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WSEAS Transactions on Mathematics最新文献

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First Hitting Time and Option Pricing Problem Under Geometric Brownian Motion with Singular Volatility 几何布朗运动与奇异波动下的首次击球时间和期权定价问题
WSEAS Transactions on Mathematics Pub Date : 2023-11-22 DOI: 10.37394/23206.2023.22.95
Haoyan Zhang, Yece Zhou, Xuan Li, Yinyin Wu
{"title":"First Hitting Time and Option Pricing Problem Under Geometric Brownian Motion with Singular Volatility","authors":"Haoyan Zhang, Yece Zhou, Xuan Li, Yinyin Wu","doi":"10.37394/23206.2023.22.95","DOIUrl":"https://doi.org/10.37394/23206.2023.22.95","url":null,"abstract":"In this paper, we discuss the first hitting time and option pricing problem under Geometric Brownian motion with singular volatility. By solving the Sturm-Liouville equation and introducing probability scheme, we derive the closed-form solutions to the target problems. At last, numerical results are provided to analyze our calculations.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139248013","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}
引用次数: 0
On the Fundamental Spinor Matrices of Real Quaternions 关于实四元数的基本自旋矩阵
WSEAS Transactions on Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23206.2023.22.93
Tülay Erişir, Emrah Yildirim
{"title":"On the Fundamental Spinor Matrices of Real Quaternions","authors":"Tülay Erişir, Emrah Yildirim","doi":"10.37394/23206.2023.22.93","DOIUrl":"https://doi.org/10.37394/23206.2023.22.93","url":null,"abstract":"In this study, the real quaternions and spinors are studied. The motivation of this study is to express the Hamilton matrices of real quaternions more shortly and elegantly, namely spinors. Therefore, firstly, two transformations between real quaternions and spinors are defined. These transformations are defined for two different spinor matrices corresponding to the left and right Hamilton matrices since the quaternion product is not commutative. Thus, the fundamental spinor matrix corresponding to the fundamental matrix of real quaternions is obtained and some properties are given for these spinor matrices. Finally, the eigenvalues and eigenvectors of the fundamental spinor matrix are obtained.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"69 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271877","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}
引用次数: 0
Rational Solutions to the Burgers' Equation From Particular Polynomials 从特定多项式求伯格斯方程的有理解
WSEAS Transactions on Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23206.2023.22.94
Pierre Gaillard
{"title":"Rational Solutions to the Burgers' Equation From Particular Polynomials","authors":"Pierre Gaillard","doi":"10.37394/23206.2023.22.94","DOIUrl":"https://doi.org/10.37394/23206.2023.22.94","url":null,"abstract":"","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271365","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}
引用次数: 0
Genetic Algorithm-Based Optimization Approach for Solving a Class of Inverse Problems with Tikhonov Regularization 一类具有Tikhonov正则化的逆问题的遗传优化求解方法
WSEAS Transactions on Mathematics Pub Date : 2023-11-14 DOI: 10.37394/23206.2023.22.92
Jamal Daoudi, Chakir Tajani
{"title":"Genetic Algorithm-Based Optimization Approach for Solving a Class of Inverse Problems with Tikhonov Regularization","authors":"Jamal Daoudi, Chakir Tajani","doi":"10.37394/23206.2023.22.92","DOIUrl":"https://doi.org/10.37394/23206.2023.22.92","url":null,"abstract":"In this paper, we are interested in solving the data completion problem for the Laplace equation. It consists to determine the missing data on the inaccessible part of the boundary from overspecified conditions in the accessible part. Knowing that this problem is severely ill-posed, we consider its formulation as an optimization problem using Tikhonov regularization. Then, we consider an optimization approach based on adapted Real Coded Genetic Algorithm (RCGA) to minimize the cost function and recover the missing data. The performed numerical simulations, with different domains, illustrate the accuracy and efficiency of the proposed method with an adequate regularization parameter, in addition to the good agreement between the numerical solutions and different noise level of the given data.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"22 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993742","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}
引用次数: 0
Exact Average Run Length Evaluation on One-Sided and Two-Sided Extended EWMA Control Chart with Correlated Data 具有相关数据的单侧和双侧扩展EWMA控制图的精确平均行程评价
WSEAS Transactions on Mathematics Pub Date : 2023-11-09 DOI: 10.37394/23206.2023.22.90
Phunsa Mongkoltawat, Yupaporn Areepong, Saowanit Sukparungsee
{"title":"Exact Average Run Length Evaluation on One-Sided and Two-Sided Extended EWMA Control Chart with Correlated Data","authors":"Phunsa Mongkoltawat, Yupaporn Areepong, Saowanit Sukparungsee","doi":"10.37394/23206.2023.22.90","DOIUrl":"https://doi.org/10.37394/23206.2023.22.90","url":null,"abstract":"The Extended Exponentially Weighted Moving Average (Extended EWMA) control chart is one of the control charts that can rapidly detect a minor shift. Using the average run length (ARL), the control charts' effectiveness can be evaluated. This research aims to derive the explicit formulations for the ARL on one-sided and two-sided Extend EWMA control charts for the MA(1) model with exponential white noise, as they have not been previously presented. The analytical solution accuracy was determined and compared to the numerical integral equation (NIE) method. The results indicate that the ARL calculated using the explicit formula and the NIE method are nearly identical, demonstrating the validity of the explicit formula. In addition, this study is extended to compare the performance with the Exponentially Weighted Moving Average (EWMA) control chart. The results show that the Extended EWMA control chart has superior efficacy to the EWMA control chart. To demonstrate the efficacy of the proposed method, the analytical solution of ARL is finally applied to real-world data on Thailand's monthly fuel price.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on 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":"135285581","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}
引用次数: 0
The Limited Validity of the Fractional Euler Finite Difference Method and an Alternative Definition of the Caputo Fractional Derivative to Justify Modification of the Method 分数阶欧拉有限差分法的有限有效性和卡普托分数阶导数的另一种定义以证明该方法的修正
WSEAS Transactions on Mathematics Pub Date : 2023-11-09 DOI: 10.37394/23206.2023.22.91
Dominic P. Clemence-Mkhope, Zachary Denton
{"title":"The Limited Validity of the Fractional Euler Finite Difference Method and an Alternative Definition of the Caputo Fractional Derivative to Justify Modification of the Method","authors":"Dominic P. Clemence-Mkhope, Zachary Denton","doi":"10.37394/23206.2023.22.91","DOIUrl":"https://doi.org/10.37394/23206.2023.22.91","url":null,"abstract":"A method, advanced as the fractional Euler finite difference method (FEFDM), a general method for the finite difference discretization of fractional initial value problems (IVPs) for 0<α≤1 for the Caputo derivative, is shown to be valid only for α=1. This is accomplished by establishing, through a recently proposed generalized difference quotient representation of the fractional derivative, that the FEFDM is valid only if a property of the Mittag-Leffler function holds that has only been shown to be valid only for α=1. It is also shown that the FEFDM is inconsistent with the exact discretization of the IVP for the Caputo fractional relaxation equation. The generalized derivative representation is also used to derive a modified generalized Euler’s method, its nonstandard finite difference alternative, their improved Euler versions, and to recover a recent result by Mainardi relating the Caputo and conformable derivatives.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135285598","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}
引用次数: 0
Half-Logistic Odd Power Generalized Weibull-inverse Lindley: Properties, Characterizations, Applications and Covid-19 Data 半逻辑奇幂广义Weibull-inverse Lindley:性质、表征、应用和covid数据
WSEAS Transactions on Mathematics Pub Date : 2023-10-30 DOI: 10.37394/23206.2023.22.89
Arbër Qoshja, Artur Stringa, Klodiana Bani, Rea Spaho
{"title":"Half-Logistic Odd Power Generalized Weibull-inverse Lindley: Properties, Characterizations, Applications and Covid-19 Data","authors":"Arbër Qoshja, Artur Stringa, Klodiana Bani, Rea Spaho","doi":"10.37394/23206.2023.22.89","DOIUrl":"https://doi.org/10.37394/23206.2023.22.89","url":null,"abstract":"Using the Half-Logistic Odd Power Generalised Weibull-G family distributions, this article constructed a novel distribution termed the Half-Logistic Odd Power Generalised Weibull-inverse Lindley. Some of its statistical features are derived by us. Selecting the most efficient estimators is among the basic issues in parameter estimation theory. We are employing maximum likelihood estimation, moment estimation, least squares estimation, weighted least estimation, L-moment estimation, Maximum Product Spacing estimation, and techniques of minimum distances for the parameter estimation for the distribution. We will examine simulation research that compares the various estimators' levels of efficiency using the Kolmogorov-Smirnov test. Lastly, an analysis is done on an actual COVID-19 data set to demonstrate the adaptability of our suggested model in comparison to the fit obtained by several other competing distributions.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136104825","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}
引用次数: 0
Initial Coefficient Estimates of Bi-Univalent Functions Linked with Balancing Coefficients 带平衡系数的双单价函数的初始系数估计
WSEAS Transactions on Mathematics Pub Date : 2023-10-23 DOI: 10.37394/23206.2023.22.87
Arzu Akgül
{"title":"Initial Coefficient Estimates of Bi-Univalent Functions Linked with Balancing Coefficients","authors":"Arzu Akgül","doi":"10.37394/23206.2023.22.87","DOIUrl":"https://doi.org/10.37394/23206.2023.22.87","url":null,"abstract":"","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"75 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135413209","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}
引用次数: 0
Dynamic Behaviors of a Commensalism Model Incorporating Nonselective Harvesting in a Partial Closure 部分闭包中包含非选择收获的共生模型的动态行为
WSEAS Transactions on Mathematics Pub Date : 2023-10-23 DOI: 10.37394/23206.2023.22.88
Qun Zhu, Shijia Lin, Runxin Wu, Fengde Chen
{"title":"Dynamic Behaviors of a Commensalism Model Incorporating Nonselective Harvesting in a Partial Closure","authors":"Qun Zhu, Shijia Lin, Runxin Wu, Fengde Chen","doi":"10.37394/23206.2023.22.88","DOIUrl":"https://doi.org/10.37394/23206.2023.22.88","url":null,"abstract":"A commensalism model incorporating nonselective harvesting in a partial closure is proposed and studied in this paper. Local and global stability properties of the equilibria are investigated, respectively. Our study shows that depending on the fraction of the stock available for harvesting, the system may be extinct, partial survival, or two species coexist in a stable state. Numeric simulations are carried out to show the feasibility of the main results.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"6 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135366472","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}
引用次数: 0
Distributed Optimization Algorithms for Heterogeneous Linear Multi-agent Systems With Inequality Constraints 不等式约束下异构线性多智能体系统的分布式优化算法
WSEAS Transactions on Mathematics Pub Date : 2023-10-20 DOI: 10.37394/23206.2023.22.83
Zhengquan Yang, Wenjie Yu, Zhiyun Gao
{"title":"Distributed Optimization Algorithms for Heterogeneous Linear Multi-agent Systems With Inequality Constraints","authors":"Zhengquan Yang, Wenjie Yu, Zhiyun Gao","doi":"10.37394/23206.2023.22.83","DOIUrl":"https://doi.org/10.37394/23206.2023.22.83","url":null,"abstract":"In this paper, for heterogeneous linear multi-agent systems, a distributed constrained optimization problem about digraphs is studied. Every agent only utilizes local interaction and information such that all agents can achieve the global objective function. The state of each agent is limited to a local inequality constraint set. First, this paper proposes a distributed continuous-time optimization algorithm by designing a left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix, which removes the imbalance of the communication graph. Next, the asymptotical convergence about the algorithm is demonstrated using Lyapunov stability. Finally, two numerical examples are given to illustrate the effectiveness of the algorithm.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617727","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}
引用次数: 0
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