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The importance of service firms cooperating with digital platforms is widely acknowledged. The authors study three contractual relationships (fixed-cost, cost-sharing, and profit-sharing) between service firms (specifically hotels) and digital platforms in a highly fragmented service supply chain to examine which of these contract types optimizes profits.

The authors extend prior models analyzing the optimal expected total profit from the travel service firm (hotel)–digital platform relationship, providing new insights into each contract type’s ability to coordinate decentralized systems and optimize profits for both parties.

This study finds that fixed cost contracts cannot coordinate the decentralized system. Cost-sharing contracts can coordinate the decentralized system but only allow one channel profit split. In contrast, profit-sharing contracts may not always perfectly coordinate the decentralized system but support alternative profit allocations. Practically, both profit-sharing and cost-sharing contracts are preferable to fixed-cost contracts.

The paper includes implications for travel service firm managers to consider when structuring contracts with digital platforms to focus on profit optimization. Profit-sharing contracts are most preferable when cost and revenue data are fully shared between parties, while cost-sharing contracts are preferable over fixed-cost contracts.

This study extends prior investigations into the utility of different contract types on the optimal profit of a travel service firm (hotel)-digital platform provider relationship. The research fills a gap in the literature concerning the contracts used in these relationship types.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

This paper assesses the co-movement between Pax gold and six fiat currencies. It also investigates the optimal time-varying hedge ratios in order to examine the properties of Pax gold as a diversifier and hedge asset.

This paper examines the volatility spillover between Pax gold and fiat currencies using the framework of wavelet analysis, BEKK-GARCH models and Range DCC-GARCH. Moreover, this paper proposes to use the covariance and variance structure obtained from the new range DCC-GARCH framework to estimate the time-varying optimal hedge ratios, the optimal weighs and the hedging effectiveness.

Wavelet coherence method reveals that, at low frequency, large zone of co-movements appears for the pairs Pax gold/EUR, Pax gold/JPY and Pax gold/RUB. Further, the BEKK results show unidirectional (bidirectional) transmission effects between Pax gold and EUR, GBP, JPY and CNY (INR, RUB) fiat currencies. Moreover, the Range DCC results show that the Pax gold and the fiat currency returns are weakly correlated with low coefficients close to zero. Thus, Pax gold seems to serve as a safe haven asset against the systematic risk of fiat currency markets. In addition, the results of optimal weights show that rational investor should invest more in Pax gold and less in fiat currencies. Concerning the hedge ratios results, the findings reveal that the INR (JPY) fiat currency appears to be the most expensive (cheapest) hedge for the Pax-gold market. However, the JPY’s fiat currency appears to be the cheapest one. As for hedging effectiveness results, the authors found that hedging strategies including fiat currencies–Pax gold pairs are most likely to sharply decrease the portfolio’s risk.

A comprehensive understanding of the relationship between Pax Gold and fiat currencies is crucial for refining portfolio strategies involving cryptocurrencies. This research underscores the significance of grasping volatility transmissions between these currencies, providing valuable insights to guide investors in their decision-making processes. Moreover, it encourages further exploration into the interdependencies of digital currencies. Additionally, this study sheds light on effective contagion risk management, particularly during crises such as Covid-19 and the Russia–Ukraine conflict. It underscores the role of Pax Gold as a safe-haven asset and offers practical guidance for adjusting portfolios across various economic conditions. Ultimately, this research advances our comprehension of Pax Gold’s risk-return profile, positioning it as a potential hedge during periods of uncertainty, thereby contributing to the evolving literature on cryptocurrencies.

This study’s primary value lies in its pioneering empirical examination of the time-varying correlations and scale dependence between Pax Gold and fiat currencies. It goes beyond by determining optimal time-varying hedge ratios through the innovative Range-DCC-GARCH model, originally introduced by Molnár (2016) and distinguished by its incorporation of both low and high prices. Significantly, this analysis unfolds within the unique context of the Covid-19 pandemic and the Russian–Ukrainian conflict, marking a novel contribution to the field.

Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis.

Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H₂O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach.

There is no fund for the research work.

This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells.

This investigation unfolds the hydrothermal changes of radiative water-based Fe₃O₄-Ag-MgO-H₂O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study.

Online reviews serve as valuable sources of information, reflecting tourists’ attentions, preferences and sentiments. However, although the existing research has demonstrated that incorporating online review data can enhance the performance of tourism demand forecasting models, the reliability of online review data and consumers’ decision-making process have not been given adequate attention. To address the aforementioned problem, the purpose of this study is to forecast tourism demand using online review data derived from the analysis of review helpfulness.

The authors propose a novel “identification-first, forecasting-second” framework. This framework prioritizes the identification of helpful reviews through a comprehensive analysis of review helpfulness, followed by the integration of helpful online review data into the forecasting system. Using the SARIMAX model with helpful online review data sourced from TripAdvisor, this study forecasts tourist arrivals in Hong Kong during the period from August 2012 to June 2019. The SNAÏVE/SARIMA model was used as the benchmark model. Additionally, artificial intelligence models including long short-term memory, back propagation neural network, extreme learning machine and random forest models were used to assess the robustness of the results.

The results demonstrate that online review data are subject to noise and bias, which can adversely affect the accuracy of predictions when used directly. However, by identifying helpful online reviews beforehand and incorporating them into the forecasting process, a notable enhancement in predictive performance can be realized.

First, to the best of the authors’ knowledge, this study is one of the first to focus on the data issue of online reviews on tourism arrivals forecasting. Second, this study pioneers the integration of the consumer decision-making process into the domain of tourism demand forecasting, marking one of the earliest endeavors in this area. Third, this study makes a novel attempt to identify helpful online reviews based on reviews helpfulness analysis.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

This paper aims to study passive control techniques for transonic flow over a backward-facing step (BFS) using square-lobed trailing edges. The study investigates the efficacy of upward and downward lobe patterns, different lobe widths and deflection angles on flow separation, aiming for a deeper understanding of the flow physics behind the passive flow control system.

Large Eddy Simulation and Reynolds-averaged Navier–Stokes were used to evaluate the results of the study. The research explores the impact of upward and downward patterns of lobes on flow separation through the effects of different lobe widths and deflection angles. Numerical methods are used to analyse the behaviour of transonic flow over BFS and compared it to existing experimental results.

The square-lobed trailing edges significantly enhance the reduction of mean reattachment length by up to 80%. At Ma = 0.8, the up-downward configuration demonstrates increased effectiveness in reducing the root mean square of pressure fluctuations at a proximity of 5-step height in the wake region, with a reduction of 50%, while the flat-downward configuration proves to be more efficient in reducing the root mean square of pressure fluctuations at a proximity of 1-step height in the near wake region, achieving a reduction of 71%. Furthermore, the study shows that the up-downward configuration triggers early spanwise velocity fluctuations, whereas the standalone flat-downward configuration displays less intense crosswise velocity fluctuations within the wake region.

The findings demonstrate the effectiveness of square-lobed trailing edges as passive control techniques, showing significant implications for improving efficiency, performance and safety of the design in aerospace and industrial systems.

This paper demonstrates that the square-lobed trailing edges are effective in reducing the mean reattachment length and pressure fluctuations in transonic conditions. The study evaluates the efficacy of different configurations, deflection angles and lobe widths on flow and provides insights into the flow physics of passive flow control systems.

This paper investigates the buy online and pick up in-store cooperation (BOPSC) of online and offline retailers. Specifically, this study solves the following questions: (1) What is the impact of BOPSC on their optimal price and sales volume of products? (2) When should an online retailer and an offline retailer conduct the BOPSC strategy with each other?

The paper first establishes two game models to explore the equilibriums of online and offline retailers in non-BOPSC and BOPSC. Then the condition for online and offline retailers to implement BOPSC strategy are determined. Furthermore, the applicability of the BOPSC strategy is enhanced by incorporating numerical analysis.

The study’s findings reveal that BOPSC strategy will not always beneficial to online and offline retailers, which depends on the total cost of online shopping and the product valuation of consumers. BOPSC strategy leads to the increase of prices and online orders, and the demand of offline retailer is eroded. Moreover, BOPS cooperation between different retailers is easier to achieve than omni-channel integration strategy. When the convenience difference between offline shopping and BOPSC pick-up is moderate, the effectiveness of BOPSC strategy can be improved.

This study has the following two main contributions: Firstly, the authors investigate the effects of BOPSC strategy on the prices of online and offline retailers. The study results show that the BOPSC strategy alleviates price competition and promotes a win–win situation between online retailers and offline retailers. Secondly, this paper mainly studies the cooperative behavior between online and offline retailers and reveals the optimal conditions for online and offline retailers to adopt BOPSC strategy. It can help small- and medium-sized online and offline retailers to choose suitable products for BOPSC strategy, so as to achieve the purpose of increasing profit.

Platform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.

This paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.

In this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.

Firstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.

Effective safety communication facilitates the sharing of relevant knowledge that helps to improve safety behaviours, such as superior hazard identification and compliance. This study aims to explore channels by which construction companies can effectively communicate health and safety (H&S) among communities of their operations.

Based on a quantitative research approach, this study addressed the knowledge gap through a cross-sectional survey of 250 contractors (comprising 155 building and 95 road contractors) involved in various projects in the Ghanaian construction industry. These contractors were selected by using a stratified simple random sampling technique. Data obtained from the survey was analysed through descriptive (i.e. frequencies, mean and standard deviation) and inferential (i.e. exploratory factor analysis) statistical analyses.

The findings from the mean scores revealed that all the 12 communication channels identified in the literature, confirmed through piloting and examined by the respondents, were important channels through which construction companies can effectively communicate H&S amongst communities of their operations. The exploratory factor analysis revealed a clustering of the 12 channels of communication into 5 components: “safety demonstration in the community”; “social media”; “mass media”; “community engagement”; and “opinion leaders”.

This study offers construction project managers the means of managing one of the major stakeholders of a construction project (the community). It provides an actionable opportunity that can be leveraged strategically to integrate community members into projects to promote synergy and local content inclusion while gaining a peaceful atmosphere to achieve their project goals.

Practically, this study provides construction project managers with a means of managing one of the major stakeholders of a construction project (the community) and also demonstrates the integration of community members into projects to promote synergy and local content inclusion. This would give construction organisations a peaceful atmosphere to accomplish their project objectives.

The social implication of this study is that the study offers society a means of creating safer Ghanaian communities by offering them the knowledge of identifying hazards and avoiding risky behaviours, creating a good safety atmosphere in these communities.

This study presents construction organisations with a unique opportunity to transfer and share novel external knowledge within a different social system (the community). It contributes to the state-of-the-art knowledge in H&S communication by providing channels through which H&S can be communicated in a developing country such as Ghana.