{"title":"Bifurcation theory for a class of second order differential equations","authors":"Alvaro Correa, Yi A. Li","doi":"10.17077/ETD.QMLJMX3C","DOIUrl":"https://doi.org/10.17077/ETD.QMLJMX3C","url":null,"abstract":"We consider the existence of positive solutions of the nonlinear two point boundary value problem u′′ + λf(u) = 0, u(−1) = u(1) = 0, where f(u) = u(u − a)(u− b)(u− c)(1−u), 0 < a < b < c < 1, as the parameter λ varies through positive values. Every solution u(x) is an even function, and when it exists, it is uniquely identified by α = u(0). We study how the number of solutions changes when the parameter varies, i.e. we will be focusing on the locations of bifurcation points. The authors P. Korman, Y. Li and T. Ouyang ( ”Computing the location and the direction of bifurcation”, Mathematical Research Letters, accepted ), prove that a necessary and sufficient condition for α to be a bifurcation point is G(α) ≡ F (α) ∫ α 0 f(α)− f(τ) [F (α)− F (τ)]3/2 dτ − 2 = 0, where F (α) = ∫ α 0 f(u) du. We will prove that G(α) has vertical asymptotes at α = b, α = 1 and at any point α ∈ (0, 1) for which ∫ α 0 f(u) du = 0. We will use the asymptotic behavior of G to estimate intervals where G(α) 6= 0, that is, intervals where there is no bifurcation point.","PeriodicalId":50398,"journal":{"name":"Houston Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68075371","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":"Relative homological algebra in categories of representations of infinite quivers","authors":"S. E. Domínguez, Ozdemir Salahattin","doi":"10.5072/ZENODO.26602","DOIUrl":"https://doi.org/10.5072/ZENODO.26602","url":null,"abstract":"","PeriodicalId":50398,"journal":{"name":"Houston Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70788096","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":"Derivational derivatives and Feynman's operational calculi","authors":"G. Johnson, B. Kim","doi":"10.1093/acprof:oso/9780198702498.003.0009","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780198702498.003.0009","url":null,"abstract":"This paper explores the differential (or derivational) calculus associated with the disentangled operators arising from Feynman's operational calculi (FOCi) for noncommuting operators. (We will use the continuous case of the approach to FOCi initiated by Jefferies and Johnson in 2000.) The central part of this paper deals with a first order infinitesimal calculus for a function of n noncommuting operators. Here the first derivatives (or differentials) are replaced by the first order derivational derivatives. The derivational derivatives of the first and higher order have been useful in, for example, operator algebras, noncommutative geometry and Maslov's discrete form of Feynman's operational calculus. In the last section of this paper we will develop some special cases of higher order expansions.","PeriodicalId":50398,"journal":{"name":"Houston Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60644922","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":"Induced maps on n-fold hyperspaces","authors":"M. D. J. López, S. Macías","doi":"10.1007/978-3-319-90902-8_8","DOIUrl":"https://doi.org/10.1007/978-3-319-90902-8_8","url":null,"abstract":"","PeriodicalId":50398,"journal":{"name":"Houston Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031289","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":"On Series of Positive Terms","authors":"K. Grosse-Erdmann, G. Bennett","doi":"10.4064/BC64-0-3","DOIUrl":"https://doi.org/10.4064/BC64-0-3","url":null,"abstract":"","PeriodicalId":50398,"journal":{"name":"Houston Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70694859","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":"Partial Dynamical Systems and AF C*-algebras","authors":"J. Peters, R. Zerr","doi":"10.31274/RTD-180813-13219","DOIUrl":"https://doi.org/10.31274/RTD-180813-13219","url":null,"abstract":"We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C*-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by utilizing the actions of these partial homeomorphisms, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show that, for a certain class of dimension groups, a groupoid can be obtained directly from the dimension group's structure whose associated C*-algebra has its dimension group isomorphic to the original dimension group.","PeriodicalId":50398,"journal":{"name":"Houston Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2003-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69350538","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}