatov’s creative life after his emigration in 1972.

Several Methods of Inventory Control

This paper would firstly introduce the Single-Period Inventory Model, a basic method of inventory control. By analyzing the Newsvendor Problem which is a simplified situation of storing inventories, this paper would discover a method using normal distribution analysis to solve the problem. Then, the paper would promote the adoption of this method into realistic inventory problems and discuss its utility. Secondly, the topic is expanded to Multi-Period Inventory System. This system focus on a more sophisticated inventory situation, and it could be basically categorized into two models: fixed-order quantity model, and fixed time period model. The paper would discuss the methods of ordering determination of the two models respectively.

Demurrage pattern analysis using logical analysis of data: A case study of the Ulsan Port Authority

Maritime logistics, which accounts for around 80% of international trade around the world, has been a driving force for economic growth. Increases in maritime traffic, however, lead to increased congestion in berths and terminals. This congestion in turn negatively affects the total ship turnaround time and leads to decreased efficiency in port operations and a higher demurrage rate, which refers to the number of vessels in queue for more than a fixed time period waiting to load/unload out of the total number of vessels entering a port. The demurrage rate directly affects a port’s operating profits; thus, this rate needs to stay as low as possible. In this study, we focus on developing a methodology to address the demurrage rate of a port. To this end, we first collect two sets of vessel data (2016 annual data for training and 2019 annual data for validating) for ships entering and leaving the Port of Ulsan in the Republic of Korea and integrate these datasets with berth data and weather data. We tailor the logical analysis of data (LAD) technique to derive the patterns from the training data that mitigate or aggravate the demurrage rate. We use these patterns to predict the demurrage rate for the validating set of data. The overall binary classification results demonstrate the proposed LAD technique’s competitive performance, compared with other state-of-the-art machine learning methods. We then analyze the patterns to derive policy suggestions that can lower the demurrage rate at the Port of Ulsan. Our computational experiments find that the availability of tugs or pilots and port arrival times mainly affect the demurrage rate at the Port of Ulsan. Finally, our study showcases new possibilities for using patterns of demurrage and non-demurrage vessels obtained by LAD to help policymakers and port operators address the growing demurrage problem.

Continuous Nonintrusive Mobile Device Soft Keyboard Biometric Authentication

Mobile banking, shopping, and in-app purchases utilize persistent authentication states for access to sensitive data. One-shot authentication permits access for a fixed time period. For instance, a username/password-based authentication allows a user access to all the shopping and payments data in the Amazon shopping app. Traditional user passwords and lock screens are easily compromised. Snooping attacks—observing an unsuspecting user entering passwords—and smudge attacks—examining touchscreen finger oil residue—enable compromised user authentication. Mobile device interactions provide robust human and device identity data. Such biometrics enhance authentication. In this paper, behavioral attributes during user input constitute the password. Adversary password reproduction difficulty increases since pure observation is insufficient. Current mobile continuous authentication schemes use, among others, touchscreen–swipe interactions or keyboard input timing. Many of these methods require cumbersome training or intrusive authentication. Software keyboard interactions provide a consistent biometric data stream. We develop biometric profiles using touch pressure, location, and timing. New interactions authenticate against a profile using a divergence measure. In our limited user–device data sets, the classification achieves virtually perfect accuracy.

Franchise network relationships and word of mouth communication in social media networks

Franchisor efforts to increase brand value by connecting and interacting with current and potential customers on social media platforms benefit the franchisor as well as franchisees in a franchise network and strengthen franchisor-franchisee relationships by stimulating customer-to-customer interaction, word of mouth (WOM) communication, and co-creation of value in social media networks. This study examines how the size of a franchise network impacts WOM communication in social media networks. It empirically investigates hypotheses linking franchise network size to WOM in social media networks via two types of customer engagement behavior: (1) loyalty to the brand, and (2) liking of the brand. Structural equation models are estimated for franchise networks in the top 200 U.S. restaurants with data from Twitter for two samples: restaurants with tweets during a fixed time period, and restaurants with a fixed number of tweets. The results indicate that loyalty and liking mediate the relationship between franchise network size and WOM in social media networks. Franchise network sales has a positive relationship with loyalty, which has a positive relationship with liking, which has a positive relationship with WOM communication. Split-sample analysis indicates that franchise network units matters only when the proportion of restaurants in the network owned by franchisees exceeds 75%. Growing the franchise network enhances loyalty and provides an opportunity for bespoke communications that customers like and spread, generating buzz about the brand.

Attribute Control Charts Based on TLT for Length‐Biased Weighted Lomax Distribution

The length‐biased weighted Lomax distribution (LBWD) is a novel continuous of two parameters lifetime distribution. In this article, we introduced an attribute control chart (CC) for the lifetime of a product that follows the LBWD in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested charts is investigated using in term of the average run length (ARL). The necessary tables of shift sizes and various sample sizes are offered for numerous values of the distribution parameters as well as specified ARL and shift constants. Some numerical examples are discussed for various scheme parameters to study the performance of the new LBWD attribute control charts.

Two surface multipactor discharge with two-frequency rf fields and space-charge effects

This paper presents two-surface multipactor discharge with two-frequency rf fields using Monte Carlo simulations and Computer Simulation Technology (CST) Particle Studio. The effects of the relative strength and phase of the second carrier mode on multipactor susceptibility and time dependent physics are studied. Compared to single-frequency rf operation, shrinkage of multipactor susceptibility regions is observed for different configurations of two-frequency rf operation. The presence of a second carrier mode in the rf field results in mixed multipactor modes in which electrons take a fixed time period to complete a round trip between the two surfaces, while the time for electrons to traverse the gap in each direction is found to be different. CST simulation reveals that the space-charge effect reduces the electron growth rate and causes shrinkage of multipactor susceptibility bands.

Joint Design of UAV Trajectory and Directional Antenna Orientation in UAV-Enabled Wireless Power Transfer Networks

In this work, we investigate an unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) network with multiple ground sensor nodes (SNs). A UAV is operated at a fixed altitude with a directional antenna array and is designed to wirelessly transfer energy to the SNs. We consider a non-linear energy harvesting (EH) model and a directional antenna structure of uniform linear array (ULA) where we apply an analog directional beamforming scheme. Taking the fairness issue into account, we consider a problem aiming at maximizing the minimum harvested energy among all SNs during a fixed time period by jointly optimizing the UAV trajectory and the orientation of the directional antenna on the UAV. However, the complex antenna pattern expression of analog directional beamforming and the implicit non-linear function in the EH model introduce significant difficulties in handling the non-convex problem of the joint design. To tackle these difficulties, we propose and adopt a modified approximate antenna pattern model, i.e., a modified cosine antenna pattern, and reformulate the original problem via quantizing the UAV trajectory in the time domain. Later, by employing a convex property in the EH model and a proved lemma, we successfully construct a tight convex approximation for the reformulated problem, based on which the problem can be solved via a proposed iterative algorithm and the objective converges to an efficient suboptimal solution. Finally, we provide numerical results to confirm the convergence of the proposed algorithm, examine the approximation error and evaluate the system performance. The results show the performance advantage of the directional antenna in UAV-enabled WPT networks than the omni-directional antenna case, and illustrate how the directional antenna of the UAV overcomes its coverage limitation