We present a criterion for the existence of a stable almost periodic solution for a cooperative almost periodic system. We also give conditions under which there is global stability of this almost periodic solution in a certain domain. We apply our results to systems arising from cell volume growth with almost periodic growth factors, and to systems arising from Michaelis–Menten formalism modeling enzyme kinetics with an almost periodic substrate input and an almost periodic enzyme replacement.
{"title":"Almost periodic solutions for seasonal cooperative systems","authors":"H. Díaz-Marín, F. J. López-Hernández, O. Osuna","doi":"10.4064/ap210128-19-8","DOIUrl":"https://doi.org/10.4064/ap210128-19-8","url":null,"abstract":"We present a criterion for the existence of a stable almost periodic solution for a cooperative almost periodic system. We also give conditions under which there is global stability of this almost periodic solution in a certain domain. We apply our results to systems arising from cell volume growth with almost periodic growth factors, and to systems arising from Michaelis–Menten formalism modeling enzyme kinetics with an almost periodic substrate input and an almost periodic enzyme replacement.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"32 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70582295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. An existence and asymptotic theory is built for second order half-linear differential equations of the form where α > 0 is constant and p ( t ) and q ( t ) are positive continuous functions on [ a, ∞ ) , in which a crucial role is played by a pair of the generalized Riccati differential equations associated with (A). An essential part of the theory is the construction of nonoscillatory solutions x ( t ) of (A) enjoying explicit exponential-integral representations in terms of solutions u ( t ) of (R1) or in terms of solutions v ( t ) of (R2).
{"title":"Extreme and moderate solutions of nonoscillatory\u0000second order half-linear differential equations","authors":"J. Jaros, T. Kusano, T. Tanigawa","doi":"10.4064/ap201216-12-8","DOIUrl":"https://doi.org/10.4064/ap201216-12-8","url":null,"abstract":". An existence and asymptotic theory is built for second order half-linear differential equations of the form where α > 0 is constant and p ( t ) and q ( t ) are positive continuous functions on [ a, ∞ ) , in which a crucial role is played by a pair of the generalized Riccati differential equations associated with (A). An essential part of the theory is the construction of nonoscillatory solutions x ( t ) of (A) enjoying explicit exponential-integral representations in terms of solutions u ( t ) of (R1) or in terms of solutions v ( t ) of (R2).","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"12 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70581587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on approximation and homotopy in $C(X,S^n)$, $n=1,3,7$","authors":"E. Becker","doi":"10.4064/AP200803-9-1","DOIUrl":"https://doi.org/10.4064/AP200803-9-1","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70581147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We prove that every ( 2 n +1 )-dimensional η -Einstein contact metric manifold (i.e., the Ricci tensor S satisfies S = αg + βη ⊗ η for some smooth functions α, β ) with purely transversal Bach tensor is Einstein.
{"title":"$eta $-Einstein contact metric manifolds with\u0000purely transversal Bach tensor","authors":"Amalendu Ghosh","doi":"10.4064/AP201007-18-2","DOIUrl":"https://doi.org/10.4064/AP201007-18-2","url":null,"abstract":". We prove that every ( 2 n +1 )-dimensional η -Einstein contact metric manifold (i.e., the Ricci tensor S satisfies S = αg + βη ⊗ η for some smooth functions α, β ) with purely transversal Bach tensor is Einstein.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70581324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bounding the length of gradient trajectories","authors":"D. D’Acunto, K. Kurdyka","doi":"10.4064/ap200527-3-6","DOIUrl":"https://doi.org/10.4064/ap200527-3-6","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70580906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a consumption-investment problem in which the investor has an access to the bond market. In our approach prices of bonds with different maturities are described by the general HJM factor model. We assume that the bond market consist of entire family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds. The investor's objective is to maximize time-additive utility of the consumption process. We solve the problem by means of the HJB equation for which we prove required regularity of its solution and all required estimates to ensure applicability of the verification theorem. Explicit calculations for certain particular models are presented.
{"title":"The investor problem based on the HJM model","authors":"S. Peszat, Dariusz Zawisza","doi":"10.4064/ap210429-12-11","DOIUrl":"https://doi.org/10.4064/ap210429-12-11","url":null,"abstract":"We consider a consumption-investment problem in which the investor has an access to the bond market. In our approach prices of bonds with different maturities are described by the general HJM factor model. We assume that the bond market consist of entire family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds. The investor's objective is to maximize time-additive utility of the consumption process. We solve the problem by means of the HJB equation for which we prove required regularity of its solution and all required estimates to ensure applicability of the verification theorem. Explicit calculations for certain particular models are presented.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45061362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.
{"title":"Convexity of the class of currents with finite relative energy","authors":"Duc-Viet Vu","doi":"10.4064/ap210930-24-3","DOIUrl":"https://doi.org/10.4064/ap210930-24-3","url":null,"abstract":"We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47856985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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