Abstract This paper considers an impulsive stochastic logistic mode l with infinite delay at the phase space Cg. Firstly, the definition of solution to an impulsive stochas tic functional differential equation with infinite delay is establi shed. Based on this definition, we show that our model has a unique global positive solution. Then we establish the sufficient conditions for extinction, nonpersistence in th e mean, weak persistence and stochastic permanence of the solution. The threshold betwe en weak persistence and extinction is obtained. In addition, the effects of impulsi ve perturbation and delay on persistence and extinction are discussed, respectively. F inally, numerical simulations are introduced to support the theoretical analysis results .
{"title":"Persistence and extinction of an impulsive stochastic logistic model with infinite delay","authors":"Chun Lu, X. Ding","doi":"10.18910/58895","DOIUrl":"https://doi.org/10.18910/58895","url":null,"abstract":"Abstract This paper considers an impulsive stochastic logistic mode l with infinite delay at the phase space Cg. Firstly, the definition of solution to an impulsive stochas tic functional differential equation with infinite delay is establi shed. Based on this definition, we show that our model has a unique global positive solution. Then we establish the sufficient conditions for extinction, nonpersistence in th e mean, weak persistence and stochastic permanence of the solution. The threshold betwe en weak persistence and extinction is obtained. In addition, the effects of impulsi ve perturbation and delay on persistence and extinction are discussed, respectively. F inally, numerical simulations are introduced to support the theoretical analysis results .","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67877305","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}
Here W is a suitable cross-section for the generic coadjoint orbit s in g , the vector space dual ofg. The condition (1.1) of this theorem depends on the choice of t he bases for which the norm of x in G is defined. We must define the norm of x in G before stating Theorem 1.3. For this we must fix a bases of g, and then define the norm of x using this bases. In addition, we shouldn’t modify this bases t hroughout the proof of Theorem 1.3. This implies that, Remark 2.5.1 in the paper is n ot correct.
{"title":"Erratum to the article ``Beurling's theorem for nilpotent Lie groups'' Osaka J. Math. 48 (2011), 127--147","authors":"K. Smaoui","doi":"10.18910/58911","DOIUrl":"https://doi.org/10.18910/58911","url":null,"abstract":"Here W is a suitable cross-section for the generic coadjoint orbit s in g , the vector space dual ofg. The condition (1.1) of this theorem depends on the choice of t he bases for which the norm of x in G is defined. We must define the norm of x in G before stating Theorem 1.3. For this we must fix a bases of g, and then define the norm of x using this bases. In addition, we shouldn’t modify this bases t hroughout the proof of Theorem 1.3. This implies that, Remark 2.5.1 in the paper is n ot correct.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67877253","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 two sided noetherian ring R such that the character modules of Gorenstein injective leftR-modules are Gorenstein flat right R-modules. We then prove that the class of Gorenstein flat right R-modules is preenveloping. We also show that the class of Gorenstein flat complexes of right R-modules is preenevloping in Ch(R). In the second part of the paper we give examples of rings with t he property that the character modules of Gorenstein injective modules are G or nstein flat. We prove that any two sided noetherian ring R with i.d.Rop R < 1 has the desired property. We also prove that ifR is a two sided noetherian ring with a dualizing bimodule RVR and such thatR is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein flat .
{"title":"Gorenstein Flat Preenvelopes","authors":"A. Iacob","doi":"10.18910/57638","DOIUrl":"https://doi.org/10.18910/57638","url":null,"abstract":"We consider a two sided noetherian ring R such that the character modules of Gorenstein injective leftR-modules are Gorenstein flat right R-modules. We then prove that the class of Gorenstein flat right R-modules is preenveloping. We also show that the class of Gorenstein flat complexes of right R-modules is preenevloping in Ch(R). In the second part of the paper we give examples of rings with t he property that the character modules of Gorenstein injective modules are G or nstein flat. We prove that any two sided noetherian ring R with i.d.Rop R < 1 has the desired property. We also prove that ifR is a two sided noetherian ring with a dualizing bimodule RVR and such thatR is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein flat .","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67867670","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}
In this paper, we determine nonminimal pseudohermitian biminimal Legendre surfaces in the unit 5-sphere S 5 . In fact, the product of a circle and a helix of order 4 is realized as a nonminimal pseudohermitian biminimal Legendre immersion into S 5 . In addition, we obtain that there exist no nonminimal pseudohermitian biminimal Legendre surfaces in a 5-dimensional Sasakian space form of non-positive constant holomorphic sectional curvature for the Tanaka–Webster connection.
{"title":"PSEUDOHERMITIAN BIMINIMAL LEGENDRE SURFACES IN THE 5-DIMENSIONAL SPHERE","authors":"Jong Taek Cho, Ji-Eun Lee","doi":"10.18910/57689","DOIUrl":"https://doi.org/10.18910/57689","url":null,"abstract":"In this paper, we determine nonminimal pseudohermitian biminimal Legendre surfaces in the unit 5-sphere S 5 . In fact, the product of a circle and a helix of order 4 is realized as a nonminimal pseudohermitian biminimal Legendre immersion into S 5 . In addition, we obtain that there exist no nonminimal pseudohermitian biminimal Legendre surfaces in a 5-dimensional Sasakian space form of non-positive constant holomorphic sectional curvature for the Tanaka–Webster connection.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67872359","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":"Involutions on a compact 4-symmetric space of exceptional type","authors":"Hiroyuki Kurihara, K. Tojo","doi":"10.18910/57685","DOIUrl":"https://doi.org/10.18910/57685","url":null,"abstract":"","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67871506","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}
In this article, we shall prove that for any finite solvable gr oup G, there exist infinitely many abelian extensions K=Q and Galois extensionsM=Q such that the Galois group Gal( M=K ) is isomorphic toG and M=K is unramified. The difference between our result and [3, 4, 6, 7, 13] is that we have a base fiel d K which is not only Galois overQ, but also has very small degree compared to their results. We will also get another proof of Nomura’s work [9], which gives u a base field of smaller degree than Nomura’s. Finally for a given finite nona beli n simple groupG, we will show there exists an unramified extension M=K 0 such that the Galois group is isomorphic toG and K 0 has relatively small degree.
{"title":"CONSTRUCTION OF UNRAMIFIED EXTENSIONS WITH A PRESCRIBED GALOIS GROUP","authors":"KwangSeob Kim","doi":"10.18910/57688","DOIUrl":"https://doi.org/10.18910/57688","url":null,"abstract":"In this article, we shall prove that for any finite solvable gr oup G, there exist infinitely many abelian extensions K=Q and Galois extensionsM=Q such that the Galois group Gal( M=K ) is isomorphic toG and M=K is unramified. The difference between our result and [3, 4, 6, 7, 13] is that we have a base fiel d K which is not only Galois overQ, but also has very small degree compared to their results. We will also get another proof of Nomura’s work [9], which gives u a base field of smaller degree than Nomura’s. Finally for a given finite nona beli n simple groupG, we will show there exists an unramified extension M=K 0 such that the Galois group is isomorphic toG and K 0 has relatively small degree.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67872257","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 introduce a method which can be used to study maximal inequalities for martingales of bounded mean oscillation. As an application, we establish sharp Φ-inequalities and tail inequalities for the one-sided maximal function of a BMO martingale. The results can be regarded as BMO counterparts of the classical maximal estimates of Doob.
{"title":"Sharp maximal estimates for BMO martingales","authors":"A. Osȩkowski","doi":"10.18910/57684","DOIUrl":"https://doi.org/10.18910/57684","url":null,"abstract":"We introduce a method which can be used to study maximal inequalities for martingales of bounded mean oscillation. As an application, we establish sharp Φ-inequalities and tail inequalities for the one-sided maximal function of a BMO martingale. The results can be regarded as BMO counterparts of the classical maximal estimates of Doob.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67871309","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 apply Forelli-Rudin construction and Nakazawa’s hodograph transformation to prove a graph theoretic closed formula for invariant theoretic coefficients in the asymptotic expansion of the Szego kernel on strictly pseudoconvex complete Reinhardt domains. The formula provides a structural analogy between the asymptotic expansion of the Bergman and Szego kernels. It can be used to effectively compute the first terms of Fefferman’s asymptotic expansion in CR invariants. Our method also works for the asymptotic expansion of the Sobolev-Bergman kernel introduced by Hirachi and Komatsu.
{"title":"FORELLI–RUDIN CONSTRUCTION AND ASYMPTOTIC EXPANSION OF SZEGÖ KERNEL ON REINHARDT DOMAINS","authors":"M. Engliš, Hao Xu","doi":"10.18910/57651","DOIUrl":"https://doi.org/10.18910/57651","url":null,"abstract":"We apply Forelli-Rudin construction and Nakazawa’s hodograph transformation to prove a graph theoretic closed formula for invariant theoretic coefficients in the asymptotic expansion of the Szego kernel on strictly pseudoconvex complete Reinhardt domains. The formula provides a structural analogy between the asymptotic expansion of the Bergman and Szego kernels. It can be used to effectively compute the first terms of Fefferman’s asymptotic expansion in CR invariants. Our method also works for the asymptotic expansion of the Sobolev-Bergman kernel introduced by Hirachi and Komatsu.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67868551","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 study zero divisors and minimal prime ideals in semirings of characteristic one. Thereafter we find a counterexample to the most obvious version of primary decomposition, but are able to establish a weaker version. Lastly, we study Evans'condition in this context.
{"title":"Prime and primary ideals in semirings","authors":"P. Lescot","doi":"10.18910/57677","DOIUrl":"https://doi.org/10.18910/57677","url":null,"abstract":"We study zero divisors and minimal prime ideals in semirings of characteristic one. Thereafter we find a counterexample to the most obvious version of primary decomposition, but are able to establish a weaker version. Lastly, we study Evans'condition in this context.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67871275","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}
Strong and weak (1, 3) homotopies are equivalence relations on knot projections, defined by the first flat Reidemeister move and each of two different types of the third flat Reidemeister moves. In this paper, we introduce the cross chord number that is the minimal number of double points of chords of a chord diagram. Cross chord numbers induce a strong (1, 3) invariant. We show that Hanaki's trivializing number is a weak (1, 3) invariant. We give a complete classification of knot projections having trivializing number two up to the first flat Reidemeister moves using cross chord numbers and the positive resolutions of double points. Two knot projections with trivializing number two are both weak (1, 3) homotopy equivalent and strong (1, 3) homotopy equivalent if and only if they can be related by only the first flat Reidemeister moves. Finally, we determine the strong (1, 3) homotopy equivalence class containing the trivial knot projection and other classes of knot projections.
{"title":"Strong and weak (1, 3) homotopies on knot projections","authors":"N. Ito, Yusuke Takimura, Kouki Taniyama","doi":"10.18910/57647","DOIUrl":"https://doi.org/10.18910/57647","url":null,"abstract":"Strong and weak (1, 3) homotopies are equivalence relations on knot projections, defined by the first flat Reidemeister move and each of two different types of the third flat Reidemeister moves. In this paper, we introduce the cross chord number that is the minimal number of double points of chords of a chord diagram. Cross chord numbers induce a strong (1, 3) invariant. We show that Hanaki's trivializing number is a weak (1, 3) invariant. We give a complete classification of knot projections having trivializing number two up to the first flat Reidemeister moves using cross chord numbers and the positive resolutions of double points. Two knot projections with trivializing number two are both weak (1, 3) homotopy equivalent and strong (1, 3) homotopy equivalent if and only if they can be related by only the first flat Reidemeister moves. Finally, we determine the strong (1, 3) homotopy equivalence class containing the trivial knot projection and other classes of knot projections.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67868624","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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