Pub Date : 2023-11-01DOI: 10.11648/j.acm.20231205.12
Dandan Ye, Fei Zhang, Yiteng Qin, Xiaojuan Zhang, Ning Zhang, Jin Qin, Wei Chen, Yingze Zhang
{"title":"Trapping Issues for Weight-dependent Walks in the Weighted Extended Cayley Networks","authors":"Dandan Ye, Fei Zhang, Yiteng Qin, Xiaojuan Zhang, Ning Zhang, Jin Qin, Wei Chen, Yingze Zhang","doi":"10.11648/j.acm.20231205.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231205.12","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"8 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139302447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.30546/1683-6154.22.4.2023.443
Yan-Fang Li, D. Lim, Feng Qi
In the paper, by virtue of the famous formula of Fa`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $frac{v^j}{1-operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives.
在这篇论文中，作者通过 Fa`a di Bruno 的著名公式，借助贝尔局部多项式的几个等式，通过两个可微分函数之比导数的公式，并利用其他技术、作者建立了伯努利数和第二类斯特林数的闭式公式，提出了行列式表达式，推导了递推关系，获得了幂级数，并计算了函数 $/frac{v^j}{1-operatorname{e}^{-v}}$、其导数以及克拉克-伊斯梅尔的两个猜想中使用的相关导数的特殊值。通过这些结果，作者还发现了海森堡矩阵的行列式公式，并推导出与函数及其导数相关的序列的对数凸性。
{"title":"Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark–İsmail’s two conjectures","authors":"Yan-Fang Li, D. Lim, Feng Qi","doi":"10.30546/1683-6154.22.4.2023.443","DOIUrl":"https://doi.org/10.30546/1683-6154.22.4.2023.443","url":null,"abstract":"In the paper, by virtue of the famous formula of Fa`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $frac{v^j}{1-operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"238 1 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139316771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-25DOI: 10.11648/j.acm.20231205.11
Ildikó Somogyi, Anna Soós
Fractal interpolation methods became an important method in data processing, even for functions with abrupt changes. In the last few decades it has attracted several authors because it can be applied in various fields. The advantage of these methods are that we can generalize the classical approximation methods and also we can combine these methods for example with Lagrange interpolation, Hermite interpolation or spline interpolation. The classical Lagrange interpolation problem give the construction of a suitable approximate function based on the values of the function on given points. These method was generalized for more than one variable functions. In this article we generalize the so-called algebraic maximal Lagrange interpolation formula in order to approximate functions on a rectangular domain with fractal functions. The construction of the fractal function is made with a so-called iterated function system. This method it has the advantage that all classical methods can be obtained as a particular case of a fractal function. We also use the construction for a polynomial type fractal function and we proof that the Lagrange-type algebraic minimal bivariate fractal function satisfies the required interpolation conditions. Also we give a delimitation of the error, using the result regarding the error of a polynomial fractal interpolation function.
{"title":"Lagrange-type Algebraic Minimal Bivariate Fractal Interpolation Formula","authors":"Ildikó Somogyi, Anna Soós","doi":"10.11648/j.acm.20231205.11","DOIUrl":"https://doi.org/10.11648/j.acm.20231205.11","url":null,"abstract":"Fractal interpolation methods became an important method in data processing, even for functions with abrupt changes. In the last few decades it has attracted several authors because it can be applied in various fields. The advantage of these methods are that we can generalize the classical approximation methods and also we can combine these methods for example with Lagrange interpolation, Hermite interpolation or spline interpolation. The classical Lagrange interpolation problem give the construction of a suitable approximate function based on the values of the function on given points. These method was generalized for more than one variable functions. In this article we generalize the so-called algebraic maximal Lagrange interpolation formula in order to approximate functions on a rectangular domain with fractal functions. The construction of the fractal function is made with a so-called iterated function system. This method it has the advantage that all classical methods can be obtained as a particular case of a fractal function. We also use the construction for a polynomial type fractal function and we proof that the Lagrange-type algebraic minimal bivariate fractal function satisfies the required interpolation conditions. Also we give a delimitation of the error, using the result regarding the error of a polynomial fractal interpolation function.","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135865299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-21DOI: 10.11648/j.acm.20231204.12
Jianbing Cao, Cheng Zhang, S. Arjika
{"title":"A <i>q</i>-Operational Equation for Carlitz’s <i>q</i>-Operators with Some Applications","authors":"Jianbing Cao, Cheng Zhang, S. Arjika","doi":"10.11648/j.acm.20231204.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231204.12","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"29 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78112145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-21DOI: 10.11648/j.acm.20231204.11
M. Nithya, K. Bhuvaneswari, S. Senthil
{"title":"A Fiedler’s Approach to LINEX Intuitionistic Fuzzy C-means Clustering Induced Spectral Initialization for Data Analysis","authors":"M. Nithya, K. Bhuvaneswari, S. Senthil","doi":"10.11648/j.acm.20231204.11","DOIUrl":"https://doi.org/10.11648/j.acm.20231204.11","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"196 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139356648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-20DOI: 10.11648/j.acm.20231203.12
M. Motalane, Z. Mpono
{"title":"Some Triple Generations of the Lyons Sporadic Simple Group <i>Ly</i>","authors":"M. Motalane, Z. Mpono","doi":"10.11648/j.acm.20231203.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231203.12","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"19 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86472166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-13DOI: 10.11648/j.acm.20231203.11
N. Egidi, J. Giacomini, Pierluigi Maponi
{"title":"A Perturbative Approach for the Solution of Sturm-Liouville Problems","authors":"N. Egidi, J. Giacomini, Pierluigi Maponi","doi":"10.11648/j.acm.20231203.11","DOIUrl":"https://doi.org/10.11648/j.acm.20231203.11","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"14 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139370108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-29DOI: 10.11648/j.acm.20231202.12
Basma Mohamed, Mohamed Amin
{"title":"Domination Number and Secure Resolving Sets in Cyclic Networks","authors":"Basma Mohamed, Mohamed Amin","doi":"10.11648/j.acm.20231202.12","DOIUrl":"https://doi.org/10.11648/j.acm.20231202.12","url":null,"abstract":"","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"1 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91215375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-11DOI: 10.11648/j.acm.20231202.11
Huei-li Lin, Kuang-Hui Lin, Y. Shyu, Feng-Bin Wang
and
和
{"title":"Impacts of Seasonal and Spatial Variations on the Transmission of Typhoid Fever","authors":"Huei-li Lin, Kuang-Hui Lin, Y. Shyu, Feng-Bin Wang","doi":"10.11648/j.acm.20231202.11","DOIUrl":"https://doi.org/10.11648/j.acm.20231202.11","url":null,"abstract":"and","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"21 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83978991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-23DOI: 10.11648/j.acm.20231201.13
Aruvi Mathivanan, M. Joseph
: In this paper, we have been found the exact values of distance version of Forgotten Topological index of various types of products such as strong, corona and tensor products of simple and connected graphs. Also we have been calculate the exact values of distance version of Forgotten Topological index of tensor product of path, cycle and complete graphs
{"title":"Distance Version of Forgotten Topological Index of Some Graph Products","authors":"Aruvi Mathivanan, M. Joseph","doi":"10.11648/j.acm.20231201.13","DOIUrl":"https://doi.org/10.11648/j.acm.20231201.13","url":null,"abstract":": In this paper, we have been found the exact values of distance version of Forgotten Topological index of various types of products such as strong, corona and tensor products of simple and connected graphs. Also we have been calculate the exact values of distance version of Forgotten Topological index of tensor product of path, cycle and complete graphs","PeriodicalId":55503,"journal":{"name":"Applied and Computational Mathematics","volume":"37 1","pages":""},"PeriodicalIF":10.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73810090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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