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Joining Iso-Structured Models with Commutative Orthogonal Block Structure 用交换正交块结构连接等结构模型
WSEAS Transactions on Mathematics Pub Date : 2023-07-27 DOI: 10.37394/23206.2023.22.64
C. Santos, C. Dias, C. Nunes, J. Mexia
{"title":"Joining Iso-Structured Models with Commutative Orthogonal Block Structure","authors":"C. Santos, C. Dias, C. Nunes, J. Mexia","doi":"10.37394/23206.2023.22.64","DOIUrl":"https://doi.org/10.37394/23206.2023.22.64","url":null,"abstract":"In this work, we focus on a special class of mixed models, named models with commutative orthogonal block structure (COBS), whose covariance matrix is a linear combination of known pairwise orthogonal projection matrices that add to the identity matrix, and for which the orthogonal projection matrix on the space spanned by the mean vector commutes with the covariance matrix. The COBS have least squares estimators giving the best linear unbiased estimators for estimable vectors. Our approach to COBS relies on their algebraic structure, based on commutative Jordan algebras of symmetric matrices, which proves to be advantageous as it leads to important results in the estimation. Specifically, we are interested in iso-structured COBS, applying to them the operation of models joining. We show that joining iso-structured COBS gives COBS and that the estimators for the joint model may be obtained from those for the individual models.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43165881","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
Bayesian Inference for a New Negative Binomial-Samade Model for Time Series Data Counts with Its Properties and Applications 一种新的时间序列数据计数负二项samade模型的贝叶斯推断及其性质和应用
WSEAS Transactions on Mathematics Pub Date : 2023-07-27 DOI: 10.37394/23206.2023.22.65
S. Aryuyuen, Issaraporn Thaimsorn, U. Tonggumnead
{"title":"Bayesian Inference for a New Negative Binomial-Samade Model for Time Series Data Counts with Its Properties and Applications","authors":"S. Aryuyuen, Issaraporn Thaimsorn, U. Tonggumnead","doi":"10.37394/23206.2023.22.65","DOIUrl":"https://doi.org/10.37394/23206.2023.22.65","url":null,"abstract":"A new distribution was developed that mixed the negative binomial (NB) and Samade distributions, called the negative binomial-Samade (NB-SA) distribution. The properties of this distribution were studied, and the newly created distribution was applied using the framework of generalized linear models to build a time series data count model. The characteristics of overdispersion and heavy-tailed distribution of the count response variables were applied in the actual dataset modeling. Distribution parameters and the regression coefficient were estimated using a Bayesian approach. Results showed that the NB-SA model had significantly the highest efficiency compared with the classical NB and Poisson models for analyzing factors influencing the daily number of COVID-19 deaths in Thailand.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41577963","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 F−flat Structures in Vector Bundles Over Foliated Manifolds 叶状流形上向量束中的F−平面结构
WSEAS Transactions on Mathematics Pub Date : 2023-07-25 DOI: 10.37394/23206.2023.22.63
C. Apreutesei
{"title":"On F−flat Structures in Vector Bundles Over Foliated Manifolds","authors":"C. Apreutesei","doi":"10.37394/23206.2023.22.63","DOIUrl":"https://doi.org/10.37394/23206.2023.22.63","url":null,"abstract":": We give the definition of the families of F − flat structures and F − flat connections in vector bundles over F − foliated manifolds. Essential: existence of a F − flat structure is equivalent to the existence of a F − flat connection. Let { λ ξ } be a family of subbundles of a vector bundle ξ . There exists a family of F − flat structure { λ Λ } in ξ , relative at λ ξ , if and only if exists a family of F − flat connections { λ ∇} in ξ (Theorem III.5). F − flat structures (Theorem III.1), and integrable F − flat structures (Theorem III.5), are considered. Finally, integrable Γ − structure and F − flat structures on total space of a vector bundle are presented (Theorem IV.1).","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48696087","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 Four Dimensional Absolute Valued Algebras With nonzero Omnipresent Idempotent 非零无不在幂等的四维绝对值代数
WSEAS Transactions on Mathematics Pub Date : 2023-07-25 DOI: 10.37394/23206.2023.22.62
Noureddine Motya, A. Moutassim
{"title":"On Four Dimensional Absolute Valued Algebras With nonzero Omnipresent Idempotent","authors":"Noureddine Motya, A. Moutassim","doi":"10.37394/23206.2023.22.62","DOIUrl":"https://doi.org/10.37394/23206.2023.22.62","url":null,"abstract":"n this paper, we studies the absolute valued algebras of dimension four, containing nonzero omnipresent idempotent. And we construct algebraically some news classes of algebras.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43900824","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 Orthogonality According to an Index in Semi–normed Spaces 关于半赋范空间中索引的正交性
WSEAS Transactions on Mathematics Pub Date : 2023-07-24 DOI: 10.37394/23206.2023.22.61
Artur Stringa, Arber Qoshja
{"title":"On Orthogonality According to an Index in Semi–normed Spaces","authors":"Artur Stringa, Arber Qoshja","doi":"10.37394/23206.2023.22.61","DOIUrl":"https://doi.org/10.37394/23206.2023.22.61","url":null,"abstract":"In a recent study, we introduce the concept of orthogonality and transversality according to an index, obtaining some results on linear dependence and independence in semi-normed spaces. In this paper, we discuss the concept of orthogonality in semi-normed spaces.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46756798","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
A Posteriori Improvement in Projection Method 投影法的后验改进
WSEAS Transactions on Mathematics Pub Date : 2023-07-24 DOI: 10.37394/23206.2023.22.60
Yu. K. Dem’yanovich, I. Burova
{"title":"A Posteriori Improvement in Projection Method","authors":"Yu. K. Dem’yanovich, I. Burova","doi":"10.37394/23206.2023.22.60","DOIUrl":"https://doi.org/10.37394/23206.2023.22.60","url":null,"abstract":"This work is devoted to the renement of the approximate solution, obtained by the projection method. The proposed approach uses expanding the design space by adding new coordinate functions. As a result, it is possible to clarify previously obtained solution using small computer resources. Applying this approach to the finite element method allows produce a local renement of the mentioned solution. Suggested Approach illustrated in the finite element method for a boundary value problem second order in one-dimensional and two-dimensional cases.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46560418","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 r-circulant Matrices Associated with k-Fermat and k-Mersenne Numbers 与k-Fermat和k-Mersenne数相关的r-循环矩阵
WSEAS Transactions on Mathematics Pub Date : 2023-07-24 DOI: 10.37394/23206.2023.22.59
B. Kuloğlu, Engin Eser, Engin Özkan
{"title":"The r-circulant Matrices Associated with k-Fermat and k-Mersenne Numbers","authors":"B. Kuloğlu, Engin Eser, Engin Özkan","doi":"10.37394/23206.2023.22.59","DOIUrl":"https://doi.org/10.37394/23206.2023.22.59","url":null,"abstract":"In this study, the main goal is to investigate the r-circulant matrices of k-Fermat and k-Mersenne numbers, then to find eigenvalues, determinants of these matrices, to evaluate their different norms (Spectral and Euclidean) and finally to find the right and skew-right circulant matrices.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45193595","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
Accurate Average Run Length Analysis for Detecting Changes in a Long-Memory Fractionally Integrated MAX Process Running on EWMA Control Chart 用于检测在EWMA控制图上运行的长内存分数积分MAX过程变化的精确平均运行长度分析
WSEAS Transactions on Mathematics Pub Date : 2023-07-24 DOI: 10.37394/23206.2023.22.58
W. Peerajit
{"title":"Accurate Average Run Length Analysis for Detecting Changes in a Long-Memory Fractionally Integrated MAX Process Running on EWMA Control Chart","authors":"W. Peerajit","doi":"10.37394/23206.2023.22.58","DOIUrl":"https://doi.org/10.37394/23206.2023.22.58","url":null,"abstract":"Numerical evaluation of the average run length (ARL) when detecting changes in the mean of an autocorrelated process running on an exponentially weighted moving average (EWMA) control chart has received considerable attention. However, accurate computation of the ARL of changes in the mean of a long-memory model with an exogenous (X) variable, which often occurs in practice, is challenging. Herein, we provide an accurate determination of the ARL for long-memory models such as the fractionally integrated MAX processes (FIMAX) with exponential white noise running on an EWMA control chart by using an analytical formula based on an integral equation. From a computational perspective, the analytical formula approach is accomplished by solving the solution for the integral equation obtained via the Fredholm integral equation of the second kind. Moreover, the existence and uniqueness of the solution for the analytical formula were confirmed via Banach’s fixed-point theorem. Its efficacy was compared with that of the ARL derived by using the well-known numerical integral equation (NIE) technique under the same circumstances in terms of the ARL percentage accuracy and computational processing time. The percentage accuracy was 100%, which indicates excellent agreement between the two methods, and the analytical formula also required much less computational processing time. An example to illustrate the effectiveness of the proposed approach with a process involving real data running on an EWMA control chart is also provided herein. The explicit formula method offers an accurate determination of the ARL and a new approach for validating its computation, especially for long-memory scenarios running on EWMA control charts.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45563807","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: 1
On the Divergence of the Sum of Prime Reciprocals 关于素数倒数和的发散性
WSEAS Transactions on Mathematics Pub Date : 2023-07-14 DOI: 10.37394/23206.2023.22.57
P. Dusart
{"title":"On the Divergence of the Sum of Prime Reciprocals","authors":"P. Dusart","doi":"10.37394/23206.2023.22.57","DOIUrl":"https://doi.org/10.37394/23206.2023.22.57","url":null,"abstract":"The sum of the reciprocals of all prime numbers diverges but the divergence is very slow. We propose effective lower and upper bounds for partial sums under the Riemann hypothesis. We give an explicit error term for all Mertens’ theorems.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47358358","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 K-Chebsyhev Sequence 关于K-Chebsyhev序列
WSEAS Transactions on Mathematics Pub Date : 2023-07-14 DOI: 10.37394/23206.2023.22.56
E. Ozkan, Hakan Akkus
{"title":"On K-Chebsyhev Sequence","authors":"E. Ozkan, Hakan Akkus","doi":"10.37394/23206.2023.22.56","DOIUrl":"https://doi.org/10.37394/23206.2023.22.56","url":null,"abstract":"In this study, firstly the k-Chebsyhev sequence is defined, and some terms of this sequence are given. Then, the relations between the terms of the k-Chebsyhev sequence are presented and the generating function of this sequence is obtained. In addition, the Catalan transformation of the sequence is given and the generating function of the Catalan k-Chebsyhev sequence is obtained. Finally, the Hankel transform is applied to the Catalan k-Chebsyhev transform.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"331 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41281689","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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