This abstract introduces a novel application of the Nelder-Mead algorithm in optimizing solutions to Ordinary Differential Equations (ODEs) with derivative boundary conditions. The study presents a refined methodology that leverages the Nelder-Mead algorithm’s adaptability to tackle ODEs characterized by intricate derivative constraints. With the aim of enhancing the toolkit for solving complex ODEs, the objective of this research is to showcase the algorithm’s efficacy in optimizing solutions under derivative boundary conditions. The methodology involves adapting the Nelder-Mead algorithm to navigate the param-eter space while satisfying both the ODEs and their derivative constraints. Experimental results demonstrate the algorithm’s capability to identify solutions that meet these stringent requirements, marking a significant advancement in addressing ODEs with derivative boundary conditions. The study concludes by emphasizing the algorithm’s potential for advancing ODE-solving techniques, particularly in scenarios where gradient-based methods struggle, thus widening the scope of applications across various scientific and engineering domains.
{"title":"Optimizing ODE solutions: application of Nelder-Mead algorithm for solving mixed boundary value problems","authors":"A. Wusu, O. Olabanjo","doi":"10.56947/amcs.v20.226","DOIUrl":"https://doi.org/10.56947/amcs.v20.226","url":null,"abstract":"This abstract introduces a novel application of the Nelder-Mead algorithm in optimizing solutions to Ordinary Differential Equations (ODEs) with derivative boundary conditions. The study presents a refined methodology that leverages the Nelder-Mead algorithm’s adaptability to tackle ODEs characterized by intricate derivative constraints. With the aim of enhancing the toolkit for solving complex ODEs, the objective of this research is to showcase the algorithm’s efficacy in optimizing solutions under derivative boundary conditions. The methodology involves adapting the Nelder-Mead algorithm to navigate the param-eter space while satisfying both the ODEs and their derivative constraints. Experimental results demonstrate the algorithm’s capability to identify solutions that meet these stringent requirements, marking a significant advancement in addressing ODEs with derivative boundary conditions. The study concludes by emphasizing the algorithm’s potential for advancing ODE-solving techniques, particularly in scenarios where gradient-based methods struggle, thus widening the scope of applications across various scientific and engineering domains.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"17 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139389475","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}
Let X be a Banach space and F a subset of X. In this paper, we showed weak and strong convergence theorems for a Krasnoselskij-type iterative method to approximate coupled solution of nonexpansive operator E: FxF-> F, where F is nonempty, depending on two variables. Furthermore, we obtained a fixed point for a (b, theta, L)-almost contraction operator E: X +X-> X using the Krasnoselskij iteration {xn}n=0infty.
让 X 是一个巴拿赫空间，F 是 X 的一个子集。在本文中，我们证明了 Krasnoselskij 型迭代法的弱收敛定理和强收敛定理，该迭代法可以近似地求解非膨胀算子 E: FxF-> F 的耦合解，其中 F 是非空的，取决于两个变量。此外，我们利用克拉斯诺瑟尔斯克迭代{xn}n=0infty得到了（b, theta, L）近似收缩算子E：X +X-> X的定点。
{"title":"Results of coupled iterative fixed point approximation","authors":"Afeez Oyekanmi, Kamilu Rauf","doi":"10.56947/amcs.v20.236","DOIUrl":"https://doi.org/10.56947/amcs.v20.236","url":null,"abstract":"Let X be a Banach space and F a subset of X. In this paper, we showed weak and strong convergence theorems for a Krasnoselskij-type iterative method to approximate coupled solution of nonexpansive operator E: FxF-> F, where F is nonempty, depending on two variables. Furthermore, we obtained a fixed point for a (b, theta, L)-almost contraction operator E: X +X-> X using the Krasnoselskij iteration {xn}n=0infty.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"35 52","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139388789","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 the paper, we study the uniqueness of powers of meromorphic functions for sharing two finite sets with finite weights and find Bi-unique range sets for meromorphic functions of power at least d. Examples are given in support of our result. We are inspired by the results due to A. Banerjee [Nihonkai Math. J. Vol.24 (2013), 121-134] and a recent result due to S. Mallick and D. Sarkar [Mat. Stud. 50(2018), 143-157.]
在本文中，我们研究了共享两个有限权集的分形函数幂的唯一性，并为幂至少为 d 的分形函数找到了双唯一范围集。我们受到了 A. Banerjee [Nihonkai Math. J. Vol.24 (2013), 121-134] 的结果以及 S. Mallick 和 D. Sarkar [Mat. Stud. 50(2018), 143-157] 的最新结果的启发。
{"title":"Bi-uniqueness range sets for powers of meromorphic functions","authors":"P. Sahoo, A. Sarkar","doi":"10.56947/amcs.v20.223","DOIUrl":"https://doi.org/10.56947/amcs.v20.223","url":null,"abstract":"In the paper, we study the uniqueness of powers of meromorphic functions for sharing two finite sets with finite weights and find Bi-unique range sets for meromorphic functions of power at least d. Examples are given in support of our result. We are inspired by the results due to A. Banerjee [Nihonkai Math. J. Vol.24 (2013), 121-134] and a recent result due to S. Mallick and D. Sarkar [Mat. Stud. 50(2018), 143-157.]","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"28 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139388922","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 (Fixed Point Theory Appl. 94:6, 2012), Wardowski introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalizes the Banach contraction principle. The aim of this paper is to introduce a modified -F-weak contractions with respect to a self-mapping on a metric space and to obtain fixed point results. Examples are provided to support results and concepts presented herein. As an application of our results, periodic point results for the F-contractions in metric spaces are proved.
在（Fixed Point Theory Appl.本文的目的是引入关于公元空间上自映射的修正-F-弱收缩，并获得定点结果。本文提供了一些例子来支持本文提出的结果和概念。作为我们结果的应用，本文证明了公度空间中 F 弱收缩的周期点结果。
{"title":"Fixed point theorems for modified F-weak contractions via α-admissible mapping with application to periodic points","authors":"Muhammed Raji, Musa Adeku Ibrahim","doi":"10.56947/amcs.v20.232","DOIUrl":"https://doi.org/10.56947/amcs.v20.232","url":null,"abstract":"In (Fixed Point Theory Appl. 94:6, 2012), Wardowski introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalizes the Banach contraction principle. The aim of this paper is to introduce a modified -F-weak contractions with respect to a self-mapping on a metric space and to obtain fixed point results. Examples are provided to support results and concepts presented herein. As an application of our results, periodic point results for the F-contractions in metric spaces are proved.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"26 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139389274","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, we prove some fixed point theorems for generalized F-alpha contraction in the setting of complete S-metric spaces and give some consequences as corollaries of the main results. Also, we furnish an illustrative example in support of the result. Our results extend, generalize and enrich several previous works from the existing literature (see, for example [6], [19], [27], [38] and some others).
在本文中，我们证明了在完全 S 度量空间中广义 F-α 收缩的一些定点定理，并给出了作为主要结果推论的一些后果。此外，我们还提供了一个示例来支持这一结果。我们的结果扩展、概括并丰富了现有文献中的一些前人成果（参见 [6]、[19]、[27]、[38] 及其他一些文献）。
{"title":"Fixed point results for generalized F-alpha contraction in complete S-metric spaces","authors":"G. Saluja","doi":"10.56947/amcs.v20.229","DOIUrl":"https://doi.org/10.56947/amcs.v20.229","url":null,"abstract":"In this paper, we prove some fixed point theorems for generalized F-alpha contraction in the setting of complete S-metric spaces and give some consequences as corollaries of the main results. Also, we furnish an illustrative example in support of the result. Our results extend, generalize and enrich several previous works from the existing literature (see, for example [6], [19], [27], [38] and some others).","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"20 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139389413","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, lower bound and upper bound on the covering radius of DNA codes over N with respect to euclidean distance are given. Also determine the covering radius of various Repetition DNA codes, Simplex DNA code Type α and Simplex DNA code Type β and bounds on the covering radius for MacDonald DNA codes of both types over N.
本文给出了关于欧几里得距离的 N 上 DNA 码覆盖半径的下限和上限。还确定了 N 上各种重复 DNA 码、α 型简约 DNA 码和β型简约 DNA 码的覆盖半径，以及两种类型的 MacDonald DNA 码的覆盖半径边界。
{"title":"On DNA code over a finite ring and its related parameters","authors":"Chella Pandian P","doi":"10.56947/amcs.v19.216","DOIUrl":"https://doi.org/10.56947/amcs.v19.216","url":null,"abstract":"In this paper, lower bound and upper bound on the covering radius of DNA codes over N with respect to euclidean distance are given. Also determine the covering radius of various Repetition DNA codes, Simplex DNA code Type α and Simplex DNA code Type β and bounds on the covering radius for MacDonald DNA codes of both types over N.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"69 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175690","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 the effects of the perturbations on the motion of the test particle variable mass in the bi-circular Sun perturbed oblate Earth-Moon system where primary is taken as oblate Earth, secondary is taken as Moon and the third body is assumed as Sun. These three bodies are moving in the same plane around barycenter. The fourth and smallest body (test particle is assumed to be having variable mass with time) is moving in the space under the perturbations such as gravitational forces of the primaries, the solar radiation pressure, the coriolis and centrifugal forces. Then we determine the equations of motion, the locations of critical points, their stability and periodic orbits.
{"title":"Bi-circular model with test particle variable mass","authors":"Abdullah A. Ansari, Saba Bano","doi":"10.56947/amcs.v19.217","DOIUrl":"https://doi.org/10.56947/amcs.v19.217","url":null,"abstract":"This paper presents the effects of the perturbations on the motion of the test particle variable mass in the bi-circular Sun perturbed oblate Earth-Moon system where primary is taken as oblate Earth, secondary is taken as Moon and the third body is assumed as Sun. These three bodies are moving in the same plane around barycenter. The fourth and smallest body (test particle is assumed to be having variable mass with time) is moving in the space under the perturbations such as gravitational forces of the primaries, the solar radiation pressure, the coriolis and centrifugal forces. Then we determine the equations of motion, the locations of critical points, their stability and periodic orbits.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"13 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175413","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 we compute the algebraic numerical range for inner product type integral transformers and show that the basic properties of the algeraic numerical range holds for this operator.
在本文中，我们计算了内积型积分变换器的代数数值范围，并证明该算子的代数数值范围的基本性质成立。
{"title":"Numerical range of inner product type integral transformers on Hilbert spaces","authors":"Priscah Moraa, D. Ambogo, F. Nyamwala","doi":"10.56947/amcs.v19.212","DOIUrl":"https://doi.org/10.56947/amcs.v19.212","url":null,"abstract":"In this paper we compute the algebraic numerical range for inner product type integral transformers and show that the basic properties of the algeraic numerical range holds for this operator.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"67 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175741","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 Interval-valued Complex Pythagorean Fuzzy Set (IVCPFS), an extension of the Pythagorean Fuzzy Set (PFS), offers a more accurate description of uncertainty than traditional fuzzy sets. It has numerous uses in fuzzy control. In this research study, we show the concept of Interval-Valued Complex Pythagorean Fuzzy Graph Structure (IVCPFGS), as well as the results of some regular IVCPFGS and totally regular IVCPFGS, along with the degree of vertex present. We also discussed the subdivision of an IVCPFGS, the complement IVCPFGS, and the strength of a Path in an IVCPFGS. Finally, we discuss a realworld example based on temperature variation and climatic data analysis in an environment with an interval-valued complex Pythagorean fuzzy framework to demonstrate the applicability of the generated results.
{"title":"Climatic analysis based on interval-valued complex Pythagorean fuzzy graph structure","authors":"S.N.SUBER Bathusha, S.ANGELIN Kavitha Raj","doi":"10.56947/amcs.v19.213","DOIUrl":"https://doi.org/10.56947/amcs.v19.213","url":null,"abstract":"The Interval-valued Complex Pythagorean Fuzzy Set (IVCPFS), an extension of the Pythagorean Fuzzy Set (PFS), offers a more accurate description of uncertainty than traditional fuzzy sets. It has numerous uses in fuzzy control. In this research study, we show the concept of Interval-Valued Complex Pythagorean Fuzzy Graph Structure (IVCPFGS), as well as the results of some regular IVCPFGS and totally regular IVCPFGS, along with the degree of vertex present. We also discussed the subdivision of an IVCPFGS, the complement IVCPFGS, and the strength of a Path in an IVCPFGS. Finally, we discuss a realworld example based on temperature variation and climatic data analysis in an environment with an interval-valued complex Pythagorean fuzzy framework to demonstrate the applicability of the generated results.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"97 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175845","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 some considerations on summation method on infinite divergent series. Irrefutably divergent series don’t have a sum in the traditional logic of the term. However there are extensions, where transformed definitions apportion changed values to the same divergent series and they rarely have agreeable properties. Particularly, at beginning and manipulating these instinctively, it easily comes across nasty paradoxes. In this article for any odd prime p, the divergent series and on using this representation for further leads to a paradoxical bewildering novel formula which evidently contradicts the basic principles of arithmetic and the definition of a divergent series identical to Ramanujan paradox. Illustrations to support this illogicality result are discussed analytically and demonstrated graphically.
{"title":"On the paradoxical behavior of divergent series","authors":"K. L. Verma","doi":"10.56947/amcs.v19.219","DOIUrl":"https://doi.org/10.56947/amcs.v19.219","url":null,"abstract":"This paper presents some considerations on summation method on infinite divergent series. Irrefutably divergent series don’t have a sum in the traditional logic of the term. However there are extensions, where transformed definitions apportion changed values to the same divergent series and they rarely have agreeable properties. Particularly, at beginning and manipulating these instinctively, it easily comes across nasty paradoxes. In this article for any odd prime p, the divergent series and on using this representation for further leads to a paradoxical bewildering novel formula which evidently contradicts the basic principles of arithmetic and the definition of a divergent series identical to Ramanujan paradox. Illustrations to support this illogicality result are discussed analytically and demonstrated graphically.","PeriodicalId":504658,"journal":{"name":"Annals of Mathematics and Computer Science","volume":"5 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139174759","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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