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Article
Publication date: 9 April 2024

Kunal Kumar Singh, Santosh Kumar Mahto and Rashmi Sinha

The purpose of this study is to introduce a new type of sensor which uses microwave metamaterials and direct-coupled split-ring resonators (DC-SRRs) to measure the dielectric…

Abstract

Purpose

The purpose of this study is to introduce a new type of sensor which uses microwave metamaterials and direct-coupled split-ring resonators (DC-SRRs) to measure the dielectric properties of solid materials in real time. The sensor uses a transmission line with a bridge-type structure to measure the differential frequency, which can be used to calculate the dielectric constant of the material being tested. The study aims to establish an empirical relationship between the dielectric properties of the material and the frequency measurements obtained from the sensor.

Design/methodology/approach

In the proposed design, the opposite arm of the bridge transmission line is loaded by DC-SRRs, and the distance between DC-SRRs is optimized to minimize the mutual coupling between them. The DC-SRRs are loaded with the material under test (MUT) to perform differential permittivity sensing. When identical MUT is placed on both resonators, a single transmission zero (notch) is obtained, but non-identical MUTs exhibit two split notches. For the design of differential sensors and comparators based on symmetry disruption, frequency splitting is highly useful.

Findings

The proposed structure is demonstrated using electromagnetic simulation, and a prototype of the proposed sensor is fabricated and experimentally validated to prove the differential sensing principle. Here, the sensor is analyzed for sensitivity by using different MUTs with relative permittivity ranges from 1.006 to 10 and with a fixed dimension of 9 mm × 10 mm ×1.2 mm. It shows a very good average frequency deviation per unit change in permittivity of the MUTs, which is around 743 MHz, and it also exhibits a very high average relative sensitivity and quality factor of around 11.5% and 323, respectively.

Originality/value

The proposed sensor can be used for differential characterization of permittivity and also as a comparator to test the purity of solid dielectric samples. This sensor most importantly strengthens robustness to environmental conditions that cause cross-sensitivity or miscalibration. The accuracy of the measurement is enhanced as compared to conventional single- and double-notch metamaterial-based sensors.

Article
Publication date: 2 May 2024

Gerasimos G. Rigatos

To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1…

Abstract

Purpose

To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

Design/methodology/approach

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

Findings

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Research limitations/implications

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

Practical implications

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

Social implications

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

Originality/value

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

Details

Robotic Intelligence and Automation, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 2754-6969

Keywords

Article
Publication date: 9 May 2024

Yufeng Zhang and Lizhen Wang

Fractional Fokker-Planck equation (FFPE) and time fractional coupled Boussinesq-Burger equations (TFCBBEs) play important roles in the fields of solute transport, fluid dynamics…

Abstract

Purpose

Fractional Fokker-Planck equation (FFPE) and time fractional coupled Boussinesq-Burger equations (TFCBBEs) play important roles in the fields of solute transport, fluid dynamics, respectively. Although there are many methods for solving the approximate solution, simple and effective methods are more preferred. This paper aims to utilize Laplace Adomian decomposition method (LADM) to construct approximate solutions for these two types of equations and gives some examples of numerical calculations, which can prove the validity of LADM by comparing the error between the calculated results and the exact solution.

Design/methodology/approach

This paper analyzes and investigates the time-space fractional partial differential equations based on the LADM method in the sense of Caputo fractional derivative, which is a combination of the Laplace transform and the Adomian decomposition method. LADM method was first proposed by Khuri in 2001. Many partial differential equations which can describe the physical phenomena are solved by applying LADM and it has been used extensively to solve approximate solutions of partial differential and fractional partial differential equations.

Findings

This paper obtained an approximate solution to the FFPE and TFCBBEs by using the LADM. A number of numerical examples and graphs are used to compare the errors between the results and the exact solutions. The results show that LADM is a simple and effective mathematical technique to construct the approximate solutions of nonlinear time-space fractional equations in this work.

Originality/value

This paper verifies the effectiveness of this method by using the LADM to solve the FFPE and TFCBBEs. In addition, these two equations are very meaningful, and this paper will be helpful in the study of atmospheric diffusion, shallow water waves and other areas. And this paper also generalizes the drift and diffusion terms of the FFPE equation to the general form, which provides a great convenience for our future studies.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 22 March 2024

Amira Said and Chokri Ouerfelli

This paper aims to examine the dynamic conditional correlation (DCC) and hedging ratios between Dow Jones markets and oil, gold and bitcoin. Using daily data, including the…

Abstract

Purpose

This paper aims to examine the dynamic conditional correlation (DCC) and hedging ratios between Dow Jones markets and oil, gold and bitcoin. Using daily data, including the COVID-19 pandemic and the Russia–Ukraine war. We employ the DCC-generalized autoregressive conditional heteroskedasticity (GARCH) and asymmetric DCC (ADCC)-GARCH models.

Design/methodology/approach

DCC-GARCH and ADCC-GARCH models.

Findings

The most of DCCs among market pairs are positive during COVID-19 period, implying the existence of volatility spillovers (Contagion-effects). This implies the lack of additional economic gains of diversification. So, COVID-19 represents a systematic risk that resists diversification. However, during the Russia–Ukraine war the DCCs are negative for most pairs that include Oil and Gold, implying investors may benefit from portfolio-diversification. Our hedging analysis carries significant implications for investors seeking higher returns while hedging their Dow Jones portfolios: keeping their portfolios unhedged is better than hedging them. This is because Islamic stocks have the ability to mitigate risks.

Originality/value

Our paper may make a valuable contribution to the existing literature by examining the hedging of financial assets, including both conventional and Islamic assets, during periods of stability and crisis, such as the COVID-19 pandemic and the Russia–Ukraine war.

Details

The Journal of Risk Finance, vol. 25 no. 3
Type: Research Article
ISSN: 1526-5943

Keywords

Open Access
Article
Publication date: 22 June 2022

Serena Summa, Alex Mircoli, Domenico Potena, Giulia Ulpiani, Claudia Diamantini and Costanzo Di Perna

Nearly 75% of EU buildings are not energy-efficient enough to meet the international climate goals, which triggers the need to develop sustainable construction techniques with…

1118

Abstract

Purpose

Nearly 75% of EU buildings are not energy-efficient enough to meet the international climate goals, which triggers the need to develop sustainable construction techniques with high degree of resilience against climate change. In this context, a promising construction technique is represented by ventilated façades (VFs). This paper aims to propose three different VFs and the authors define a novel machine learning-based approach to evaluate and predict their energy performance under different boundary conditions, without the need for expensive on-site experimentations

Design/methodology/approach

The approach is based on the use of machine learning algorithms for the evaluation of different VF configurations and allows for the prediction of the temperatures in the cavities and of the heat fluxes. The authors trained different regression algorithms and obtained low prediction errors, in particular for temperatures. The authors used such models to simulate the thermo-physical behavior of the VFs and determined the most energy-efficient design variant.

Findings

The authors found that regression trees allow for an accurate simulation of the thermal behavior of VFs. The authors also studied feature weights to determine the most relevant thermo-physical parameters. Finally, the authors determined the best design variant and the optimal air velocity in the cavity.

Originality/value

This study is unique in four main aspects: the thermo-dynamic analysis is performed under different thermal masses, positions of the cavity and geometries; the VFs are mated with a controlled ventilation system, used to parameterize the thermodynamic behavior under stepwise variations of the air inflow; temperatures and heat fluxes are predicted through machine learning models; the best configuration is determined through simulations, with no onerous in situ experimentations needed.

Details

Construction Innovation , vol. 24 no. 7
Type: Research Article
ISSN: 1471-4175

Keywords

Open Access
Article
Publication date: 1 April 2024

Ying Miao, Yue Shi and Hao Jing

This study investigates the relationships among digital transformation, technological innovation, industry–university–research collaborations and labor income share in…

Abstract

Purpose

This study investigates the relationships among digital transformation, technological innovation, industry–university–research collaborations and labor income share in manufacturing firms.

Design/methodology/approach

The relationships are tested using an empirical method, constructing regression models, by collecting 1,240 manufacturing firms and 9,029 items listed on the A-share market in China from 2013 to 2020.

Findings

The results indicate that digital transformation has a positive effect on manufacturing companies’ labor income share. Technological innovation can mediate the effect of digital transformation on labor income share. Industry–university–research cooperation can positively moderate the promotion effect of digital transformation on labor income share but cannot moderate the mediating effect of technological innovation. Heterogeneity analysis also found that firms without service-based transformation and nonstate-owned firms are better able to increase their labor income share through digital transformation.

Originality/value

This study provides a new path to increase the labor income share of enterprises to achieve common prosperity, which is important for manufacturing enterprises to better transform and upgrade to achieve high-quality development.

Article
Publication date: 14 March 2024

Arjun J Nair, Sridhar Manohar and Amit Mittal

Amidst unpredictable and turbulent periods, such as the COVID-19 pandemic, service organization’s responses are required to be innovative, adaptable and resilient. The purpose of…

Abstract

Purpose

Amidst unpredictable and turbulent periods, such as the COVID-19 pandemic, service organization’s responses are required to be innovative, adaptable and resilient. The purpose of this study is to explore the utilization of both reconfiguration and transformational strategies as instruments for cultivating resilience and advancing sustainability in service organizations.

Design/methodology/approach

The study examines a proposed resilience model using fuzzy logic. The research also used a semantic differential scale to capture nuanced and intricate attitudes. Finally, to augment the validity of the resilience model, a measurement scale was formulated using business mathematics and expert opinions.

Findings

Although investing in resilience training can help organizations gain control and maintain their operations in times of crisis, it may not directly help service organizations understand the external turmoil, seek available resources or create adaptive remedies. Conversely, high levels of reconfiguration and transformation management vigour empower a service organization’s revolutionary, malleable vision, organizational structure and decision-making processes, welcoming talented and innovative employees to enhance capabilities during crises.

Research limitations/implications

The resilience model bestows a comprehensive understanding of the pertinence of building resilience for service organizations identifying the antecedents that influence the adoption of these strategies and introduces a range of theoretical perspectives that empowers service organizations to conceptualize and plan for building resilience. The research guides service organizations to become more resilient to external shocks and adapt to changing circumstances by diversifying their offerings, optimizing their resources and adopting flexible work arrangements. The study elaborates on the enhancement of resilience, increasing innovation, improving efficiency and enhancing customer satisfaction for service organizations to remain competitive and contribute to positive social and economic outcomes through the adoption of both reconfiguration and transformational strategies.

Practical implications

The study also guides the service organizations to become more resilient to external shocks and adapt to changing circumstances by diversifying their offerings, optimizing their resources and adopting flexible work arrangements. Rapid innovation and business model innovation are essential components, enabling service organizations to foster a culture of innovation and remain competitive. In addition, the adoption can lead to improved financial performance, job creation and economic growth, contributing to positive social and economic impacts.

Social implications

The resilience model bestows a comprehensive understanding of the pertinence of building resilience for service organizations. It identifies the antecedents that influence the adoption of these strategies and introduces a range of theoretical perspectives that empowers service organizations to conceptualize and plan for building resilience. The research also provides a foundation for further investigation into the effectiveness of these strategies and their impact on organizational performance and sustainability. By better preparing service organizations for disruptions and uncertainties, this research triggers ameliorated organizational performance and sustainability.

Originality/value

Within the realm of the service industry, the present investigation has undertaken the development, quantification and scrutiny of both resilience and tenacity. In addition, it has delved into the intricate dynamics surrounding the influencing factors and antecedents that bear upon resilience, elucidating their consequential impact on the operational performance and outlook of service-oriented organizations. The findings derived from this research furnish valuable insights germane to enhancing operational efficacy and surmounting impediments within the sector.

Details

Journal of Services Marketing, vol. 38 no. 4
Type: Research Article
ISSN: 0887-6045

Keywords

Article
Publication date: 8 May 2024

Qingli Lu, Ruisheng Sun and Yu Lu

This paper aims to propose and verify an improved cascade active disturbance rejection control (ADRC) scheme based on output redefinition for hypersonic vehicles (HSVs) with…

Abstract

Purpose

This paper aims to propose and verify an improved cascade active disturbance rejection control (ADRC) scheme based on output redefinition for hypersonic vehicles (HSVs) with nonminimum phase characteristic and model uncertainties.

Design/methodology/approach

To handle the nonminimum phase characteristic, a tuning factor stabilizing internal dynamics is introduced to redefine the system output states; its effective range is determined by analyzing Byrnes–Isidori normalized form of the redefined system. The extended state observers (ESOs) are used to estimate the uncertainties, which include matched and mismatched items in the system. The controller compensates observations in real time and appends integral terms to improve robustness against the estimation errors of ESOs.

Findings

Theoretical and simulation results show that the stability of internal dynamics is guaranteed by the tuning factor and the tracking errors of external commands are globally asymptotically stable.

Practical implications

The control scheme in this paper is expected to generate a reliable way for dealing with nonminimum phase characteristic and model uncertainties of HSVs.

Originality/value

In the framework of ADRC, a concise form of redefined outputs is proposed, in which the tuning factor performs a decisive role in stabilizing the internal dynamics of HSVs. By introducing an integral term into the cascade ADRC scheme, the compensation accuracy of matched and mismatched disturbances is improved.

Details

Aircraft Engineering and Aerospace Technology, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1748-8842

Keywords

Open Access
Article
Publication date: 6 May 2024

Andreas Gschwentner, Manfred Kaltenbacher, Barbara Kaltenbacher and Klaus Roppert

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various…

Abstract

Purpose

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

Design/methodology/approach

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

Findings

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

Originality/value

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 15 February 2024

Aamir Rashid, Rizwana Rasheed, Abdul Hafaz Ngah, Mahawattage Dona Ranmali Pradeepa Jayaratne, Samar Rahi and Muhammad Nawaz Tunio

Supply chain (SC) management is more challenging than ever. Significantly, the pandemic has provoked global and economic destruction that appeared in the manufacturing industry as…

Abstract

Purpose

Supply chain (SC) management is more challenging than ever. Significantly, the pandemic has provoked global and economic destruction that appeared in the manufacturing industry as a “black swan.” Therefore, the purpose of this study was to examine the role of information processing and digital supply chain in supply chain resilience through supply chain risk management.

Design/methodology/approach

This study examines SC risk management and resilience from an information processing theory perspective. The authors used data collected from 251 SC professionals in the manufacturing industry, and the authors used a quantitative method to analyze the data. The data was analyzed using partial least squares-structural equation modeling. To confirm the higher-order measurement model, the authors used SmartPLS version 4 software.

Findings

This study found that information processing capability (disruptive orientation and visibility in high-order) and digital SC significantly and positively affect SC risk management and resilience. Similarly, SC risk management positively mediates the relationship between information processing capability and digital SC. However, information processing capability was found to have a more substantial effect on SC risk management than the digital SC.

Research limitations/implications

This study has both academic and practical contributions. It contributed to existing information processing theory, and manufacturing firms can improve their performance by proactively responding to SC disruptions by recognizing the pivotal role of study variables in risk management for a resilient SC.

Originality/value

The conceptual model of this study is based on information processing theory, which asserts that synchronizing information processing capabilities and digital SCs allows a firm to deal with unplanned events. SC disruption orientation and visibility are considered risk controllers as they allow the firms to be more proactive. An integrated model of conceptualizing the disruption orientation, visibility (higher-order) and digital SC with information processing theory makes this research novel.

Details

Journal of Global Operations and Strategic Sourcing, vol. 17 no. 2
Type: Research Article
ISSN: 2398-5364

Keywords

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