This paper aims to analyze the steady-state behavior of bulk input general service queue with a second optional service (SOS), balking, and feedback facility. In this study, the server provides two kinds of services such as first essential service (FES) and SOS. The FES is provided to all arriving customers to the system while SOS is only to those customers who demand additional service. When the customer completes FES and is not satisfied with the service, he may choose to rejoin the queue (feedback) or opt for SOS or depart from the system with a certain probability. We have computed the probability-generating function of the queue-length distribution after converting the non-Markovian to Markovian process by using a supplementary variable technique. This technique is used to solve the non-Markov queue model by taking the elapsed service times as the supplementary variable so that the process becomes Markovian. This study contributes to filling the gap in the analysis of batch arrival general service queues with balking, feedback, and SOS. Furthermore, we have presented the numerical results and cost optimization. The results reveal that the higher service rate in both FES and SOS helps the system manager to run the system effectively. Similarly, in cost optimization, the system manager should make emphasize choosing optimal service rates to have a cost-benefit and less congestion in the queueing system.
本文旨在分析带有第二选择服务（SOS）、逡巡和反馈设施的批量输入一般服务队列的稳态行为。在本研究中，服务器提供两种服务，如第一基本服务（FES）和第二可选服务（SOS）。FES 提供给所有到达系统的客户，而 SOS 只提供给那些需要额外服务的客户。当客户完成 FES 并对服务不满意时，他可以选择重新加入队列（反馈）或选择 SOS 或以一定的概率离开系统。我们利用补充变量技术将非马尔可夫过程转换为马尔可夫过程后，计算了队列长度分布的概率生成函数。该技术用于求解非马尔可夫队列模型，将经过的服务时间作为补充变量，从而使该过程成为马尔可夫过程。这项研究有助于填补具有逡巡、反馈和 SOS 的批量到达一般服务队列分析的空白。此外，我们还给出了数值结果和成本优化。结果表明，在 FES 和 SOS 中，较高的服务率有助于系统管理员有效地运行系统。同样，在成本优化中，系统管理员应强调选择最佳服务率，以获得成本效益并减少排队系统的拥堵。
{"title":"Analysis of Batch Arrival General Service Queue with Balking, Feedback and Second Optional Service","authors":"Vijaya Laxmi, H. A. Qrewi, A. A. George","doi":"10.37256/cm.4420232688","DOIUrl":"https://doi.org/10.37256/cm.4420232688","url":null,"abstract":"This paper aims to analyze the steady-state behavior of bulk input general service queue with a second optional service (SOS), balking, and feedback facility. In this study, the server provides two kinds of services such as first essential service (FES) and SOS. The FES is provided to all arriving customers to the system while SOS is only to those customers who demand additional service. When the customer completes FES and is not satisfied with the service, he may choose to rejoin the queue (feedback) or opt for SOS or depart from the system with a certain probability. We have computed the probability-generating function of the queue-length distribution after converting the non-Markovian to Markovian process by using a supplementary variable technique. This technique is used to solve the non-Markov queue model by taking the elapsed service times as the supplementary variable so that the process becomes Markovian. This study contributes to filling the gap in the analysis of batch arrival general service queues with balking, feedback, and SOS. Furthermore, we have presented the numerical results and cost optimization. The results reveal that the higher service rate in both FES and SOS helps the system manager to run the system effectively. Similarly, in cost optimization, the system manager should make emphasize choosing optimal service rates to have a cost-benefit and less congestion in the queueing system.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"7 7","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139273953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The cryptocurrency market, specifically the non-fungible token (NFT) market, has been gaining popularity with the rise of social finance, game finance, metaverse, and web 3.0 technologies. With the increasing interest in cryptocurrency, it is essential to develop a comprehensive understanding of the market dynamics to aid investment decisions. This paper aims to analyze the impact of news sentiment on the prices of two cryptocurrencies, Green Satoshi Token (GST) and Green Metaverse Token (GMT). The sentiment analysis model used in this study is Finance Bidirectional Encoder Representations from Transformers (FinBERT), a pre-trained deep neural network model designed for financial sentiment analysis. Additionally, we introduce the use of the Extreme Gradient Boosting (XGBoost) algorithm to evaluate the sentiment result on the model’s performance. The study period covered from March 2022 to April 2022, and the sentiment score of the result generated by FinBERT on crypto, stock market, and finance news was found to be correlated with the prices of GST and GMT. The findings suggest that the sentiment score of GST reflects changes in the price earlier than GMT. These findings have significant implications for decision-making strategies and can aid investors in making more informed decisions. The research highlights the importance of sentiment analysis in understanding the market dynamics and its potential impact on the prices of cryptocurrencies. The use of FinBERT and XGBoost algorithms provides valuable insights into market trends and can aid investors in making informed decisions.
{"title":"Predicting Price Trends Using Sentiment Analysis: A Study of StepN’s SocialFi and GameFi Cryptocurrencies","authors":"Eik Den Yeoh, Tinfah Chung, Yuyang Wang","doi":"10.37256/cm.4420232572","DOIUrl":"https://doi.org/10.37256/cm.4420232572","url":null,"abstract":"The cryptocurrency market, specifically the non-fungible token (NFT) market, has been gaining popularity with the rise of social finance, game finance, metaverse, and web 3.0 technologies. With the increasing interest in cryptocurrency, it is essential to develop a comprehensive understanding of the market dynamics to aid investment decisions. This paper aims to analyze the impact of news sentiment on the prices of two cryptocurrencies, Green Satoshi Token (GST) and Green Metaverse Token (GMT). The sentiment analysis model used in this study is Finance Bidirectional Encoder Representations from Transformers (FinBERT), a pre-trained deep neural network model designed for financial sentiment analysis. Additionally, we introduce the use of the Extreme Gradient Boosting (XGBoost) algorithm to evaluate the sentiment result on the model’s performance. The study period covered from March 2022 to April 2022, and the sentiment score of the result generated by FinBERT on crypto, stock market, and finance news was found to be correlated with the prices of GST and GMT. The findings suggest that the sentiment score of GST reflects changes in the price earlier than GMT. These findings have significant implications for decision-making strategies and can aid investors in making more informed decisions. The research highlights the importance of sentiment analysis in understanding the market dynamics and its potential impact on the prices of cryptocurrencies. The use of FinBERT and XGBoost algorithms provides valuable insights into market trends and can aid investors in making informed decisions.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"70 2","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139276109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Boubekeur Gasmi, Lama Alhakim, Yazid Mati, Alaaeddin Moussa, Ali Akgül, Rania Wannan, Jihad Asad
The purpose of this research is to find analytical solutions to the time-fractional nonlinear Maccari system. The double auxiliary equation method, which has never been used before, is used to obtain these solutions. The method is cleverly applied, resulting in the generation of nine new exact solitary wave solutions that have never been found before. We also describe the system’s dynamic behavior and the bifurcation of traveling waves. Finally, we show some solutions with different coefficient values that correspond to the nine discovered solutions graphically.
{"title":"Novel Exact and Solitary Wave Solutions for The Time-Fractional Nonlinear Maccari's System","authors":"Boubekeur Gasmi, Lama Alhakim, Yazid Mati, Alaaeddin Moussa, Ali Akgül, Rania Wannan, Jihad Asad","doi":"10.37256/cm.4420232660","DOIUrl":"https://doi.org/10.37256/cm.4420232660","url":null,"abstract":"The purpose of this research is to find analytical solutions to the time-fractional nonlinear Maccari system. The double auxiliary equation method, which has never been used before, is used to obtain these solutions. The method is cleverly applied, resulting in the generation of nine new exact solitary wave solutions that have never been found before. We also describe the system’s dynamic behavior and the bifurcation of traveling waves. Finally, we show some solutions with different coefficient values that correspond to the nine discovered solutions graphically.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"35 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134992832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we find approximate series solutions to fractional-order Swift-Hohenberg equations by using the hybrid method, i.e., accelerated homotopy perturbation transformation method (AHPTM). The accelerated homotopy perturbation method was merged with the Laplace transform to create the proposed method. We also compare the results of our proposed method with the exact solution and demonstrate that it is the useful tool for tackling nonlinear problems of fractional order. Results are presented through graphs using Mathematica software.
{"title":"A Semi-Analytical Method for Solving Nonlinear Fractional-Order Swift-Hohenberg Equations","authors":"Shabnam Jasrotia, Prince Singh","doi":"10.37256/cm.4420232811","DOIUrl":"https://doi.org/10.37256/cm.4420232811","url":null,"abstract":"In this study, we find approximate series solutions to fractional-order Swift-Hohenberg equations by using the hybrid method, i.e., accelerated homotopy perturbation transformation method (AHPTM). The accelerated homotopy perturbation method was merged with the Laplace transform to create the proposed method. We also compare the results of our proposed method with the exact solution and demonstrate that it is the useful tool for tackling nonlinear problems of fractional order. Results are presented through graphs using Mathematica software.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"83 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Victorien F. Konane, Claude Yaméogo, Wahabo Baguian
In this article, we approach a class of problems in probability theory, namely, the asymptotic expansion of probability. We consider an independent, identically distributed, and normalized stochastic process in a separable Hilbert space H, and associate it with the normalized partial sum.As a result, we built on the ball with a fixed center asymptotic expansion of non-uniform probabilities; our conditions on the moments are minimal, and the dependency of estimates on the covariance operator is expressed with the terms of the eigenvalue series. Likewise, the covariance operators of the random elements do not coincide. In the open ball set with fixed center a and radius , we estimate the optimal result of the Berry-Esseen type of the remainder, and the terms of the probability by the Fourier method.
{"title":"Asymptotic Probability Expansions for Random Elements in a Hilbert space","authors":"Victorien F. Konane, Claude Yaméogo, Wahabo Baguian","doi":"10.37256/cm.4420232651","DOIUrl":"https://doi.org/10.37256/cm.4420232651","url":null,"abstract":"In this article, we approach a class of problems in probability theory, namely, the asymptotic expansion of probability. We consider an independent, identically distributed, and normalized stochastic process in a separable Hilbert space H, and associate it with the normalized partial sum.As a result, we built on the ball with a fixed center asymptotic expansion of non-uniform probabilities; our conditions on the moments are minimal, and the dependency of estimates on the covariance operator is expressed with the terms of the eigenvalue series. Likewise, the covariance operators of the random elements do not coincide. In the open ball set with fixed center a and radius , we estimate the optimal result of the Berry-Esseen type of the remainder, and the terms of the probability by the Fourier method.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, new operational matrices (OMs) of ordinary and fractional derivatives (FDs) of a first finite class of classical orthogonal polynomials (FFCOP) are introduced. Also, two algorithms are proposed for using the tau and collocation spectral methods (SPMs) to get new approximate solutions to the given fractional differential equations (FDEs). These algorithms convert the given FDEs subject to initial/boundary conditions (I/BCs) into linear or nonlinear systems of algebraic equations that can be solved using appropriate solvers. To demonstrate the robustness, efficiency, and accuracy of the proposed spectral solutions, several illustrative examples are presented. The obtained results show that the proposed algorithms exhibit higher accuracy compared to existing techniques in the literature. Furthermore, an error analysis is provided.
{"title":"A New First Finite Class of Classical Orthogonal Polynomials Operational Matrices: An Application for Solving Fractional Differential Equations","authors":"H. M. Ahmed","doi":"10.37256/cm.4420232716","DOIUrl":"https://doi.org/10.37256/cm.4420232716","url":null,"abstract":"In this paper, new operational matrices (OMs) of ordinary and fractional derivatives (FDs) of a first finite class of classical orthogonal polynomials (FFCOP) are introduced. Also, two algorithms are proposed for using the tau and collocation spectral methods (SPMs) to get new approximate solutions to the given fractional differential equations (FDEs). These algorithms convert the given FDEs subject to initial/boundary conditions (I/BCs) into linear or nonlinear systems of algebraic equations that can be solved using appropriate solvers. To demonstrate the robustness, efficiency, and accuracy of the proposed spectral solutions, several illustrative examples are presented. The obtained results show that the proposed algorithms exhibit higher accuracy compared to existing techniques in the literature. Furthermore, an error analysis is provided.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mir Sajjad Hashemi, Mohammad Mirzazadeh, Dumitru Baleanu
In this work, a well-known non-homogeneous wave equation with temporal fractional derivative is approximately investigated. A recently defined generalized non-local fractional derivative is utilized as the fractional operator. A novel technique is proposed to approximate the solutions of wave equation with generalized fractional derivative. The proposed method is based on the shifted Chebyshev polynomials and a combination of collocation and residual function methods. Theoretical analysis of the convergence of the proposed method is performed. Approximate solutions are derived in both rectangular and non-rectangular (general) domains.
{"title":"Innovative Method for Computing Approximate Solutions of Non-Homogeneous Wave Equations with Generalized Fractional Derivatives","authors":"Mir Sajjad Hashemi, Mohammad Mirzazadeh, Dumitru Baleanu","doi":"10.37256/cm.4420233593","DOIUrl":"https://doi.org/10.37256/cm.4420233593","url":null,"abstract":"In this work, a well-known non-homogeneous wave equation with temporal fractional derivative is approximately investigated. A recently defined generalized non-local fractional derivative is utilized as the fractional operator. A novel technique is proposed to approximate the solutions of wave equation with generalized fractional derivative. The proposed method is based on the shifted Chebyshev polynomials and a combination of collocation and residual function methods. Theoretical analysis of the convergence of the proposed method is performed. Approximate solutions are derived in both rectangular and non-rectangular (general) domains.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135290531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Pérez-Díaz, M.A. Fernández de Sevilla, J.R. Magdalena-Benedicto
Starting from the concept of infinite branches and approximation surfaces, we present a method to compute infinite branches and surfaces having the same asymptotic behavior as an input parametric surface. The results obtained in this work represent a breakthrough for the study of surfaces and their applications.
{"title":"Asymptotic Behavior of a Parametric Algebraic Surface","authors":"S. Pérez-Díaz, M.A. Fernández de Sevilla, J.R. Magdalena-Benedicto","doi":"10.37256/cm.4420232693","DOIUrl":"https://doi.org/10.37256/cm.4420232693","url":null,"abstract":"Starting from the concept of infinite branches and approximation surfaces, we present a method to compute infinite branches and surfaces having the same asymptotic behavior as an input parametric surface. The results obtained in this work represent a breakthrough for the study of surfaces and their applications.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":" 111","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a comprehensive analysis of the concatenation model with power-law nonlinearity. The research encompasses multiple key aspects, providing a detailed exploration of the model's behavior and implications within the context of nonlinear dynamics and optics. The study commences with an in-depth bifurcation analysis, aiming to unravel the intricate dynamics and transitions within the system. This analysis not only uncovers the system's behavior under varying conditions but also sheds light on its stability and the emergence of bifurcation phenomena. Our research delves into the retrieval of soliton solutions within the model. The exploration of solitons is of paramount significance, offering insights into localized, self-sustaining waveforms that often play a crucial role in nonlinear systems. These soliton solutions are identified, characterized, and their relevance to the model is established. The paper addresses the complex dynamics of the system in the presence of perturbation terms. By incorporating perturbations into the analysis, we elucidate how external influences impact the system's behavior and lead to chaotic phenomena. This analysis helps uncover the system's sensitivity to external factors and provides a deeper understanding of chaotic behavior.
{"title":"Bifurcation Analysis and Chaotic Behavior of the Concatenation Model with Power-Law Nonlinearity","authors":"Lu Tang, Anjan Biswas, Yakup Yildirim, Asim Asiri","doi":"10.37256/cm.4420233606","DOIUrl":"https://doi.org/10.37256/cm.4420233606","url":null,"abstract":"This paper presents a comprehensive analysis of the concatenation model with power-law nonlinearity. The research encompasses multiple key aspects, providing a detailed exploration of the model's behavior and implications within the context of nonlinear dynamics and optics. The study commences with an in-depth bifurcation analysis, aiming to unravel the intricate dynamics and transitions within the system. This analysis not only uncovers the system's behavior under varying conditions but also sheds light on its stability and the emergence of bifurcation phenomena. Our research delves into the retrieval of soliton solutions within the model. The exploration of solitons is of paramount significance, offering insights into localized, self-sustaining waveforms that often play a crucial role in nonlinear systems. These soliton solutions are identified, characterized, and their relevance to the model is established. The paper addresses the complex dynamics of the system in the presence of perturbation terms. By incorporating perturbations into the analysis, we elucidate how external influences impact the system's behavior and lead to chaotic phenomena. This analysis helps uncover the system's sensitivity to external factors and provides a deeper understanding of chaotic behavior.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"11 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To unify and extend the study of various subclasses of starlike and convex functions, here we introduce a new subclass of λ-pseudo starlike symmetric functions. To add more versatility to our study, we have defined a new class of functions subordinate to a conic region impacted by the well-known Janowski functions. This study extends well-known results and unifies the studies of various subclasses of α-convex functions. Coefficient estimates of the inverse function and the Fekete-Szegő result for the function class are the main results. Some interesting special cases of our main results are also presented here.
{"title":"Unified Solution of Some Properties Related to λ-Pseudo Starlike Functions","authors":"Musthafa Ibrahim, K. R. Karthikeyan","doi":"10.37256/cm.4420232366","DOIUrl":"https://doi.org/10.37256/cm.4420232366","url":null,"abstract":"To unify and extend the study of various subclasses of starlike and convex functions, here we introduce a new subclass of λ-pseudo starlike symmetric functions. To add more versatility to our study, we have defined a new class of functions subordinate to a conic region impacted by the well-known Janowski functions. This study extends well-known results and unifies the studies of various subclasses of α-convex functions. Coefficient estimates of the inverse function and the Fekete-Szegő result for the function class are the main results. Some interesting special cases of our main results are also presented here.","PeriodicalId":29767,"journal":{"name":"Contemporary Mathematics","volume":"54 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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