Pub Date : 2023-03-08DOI: 10.48550/arXiv.2303.04434
A. Vavpetic, Emil Žagar
In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal approximation of spherical squares. A detailed analysis and a numerical algorithm are given, providing the best approximant according to the (simplified) radial error, which differs from the one obtained in [1]. The sphere is then approximated by the continuous spline of two and six tensor product quadratic B'ezier patches. It is further shown that the $G^1$ smooth spline of six patches approximating the sphere exists, but it is not a good approximation. The problem of an approximation of spherical rectangles is also addressed and numerical examples indicate that several optimal approximants might exist in some cases, making the problem extremely difficult to handle. Finally, numerical examples are provided that confirm theoretical results.
{"title":"Optimal approximation of spherical squares by tensor product quadratic Bézier patches","authors":"A. Vavpetic, Emil Žagar","doi":"10.48550/arXiv.2303.04434","DOIUrl":"https://doi.org/10.48550/arXiv.2303.04434","url":null,"abstract":"In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B'ezier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal approximation of spherical squares. A detailed analysis and a numerical algorithm are given, providing the best approximant according to the (simplified) radial error, which differs from the one obtained in [1]. The sphere is then approximated by the continuous spline of two and six tensor product quadratic B'ezier patches. It is further shown that the $G^1$ smooth spline of six patches approximating the sphere exists, but it is not a good approximation. The problem of an approximation of spherical rectangles is also addressed and numerical examples indicate that several optimal approximants might exist in some cases, making the problem extremely difficult to handle. Finally, numerical examples are provided that confirm theoretical results.","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"79 1","pages":"128196"},"PeriodicalIF":0.0,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82493698","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}
{"title":"Investigation of chaotic resonance in Type-I and Type-II Morris-Lecar neurons","authors":"Veli Baysal, R. Solmaz, Jun Ma","doi":"10.2139/ssrn.4291549","DOIUrl":"https://doi.org/10.2139/ssrn.4291549","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"1 1","pages":"127940"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73405412","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}
Pub Date : 2022-12-01DOI: 10.1016/j.amc.2022.127421
S. Saha, A. Singh, A. Chattopadhyay
{"title":"Rayleigh-type wave propagation in exponentially graded initially stressed composite structure resting on rigid and yielding foundations","authors":"S. Saha, A. Singh, A. Chattopadhyay","doi":"10.1016/j.amc.2022.127421","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127421","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"125 1","pages":"127421"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73261023","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}
Pub Date : 2022-12-01DOI: 10.1016/j.amc.2022.127460
An Lin, Jun Cheng, Jinde Cao, Hailing Wang, A. Alsaedi
{"title":"Fault detection filtering for MNNs with dynamic quantization and improved protocol","authors":"An Lin, Jun Cheng, Jinde Cao, Hailing Wang, A. Alsaedi","doi":"10.1016/j.amc.2022.127460","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127460","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"13 1","pages":"127460"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82498777","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}
Pub Date : 2022-12-01DOI: 10.1016/j.amc.2022.127435
Dongsun Lee, Chaeyoung Lee
{"title":"Numerical solutions of the Allen-Cahn equation with the p-Laplacian","authors":"Dongsun Lee, Chaeyoung Lee","doi":"10.1016/j.amc.2022.127435","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127435","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"12 1","pages":"127435"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75182742","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}
Pub Date : 2022-12-01DOI: 10.1016/j.amc.2022.127455
W. Lee, B. Park, S. Kim
{"title":"Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme","authors":"W. Lee, B. Park, S. Kim","doi":"10.1016/j.amc.2022.127455","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127455","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"46 1","pages":"127455"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90808652","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}
Pub Date : 2022-12-01DOI: 10.1016/j.amc.2022.127447
Mohanasubha Ramasamy, Subhasri Devarajan, S. Kumarasamy, K. Rajagopal
{"title":"Effect of higher-order interactions on synchronization of neuron models with electromagnetic induction","authors":"Mohanasubha Ramasamy, Subhasri Devarajan, S. Kumarasamy, K. Rajagopal","doi":"10.1016/j.amc.2022.127447","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127447","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"15 1","pages":"127447"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84262816","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}
Pub Date : 2022-12-01DOI: 10.1016/j.amc.2022.127458
Andrii Dmytryshyn, M. Fasi, M. Gulliksson
{"title":"The dynamical functional particle method for multi-term linear matrix equations","authors":"Andrii Dmytryshyn, M. Fasi, M. Gulliksson","doi":"10.1016/j.amc.2022.127458","DOIUrl":"https://doi.org/10.1016/j.amc.2022.127458","url":null,"abstract":"","PeriodicalId":7991,"journal":{"name":"Appl. Math. Comput.","volume":"19 1","pages":"127458"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87439865","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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