Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions under which the dynamical structures of the original continuous dynamical systems are retained in their discretized dynamical systems, and the types of fixed points are identified if they change due to discretization. We also discuss stability of the fixed points in the discrete dynamical systems. The obtained general results are applied to Sel'kov model and Lengyel-Epstein model.
{"title":"Types and stability of fixed points for positivity-preserving discretized dynamical systems in two dimensions","authors":"S. Ohmori, Y. Yamazaki","doi":"10.14495/jsiaml.15.73","DOIUrl":"https://doi.org/10.14495/jsiaml.15.73","url":null,"abstract":"Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions under which the dynamical structures of the original continuous dynamical systems are retained in their discretized dynamical systems, and the types of fixed points are identified if they change due to discretization. We also discuss stability of the fixed points in the discrete dynamical systems. The obtained general results are applied to Sel'kov model and Lengyel-Epstein model.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73702250","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":"Numerical verification method on complex ODEs for existence of global solutions within finite domains","authors":"Koki Nitta, N. Yamamoto","doi":"10.14495/jsiaml.15.69","DOIUrl":"https://doi.org/10.14495/jsiaml.15.69","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72778547","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":"Stable probability of reduced matrix obtained by Gaussian random projection","authors":"Hiroki Sakamoto, Kazuhiro Sato","doi":"10.14495/jsiaml.15.77","DOIUrl":"https://doi.org/10.14495/jsiaml.15.77","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89269206","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":"Improvement of the square-root Vélu's formulas for isogeny-based cryptography","authors":"Saki Otsuki, Hiroshi Onuki, T. Takagi","doi":"10.14495/jsiaml.15.61","DOIUrl":"https://doi.org/10.14495/jsiaml.15.61","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87430707","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 attempt to provide an elementary introduction to the excursion risk theory by constructing a discrete-time analogue. The excursion risk theory is a theory of calculating risks in investments that use mean-reverting trading signals. We consider the case where the trading signal is a simple symmetric random walk (RW) and use the excursions of them to compute several quantities of risks in the investments. It may be said that this paper gives one way of applying the excursion theory of RWs that mathematicians have been studying for a long time to mathematical finance.
{"title":"An introduction to excursion risk through discrete-time excursions","authors":"Takahiko Fujita, Naohiro Yoshida","doi":"10.14495/jsiaml.15.97","DOIUrl":"https://doi.org/10.14495/jsiaml.15.97","url":null,"abstract":"In this paper, we attempt to provide an elementary introduction to the excursion risk theory by constructing a discrete-time analogue. The excursion risk theory is a theory of calculating risks in investments that use mean-reverting trading signals. We consider the case where the trading signal is a simple symmetric random walk (RW) and use the excursions of them to compute several quantities of risks in the investments. It may be said that this paper gives one way of applying the excursion theory of RWs that mathematicians have been studying for a long time to mathematical finance.","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800424","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":"Counting and detecting figures using persistent homology","authors":"Haruhisa Oda","doi":"10.14495/jsiaml.15.33","DOIUrl":"https://doi.org/10.14495/jsiaml.15.33","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90250487","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}
M. Kishida, T. Kurahashi, Kazuhiko Akeda, Kenichi Okumura, N. Nakagawa, Syuichi Yamaguchi, Hidetoshi Kaida
{"title":"Topology optimization based on the modified optimality criteria method for application to products","authors":"M. Kishida, T. Kurahashi, Kazuhiko Akeda, Kenichi Okumura, N. Nakagawa, Syuichi Yamaguchi, Hidetoshi Kaida","doi":"10.14495/jsiaml.15.65","DOIUrl":"https://doi.org/10.14495/jsiaml.15.65","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74081256","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":"Analysis of the limit values of chaos degree for infinite number of partitions in asymmetric tent maps","authors":"Tomoyuki Mao, Hidetoshi Okutomi, K. Umeno","doi":"10.14495/jsiaml.15.41","DOIUrl":"https://doi.org/10.14495/jsiaml.15.41","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85444274","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":"Tidal current estimation analysis and calculation of tidal power generation potential for a Tokyo Bay model using the extended Kalman filter FEM","authors":"T. Kurahashi","doi":"10.14495/jsiaml.15.89","DOIUrl":"https://doi.org/10.14495/jsiaml.15.89","url":null,"abstract":"","PeriodicalId":42099,"journal":{"name":"JSIAM Letters","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77648524","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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