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Keywords = BS equations

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19 pages, 2789 KiB  
Article
A Proposal for a Deflection-Based Evaluation Method for Barrel Support Brackets in the Extended Application of Fire Shutters in Logistics Facilities
by Jong Won Shon, Heewon Seo, Daehoi Kim, Seungjea Lee, Sungho Hong and Subin Jung
Fire 2025, 8(7), 253; https://doi.org/10.3390/fire8070253 - 27 Jun 2025
Viewed by 237
Abstract
This study proposes a deflection-based criterion for the assessment of barrel support brackets to ensure the structural stability of large fire shutters installed in large-scale buildings such as logistics facilities. While the current extended application method in the BS EN 15269 standard allows [...] Read more.
This study proposes a deflection-based criterion for the assessment of barrel support brackets to ensure the structural stability of large fire shutters installed in large-scale buildings such as logistics facilities. While the current extended application method in the BS EN 15269 standard allows for the evaluation of the structural adequacy of the barrel—primarily based on stress analysis—this research aims to establish a more reliable design guideline by additionally considering the deflection of barrel support brackets, which may become structurally vulnerable under high-temperature conditions. To achieve this, the bracket was modeled as a cantilever beam, and deflection equations were applied. The deflection and stress were analyzed for various rectangular hollow sections. Furthermore, the support capacities at ambient temperature and at 700 °C were compared, and regression analysis was conducted to assess the Accuracy and error rates associated with different deflection limits (L/180 to L/480). The results indicate that setting the deflection limit to L/180 yields the most favorable outcome in terms of structural safety and error minimization across most conditions. It is expected that the adoption of deflection criteria for barrel support brackets in the design of large fire shutters will contribute significantly to preventing the spread of fire and ensuring structural safety. Full article
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18 pages, 1301 KiB  
Article
Numerical Investigation for the Temporal Fractional Financial Option Pricing Partial Differential Equation Utilizing a Multiquadric Function
by Jia Li, Tao Liu, Jiaqi Xu, Xiaoxi Hu, Changan Xu and Yanlong Wei
Fractal Fract. 2025, 9(7), 414; https://doi.org/10.3390/fractalfract9070414 - 26 Jun 2025
Viewed by 448
Abstract
This paper proposes a computational procedure to resolve the temporal fractional financial option pricing partial differential equation (PDE) using a localized meshless approach via the multiquadric radial basis function (RBF). Given that financial market information is best characterized within a martingale framework, the [...] Read more.
This paper proposes a computational procedure to resolve the temporal fractional financial option pricing partial differential equation (PDE) using a localized meshless approach via the multiquadric radial basis function (RBF). Given that financial market information is best characterized within a martingale framework, the resulting option pricing model follows a modified Black–Sholes (BS) equation, requiring efficient numerical techniques for practical implementation. The key innovation in this study is the derivation of analytical weights for approximating first and second derivatives, ensuring improved numerical stability and accuracy. The construction of these weights is grounded in the second integration of a variant of the multiquadric RBF, which enhances smoothness and convergence properties. The performance of the presented solver is analyzed through computational tests, where the analytical weights exhibit superior accuracy and stability in comparison to conventional numerical weights. The results confirm that the new approach reduces absolute errors, demonstrating its effectiveness for financial option pricing problems. Full article
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29 pages, 1378 KiB  
Article
A General Conformable Black–Scholes Equation for Option Pricing
by Paula Morales-Bañuelos, Sebastian Elias Rodríguez Bojalil, Luis Alberto Quezada-Téllez and Guillermo Fernández-Anaya
Mathematics 2025, 13(10), 1576; https://doi.org/10.3390/math13101576 - 10 May 2025
Viewed by 529
Abstract
Since the emergence of the Black–Scholes model (BSM) in the early 1970s, models for the pricing of financial options have been developed and evolved with mathematical tools that provide greater efficiency and accuracy in the valuation of these assets. In this research, we [...] Read more.
Since the emergence of the Black–Scholes model (BSM) in the early 1970s, models for the pricing of financial options have been developed and evolved with mathematical tools that provide greater efficiency and accuracy in the valuation of these assets. In this research, we have used the generalized conformable derivatives associated with seven obtained conformable models with a closed-form solution that is similar to the traditional Black and Scholes. In addition, an empirical analysis was carried out to test the models with Mexican options contracts listed in 2023. Six foreign options were also tested, in particular three London options and three US options. With this sample, in addition to applying the seven generalized conformable models, we compared the results with the Heston model. We obtained much better results with the conformable models. Similarly, we decided to apply the seven conformable models to the data of the Morales et al. article, and we again determined that the conformable models greatly outperform the approximation of the Black, Scholes (BS), and Merton model with time-varying parameters and the basic Khalil conformable equation. In addition to the base sample, it was decided to test the strength of the seven generalized conformable models on 10 stock options that were out-sampled. In addition to the MSE results, for the sample of six options whose shares were traded in the London and New York stock markets, we tested the positivity and stability of the results. We plotted the values of the option contracts obtained by applying each of the seven generalized conformable models, the values of the contracts obtained by applying the traditional Heston model, and the market value of the contracts. Full article
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19 pages, 11511 KiB  
Article
Numerical Study on the Influence of Catamaran Hull Arrangement and Demihull Angle on Calm Water Resistance
by Sumin Guo, Xianhe Yang, Hongyu Li, Weizhuang Ma, Qunhong Tian, Qingfeng Ma, Xin Su and Zongsheng Wang
J. Mar. Sci. Eng. 2025, 13(4), 815; https://doi.org/10.3390/jmse13040815 - 19 Apr 2025
Viewed by 543
Abstract
This study investigates the WAM-V (Wave Adaptive Modular Vessel) catamaran configuration, focusing on the hydrodynamic interaction between its articulated hulls. The unique hinged connection mechanism induces a relative angular displacement between the demihulls during operation, significantly modifying the calm water resistance characteristics. Such [...] Read more.
This study investigates the WAM-V (Wave Adaptive Modular Vessel) catamaran configuration, focusing on the hydrodynamic interaction between its articulated hulls. The unique hinged connection mechanism induces a relative angular displacement between the demihulls during operation, significantly modifying the calm water resistance characteristics. Such resistance variations critically influence both vessel maneuverability and the operational effectiveness of onboard acoustic detection systems. This study using computational fluid dynamics (CFD) technology, the effects of varying demihull spacing and the angles of the demihulls on resistance were calculated. Numerical simulations were performed using STAR-CCM+, employing the Reynolds-averaged Navier–Stokes equations (RANS) method combined with the k-epsilon turbulence model. The study investigates the free surface and double body viscous flow at different Froude numbers in the range of 0.3 to 0.75. The analysis focuses on the effects of the demihull spacing ratio (BS/LPP, Demihull spacing/Length between perpendiculars) on calm water resistance. Specifically, the resistance coefficient at BS/LPP = 0.2 is on average 14% higher than that at BS/LPP = 0.5. Additionally, the influence of demihull angles on resistance was simulated at BS/LPP = 0.42. The results indicate that inner demihull angles result in higher resistance compared to outer angles, with the maximum increase in resistance being approximately 9%, with specific outer angles effectively reducing resistance. This study provides a scientific basis for optimizing catamaran design and offers valuable insights for enhancing sailing performance. Full article
(This article belongs to the Section Ocean Engineering)
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40 pages, 421 KiB  
Article
Bowen’s Equations for Weighted Upper Metric Mean Dimension with Potential
by Yuanyuan Zhang, Yong Ji and Yunping Wang
Mathematics 2025, 13(8), 1271; https://doi.org/10.3390/math13081271 - 12 Apr 2025
Viewed by 207
Abstract
In this paper, we define the weighted upper metric mean dimension with potential and derive its corresponding Bowen’s equation. Furthermore, we introduce the weighted BS metric mean dimension and the weighted packing BS metric mean dimension on the subsets, and prove Bowen’s equations [...] Read more.
In this paper, we define the weighted upper metric mean dimension with potential and derive its corresponding Bowen’s equation. Furthermore, we introduce the weighted BS metric mean dimension and the weighted packing BS metric mean dimension on the subsets, and prove Bowen’s equations for both. Additionally, we establish variational principles for these dimensions, linking them to the weighted local measure-theoretic entropy. Full article
15 pages, 1325 KiB  
Article
Host–Tourist Relationship Quality in Evaluating B&B: The Impacts of Personality Traits and Emotional Labor
by Shih-Yen Lin, Shao-De Liu and Wei-Ling Chang
Tour. Hosp. 2025, 6(2), 50; https://doi.org/10.3390/tourhosp6020050 - 22 Mar 2025
Cited by 1 | Viewed by 639
Abstract
With the development of Taiwanese society, the tourist B&B industry has become particularly important, marking the origin of the significant development of the tourism industry. This study focuses on the quality of host–tourist relationships in B&Bs. It is proposed that tourists “discover” the [...] Read more.
With the development of Taiwanese society, the tourist B&B industry has become particularly important, marking the origin of the significant development of the tourism industry. This study focuses on the quality of host–tourist relationships in B&Bs. It is proposed that tourists “discover” the emotions and feelings of B&B hosts through service contact processes. Although researchers have pointed out that frontline service employee personality traits affect the quality of interactions and satisfaction from the consumers’ point of view, very few studies have investigated the relationships between tourists and B&B hosts, the latter playing a double role—both as a host and a service worker. Data were collected from 422 tourists who had utilized B&B services. A quantitative analysis of the questionnaires was conducted through descriptive statistics, K-means clustering, one-way ANOVA and structural equation modeling (SEM), in order to determine the relationships among the three sets of variables. The results of this study reveal that the personality traits of B&B hosts directly affect their emotional labor and the quality of their relationships with tourists. However, the emotional labor of B&B hosts is found not to affect the quality of relationships; in this respect, our findings go counter to those of previous studies. Full article
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17 pages, 2863 KiB  
Article
Adaptive Distributed Student’s T Extended Kalman Filter Employing Allan Variance for UWB Localization
by Yanli Gao, Maosheng Yang, Xin Zang, Lei Deng, Manman Li, Yuan Xu and Mingxu Sun
Sensors 2025, 25(6), 1883; https://doi.org/10.3390/s25061883 - 18 Mar 2025
Cited by 1 | Viewed by 510
Abstract
This study proposes an adaptive distributed Student’s t extended Kalman filter (EKF) using Allan variance for ultrawide-band (UWB) localization. First of all, we model the state equation using the target’s position and velocity in east and north directions and the measurement equation by [...] Read more.
This study proposes an adaptive distributed Student’s t extended Kalman filter (EKF) using Allan variance for ultrawide-band (UWB) localization. First of all, we model the state equation using the target’s position and velocity in east and north directions and the measurement equation by using distance between the UWB base station (BS) and the target object. Then, the adaptive distributed filter employs a federation structure: A local t EKF is designed to estimate the target’s position by fusing the distance between the UWB base station and the target object. The main filter fuses the local filter’s outputs and computes the final output. For the local t EKF, in order to overcome the problem that noise in the Kalman method is assumed to be white noise and difficult to adapt to practical application environments, the t distribution is used to model noise. Meanwhile, Allan variance is calculated to assist the local filter, which improves the adaptive ability. Experimental results show that the proposed method effectively enhances navigation accuracy compared to the distributed EKF. Full article
(This article belongs to the Topic Multi-Sensor Integrated Navigation Systems)
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20 pages, 503 KiB  
Article
Local Equivalence of the Black–Scholes and Merton–Garman Equations
by Ivan Arraut
Axioms 2025, 14(3), 215; https://doi.org/10.3390/axioms14030215 - 15 Mar 2025
Viewed by 331
Abstract
It has been previously demonstrated that stochastic volatility emerges as the gauge field necessary to restore local symmetry under changes in stock prices in the Black–Scholes (BS) equation. When this occurs, a Merton–Garman-like equation emerges. From the perspective of manifolds, this means that [...] Read more.
It has been previously demonstrated that stochastic volatility emerges as the gauge field necessary to restore local symmetry under changes in stock prices in the Black–Scholes (BS) equation. When this occurs, a Merton–Garman-like equation emerges. From the perspective of manifolds, this means that the Black–Scholes and Merton–Garman (MG) equations can be considered locally equivalent. In this scenario, the MG Hamiltonian is a special case of a more general Hamiltonian, here referred to as the gauge Hamiltonian. We then show that the gauge character of volatility implies a specific functional relationship between stock prices and volatility. The connection between stock prices and volatility is a powerful tool for improving volatility estimations in the stock market, which is a key ingredient for investors to make good decisions. Finally, we define an extended version of the martingale condition, defined for the gauge Hamiltonian. Full article
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21 pages, 70620 KiB  
Article
Experimental Investigation on Flexural Behavior of Precast Segmental Ultra-High-Performance Concrete Box-Girder with External Tendons for Long-Span Highway Bridges
by Hua Zhao, Sui Luo, Junde Hu, Chengjun Tan, Peirou Qian, Huangguo Qian, Zhilian Liao, Zhentao Hu and Dutao Yi
Buildings 2025, 15(4), 642; https://doi.org/10.3390/buildings15040642 - 19 Feb 2025
Cited by 1 | Viewed by 720
Abstract
A precast concrete segmental box-girder bridge (PCSBGB) is one of the most popular styles of Accelerated Bridge Construction (ABC). To address some common challenges (low durability, poor integrity, and construction inconvenience) in PCSBGBs, this paper proposes a precast ultra-high-performance concrete (UHPC) segmental box-girder [...] Read more.
A precast concrete segmental box-girder bridge (PCSBGB) is one of the most popular styles of Accelerated Bridge Construction (ABC). To address some common challenges (low durability, poor integrity, and construction inconvenience) in PCSBGBs, this paper proposes a precast ultra-high-performance concrete (UHPC) segmental box-girder bridge (PUSBGB). In comparison to conventional PCSBGBs that use three-dimensional prestress, the PUSBGB adopts only one-dimensional (longitudinal) prestress. In addition, the thickness of the bottom/top plate and web of the UHPC box-girder are relatively thin, and as a result, the self-weight is significantly reduced. Considering the fact that the thickness of box-girder is thinner than the NC structure, the shear lag effect and risk of girder cracking may correspondingly increase when a PUSBGB is adopted in a long-span bridge. Thus, it is of essential necessity to explore the flexural behavior of a PUSBGB. In this work, a specimen with a scale (1:4) associated with a field bridge (a 102 m long simply supported PUSBGB with externally unbonded tendons) is fabricated and experimentally investigated. The mechanical behaviors of the PUSBGB are discussed, including the failure mode, the crack distribution pattern, the longitudinal strain of the UHPC plate, and the variation of tendon strain. It is found that in the elastic stage, the top slab of the UHPC box girder exhibits a significant shear lag effect, and this phenomenon is even more obvious after cracking. With the development of the cracks, the effective flange width is decreased (with a minimum value of 0.76), and the second-order effect is kept the same before the dominant crack appears (the reduction factor is around 0.95). Moreover, four existing code equations, e.g., ACI 440, ACI 318, ASSHTO, BS 8100, used to predict the stress in the externally unbonded tendons are examined. Furthermore, a finite element analysis (FEA) of the field bridge is conducted, and the theoretical calculation demonstrates that the flexural resistances of the proposed PUSBGB can comply with the design requirements of Chinese code under the ultimate limit states (ULSs). Full article
(This article belongs to the Section Building Structures)
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12 pages, 5896 KiB  
Article
Comparison of the Modified CTOD Measurement Method with the Double Clip Gauge Method in a Compact Tension Specimen
by Jeong Yeol Park, Myung Hyun Kim and Chang Wook Ji
Materials 2025, 18(2), 310; https://doi.org/10.3390/ma18020310 - 11 Jan 2025
Viewed by 1051
Abstract
For allowable defect analyses, the fracture toughness of materials needs to be accurately predicted. In this regard, a lower fluctuation of fracture toughness can lead to reduction in safety and economic risks. Crack tip opening displacement (CTOD), which is the representative parameter for [...] Read more.
For allowable defect analyses, the fracture toughness of materials needs to be accurately predicted. In this regard, a lower fluctuation of fracture toughness can lead to reduction in safety and economic risks. Crack tip opening displacement (CTOD), which is the representative parameter for fracture toughness, can be measured by various methods, such as the δ5, the J-conversion method, the single clip gauge method, and the double clip gauge method. When calculating CTOD from test results, the principle of similar triangles, which adopts the plastic hinge model, is influenced by the rotation factor, rp. Therefore, in order to reduce the fluctuation of CTOD, the exact value of rp must be defined. This study investigates various methods to predict fracture toughness in metallic materials, and assess the pros and cons of each method. Moreover, the equation of rp is modified by using a double clip gauge in compact tension (CT) to reduce the fluctuation of CTOD. The rp value is derived from 0.55 to 0.68, using the double clip gauge method. Finite element analysis is used to derive the rp values, which range from 0.50 to 0.66, in order to verify the validity of the derived rp values. This ensures the validity of the rp value derived from the experiment. In addition, the fluctuation of CTOD, based on the modified equation of rp, is lower than that using the single clip gauge method, according to BS 7448. Full article
(This article belongs to the Special Issue Engineering Materials and Structural Integrity)
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18 pages, 967 KiB  
Article
Purchase Intention of Healthy Foods: The Determinant Role of Brand Image in the Market of a Developing Country
by Elizabeth Emperatriz García-Salirrosas, Manuel Escobar-Farfán, Iván Veas-González, Jorge Alberto Esponda-Perez, Rodrigo Gallardo-Canales, Rodrigo Ruiz-Andia, Virginia Mercedes Fernandez-Daza and Rosa Fabiana Zabalaga-Davila
Foods 2024, 13(20), 3242; https://doi.org/10.3390/foods13203242 - 12 Oct 2024
Cited by 9 | Viewed by 6560
Abstract
In the current consumer context, the trend towards a healthy lifestyle has significantly increased the demand for healthy foods. This study aims to identify the relationship between the brand image (BI) and purchase intention (PI) of these products and how variables such as [...] Read more.
In the current consumer context, the trend towards a healthy lifestyle has significantly increased the demand for healthy foods. This study aims to identify the relationship between the brand image (BI) and purchase intention (PI) of these products and how variables such as perceived brand quality (BPQ) and brand satisfaction (BS) influence brand trust (BT) and brand loyalty (BL) in this relationship. The methodology includes a quantitative approach, using non-probability convenience sampling. Using an online survey, data were collected from 637 consumers. Analyses were performed using structural equation modeling (SEM-PLS). The results show no significant correlation between BI and PI, but BI significantly impacts BPQ, BS, BT, and BL. Furthermore, BPQ positively influences BS, BT, and BL, but it does not have a direct influence on PI. The findings suggest that a positive brand image satisfies consumers and generates long-term trust and loyalty. However, perceived quality does not always translate into purchase intention due to various barriers. Practical implications highlight the importance of building a strong and positive brand image to encourage demand for healthy products. Full article
(This article belongs to the Special Issue How Does Consumers’ Perception Influence Their Food Choices?)
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22 pages, 3564 KiB  
Article
An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis
by Samuel M. Nuugulu, Frednard Gideon and Kailash C. Patidar
Fractal Fract. 2024, 8(8), 461; https://doi.org/10.3390/fractalfract8080461 - 6 Aug 2024
Cited by 2 | Viewed by 1260
Abstract
Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering. It has now become obvious, even to casual observers, that the classical BS models [...] Read more.
Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering. It has now become obvious, even to casual observers, that the classical BS models derived under the EMH framework fail to account for a number of realistic price evolutions in real-time market data. An alternative approach to the EMH framework is the Fractal Market Hypothesis (FMH), which proposes better and clearer explanations of market behaviours during unfavourable market conditions. The FMH involves non-local derivatives and integral operators, as well as fractional stochastic processes, which provide better tools for explaining the dynamics of evolving market anomalies, something that classical BS models may fail to explain. In this work, using the FMH, we derive a time-fractional Black–Scholes partial differential equation (tfBS-PDE) and then transform it into a heat equation, which allows for ease of implementing a high-order numerical scheme for solving it. Furthermore, the stability and convergence properties of the numerical scheme are discussed, and overall techniques are applied to pricing European put option problems. Full article
(This article belongs to the Section Numerical and Computational Methods)
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18 pages, 4545 KiB  
Article
Digital Image Correlation-Based Investigation of the Shear Performance of Connection Systems of Assembled Bamboo Scrimber–Lightweight Concrete Composite Beams
by Zhiyuan Wang, Feng Wang and Huihui Liu
Materials 2024, 17(13), 3268; https://doi.org/10.3390/ma17133268 - 2 Jul 2024
Cited by 1 | Viewed by 1515
Abstract
To investigate the shear performance of assembled bamboo scrimber (BS)-lightweight concrete (LC) connection systems, three groups of nine BS-LC shear connections were fabricated in this work using BS, LC, dowels, and grout. The experimental parameters included the dowel diameter and fabrication process (cast-in-place [...] Read more.
To investigate the shear performance of assembled bamboo scrimber (BS)-lightweight concrete (LC) connection systems, three groups of nine BS-LC shear connections were fabricated in this work using BS, LC, dowels, and grout. The experimental parameters included the dowel diameter and fabrication process (cast-in-place vs. assembly). Push-out tests were conducted on the specimens, and traditional linear variable displacement transducer (LVDT) measurements and the advanced digital image correlation (DIC) technique were employed to determine performance indicators such as the cross-section slip of composite members. Subsequently, the method for calculating the shear capacity of assembled BS-LC connection systems was theoretically analyzed. The research results showed that the load-slip curves measured by DIC were highly correlated with those measured by LVDT, thus, validating the reliability of the DIC data. According to the DIC data, the variations in slip of the shear connection over the interface height were further analyzed. An equation for calculating the shear capacity of dowel shear connectors was proposed based on theoretical analysis with comprehensive consideration of the experimental indicators such as the failure mode, load-slip curve, shear stiffness, and shear capacity of the specimens. The theoretical calculation values were in good agreement with the experimental results. Full article
(This article belongs to the Section Construction and Building Materials)
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24 pages, 1380 KiB  
Article
Green Entrepreneurship for Business Sustainability: Do Environmental Dynamism and Green Structural Capital Matter?
by Khaled Tekala, Sarvnaz Baradarani, Ahmad Alzubi and Ayşen Berberoğlu
Sustainability 2024, 16(13), 5291; https://doi.org/10.3390/su16135291 - 21 Jun 2024
Cited by 10 | Viewed by 6244
Abstract
With the appearance of rising environmental challenges, businesses are increasingly recognizing the imperative of adopting sustainable practices. Within this context, the concept of green entrepreneurship has emerged as a pivotal force driving environmentally responsible innovation and economic growth. Employing Green Theory, this study [...] Read more.
With the appearance of rising environmental challenges, businesses are increasingly recognizing the imperative of adopting sustainable practices. Within this context, the concept of green entrepreneurship has emerged as a pivotal force driving environmentally responsible innovation and economic growth. Employing Green Theory, this study examines the impact of green entrepreneurship (GEN) on business sustainability (BS) through the mediation role of green structural capital (GSC) and the moderation influence of environmental dynamism (ED). Using a quantitative research approach, 443 owners and managers of small and medium-sized enterprises (SMEs) (e.g., wholesale and retail trade, manufacturing, building materials, and scientific, professional, and technical activity enterprises) in Istanbul and Izmir, Turkey, were surveyed using both on site and electronic questionnaires. The data from the study were statistically analyzed using SPSS V.27 and structural equation modeling (SEM). The findings of this study show that green entrepreneurship (GEN) significantly enhances business sustainability (BS) and green structural capital (GSC), with GSC serving as a vital mediator in the GEN-BS relationship; however, environmental dynamism (ED) does negatively moderate the GEN-BS relationship, indicating that GEN’s positive impact on BS is accentuated under lower environmental uncertainties. Additionally, ED’s moderation effect is observed in the GEN-BS relationship via GSC, particularly under conditions of reduced dynamism, underscoring the nuanced role of environmental factors in sustainable entrepreneurship. The findings demonstrate green entrepreneurship and structural capital as key drivers for SME sustainability amidst environmental fluctuations. Full article
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18 pages, 683 KiB  
Article
Outdoor-to-Indoor mmWave Relaying with Massive MIMO: Impact of Imperfect Channel Estimation
by Nawal Bounouader, Houda Chafnaji and Mustapha Benjillali
Electronics 2024, 13(10), 1857; https://doi.org/10.3390/electronics13101857 - 10 May 2024
Cited by 1 | Viewed by 1361
Abstract
Assuming incomplete knowledge of the channel state information (CSI), we investigate two scenarios involving millimeter wave (mmWave) relaying to support outdoor-to-indoor communications. We proceed to derive the average signal-to-noise ratio (SNR) expressions for two relaying scenarios and quantify the asymptotic SNR. The performance [...] Read more.
Assuming incomplete knowledge of the channel state information (CSI), we investigate two scenarios involving millimeter wave (mmWave) relaying to support outdoor-to-indoor communications. We proceed to derive the average signal-to-noise ratio (SNR) expressions for two relaying scenarios and quantify the asymptotic SNR. The performance of the two relaying scenarios is evaluated using the outage probability—for which we have derived closed-form equations—the end-to-end channel capacity, and the energy efficiency. The obtained results are compared with those derived assuming complete knowledge of the CSI. The effect of the imperfect CSI is therefore assessed in relation to the reference of perfect CSI. In these scenarios, an outside base station (BS) in an urban cellular network serves several indoor users. In the context of a two-hop full-duplex (FD) relaying scheme, we initially suggest a method in which the base station (BS) utilizes zero-forcing (ZF) precoding, and we take into account the overall channel response. Furthermore, we make the assumption that the base station (BS) engages in precoding only depending on the response of the channel in the first hop; in this second design, the relay precodes (using the response of the second-hop channel), amplifies, and sends the signals. Both techniques utilize massive multiple-input–multiple-output (mMIMO) arrays to permit transmission. We also present Monte Carlo simulation results to assess the accuracy of our analytical results. Finally, the two systems are compared in terms of channel estimation and precoding complexity, the number of antennas, as well as the number of users. Practical deployment recommendations are formulated at the end of this work. Full article
(This article belongs to the Special Issue New Trends and Methods in Communication Systems, 2nd Edition)
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