In this short article, we give a necessary and su ffi cient condition for the form (1.3), like the one in Hamza’s theorem, to be closable and prove that every regular and strongly local Dirichlet form is the closure of a form of Hamza’s type, which can be represented in terms of e ff ective intervals introduced in [7].
{"title":"More about Hamza's Theorem","authors":"Wenjie Sun, J. Ying","doi":"10.18910/76673","DOIUrl":"https://doi.org/10.18910/76673","url":null,"abstract":"In this short article, we give a necessary and su ffi cient condition for the form (1.3), like the one in Hamza’s theorem, to be closable and prove that every regular and strongly local Dirichlet form is the closure of a form of Hamza’s type, which can be represented in terms of e ff ective intervals introduced in [7].","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44919299","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}
Given a rational fibered surface f : X → P1 of genus g we prove the inequality 6n+5 n+1 − 9n+12 2g ≤ λ f , provided that the genus g is sufficiently high with respect to the gonality 2n+3 of the general fibre.
{"title":"On the slope of rational fibered surfaces","authors":"M. Castañeda-Salazar, A. Zamora","doi":"10.18910/75922","DOIUrl":"https://doi.org/10.18910/75922","url":null,"abstract":"Given a rational fibered surface f : X → P1 of genus g we prove the inequality 6n+5 n+1 − 9n+12 2g ≤ λ f , provided that the genus g is sufficiently high with respect to the gonality 2n+3 of the general fibre.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43790506","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}
A generalization of the Einstein equations with the cosmological constant is considered for complex line elements. Several second order semilinear partial differential equations are derived from them as semilinear field equations in homogeneous and isotropic spaces. The nonrelativistic limits of the field equations are also considered. The properties of spatial expansion and contraction are studied based on energy estimates of the field equations. Several dissipative and anti-dissipative properties are remarked.
{"title":"REMARKS ON THE DERIVATION OF SEVERAL SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS FROM A GENERALIZATION OF THE EINSTEIN EQUATIONS","authors":"Makoto Nakamura","doi":"10.18910/75916","DOIUrl":"https://doi.org/10.18910/75916","url":null,"abstract":"A generalization of the Einstein equations with the cosmological constant is considered for complex line elements. Several second order semilinear partial differential equations are derived from them as semilinear field equations in homogeneous and isotropic spaces. The nonrelativistic limits of the field equations are also considered. The properties of spatial expansion and contraction are studied based on energy estimates of the field equations. Several dissipative and anti-dissipative properties are remarked.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46484102","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 family of quasidistances in ${mathbb R}^d$, such that some of them are equivalent to natural distances on Carnot groups. We find the sufficient conditions for the balls w.r.t. a quasidistance from our family to be comparable to ellipsoids. Using comparability to ellipsoids we find asymptotics of surface measure of intersections of small balls with linear submanifolds and the conditions for finiteness of the integral w.r.t. the surface measure of negative power of the distance. We provide several examples of Carnot groups, where comparability to ellipsoids can be shown for natural distances, and therefore we can study the asymptotics and finitness of the integrals explicitly. We also show an example of a Carnot group, where the comparability to ellipsoids does not hold.
{"title":"An estimate for surface measure of small balls in Carnot groups","authors":"A. Rudenko","doi":"10.18910/75920","DOIUrl":"https://doi.org/10.18910/75920","url":null,"abstract":"We introduce a family of quasidistances in ${mathbb R}^d$, such that some of them are equivalent to natural distances on Carnot groups. We find the sufficient conditions for the balls w.r.t. a quasidistance from our family to be comparable to ellipsoids. Using comparability to ellipsoids we find asymptotics of surface measure of intersections of small balls with linear submanifolds and the conditions for finiteness of the integral w.r.t. the surface measure of negative power of the distance. We provide several examples of Carnot groups, where comparability to ellipsoids can be shown for natural distances, and therefore we can study the asymptotics and finitness of the integrals explicitly. We also show an example of a Carnot group, where the comparability to ellipsoids does not hold.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48050865","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 establish the existence in the sense of sequences of solutions for some integrodifferential type equations containing the drift term and the square root of the one dimensional negative Laplacian, on the whole real line or on a finite interval with periodic boundary conditions in the corresponding H spaces. The argument relies on the fixed point technique when the elliptic equations involve first order differential operators with and without Fredholm property. It is proven that, under the reasonable technical assumptions, the convergence in L of the integral kernels implies the existence and convergence in H of solutions.
{"title":"SOLVABILITY OF SOME INTEGRO-DIFFERENTIAL EQUATIONS WITH DRIFT","authors":"M. Efendiev, V. Vougalter","doi":"10.18910/75913","DOIUrl":"https://doi.org/10.18910/75913","url":null,"abstract":"We establish the existence in the sense of sequences of solutions for some integrodifferential type equations containing the drift term and the square root of the one dimensional negative Laplacian, on the whole real line or on a finite interval with periodic boundary conditions in the corresponding H spaces. The argument relies on the fixed point technique when the elliptic equations involve first order differential operators with and without Fredholm property. It is proven that, under the reasonable technical assumptions, the convergence in L of the integral kernels implies the existence and convergence in H of solutions.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44150174","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 consider the influence that the number of separated maximum points of the norm of a meromorphic minimal surface (m.m.s) has on the magnitudes of growth and value distribution. We present sharp estimations of spread of m.m.s in terms of Nevanlinna’s defect, magnitude of deviation and the number of separated points of the norm of m.m.s. We also give examples showing that the estimates are sharp.
{"title":"On Deviations and Spreads of Meromorphic Minimal Surfaces","authors":"A. Kowalski, I. Marchenko","doi":"10.18910/73739","DOIUrl":"https://doi.org/10.18910/73739","url":null,"abstract":"In this paper we consider the influence that the number of separated maximum points of the norm of a meromorphic minimal surface (m.m.s) has on the magnitudes of growth and value distribution. We present sharp estimations of spread of m.m.s in terms of Nevanlinna’s defect, magnitude of deviation and the number of separated points of the norm of m.m.s. We also give examples showing that the estimates are sharp.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67914510","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 investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.
{"title":"Global asymptotics toward the rarefaction waves for solutions to the Cauchy problem of the scalar conservation law with nonlinear viscosity","authors":"A. Matsumura, Natsumi Yoshida","doi":"10.18910/73745","DOIUrl":"https://doi.org/10.18910/73745","url":null,"abstract":"In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of non-Newtonian type, including a pseudo-plastic case. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, under a condition on nonlinearity of the viscosity, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity, without any smallness conditions.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67914101","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":"INITIAL BOUNDARY VALUE PROBLEM FOR 3D BOUSSINESQ SYSTEM WITH THE THERMAL DAMPING","authors":"Yanghai Yu, Yanbin Tang","doi":"10.18910/73738","DOIUrl":"https://doi.org/10.18910/73738","url":null,"abstract":"","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67914484","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}
Let G be a finite group and Σ a homology sphere with smooth G-action. If the G-fixed-point set of Σ consists of odd-number points then the dimension of Σ could be restrictive. In this article we confirm the claim in the cases where G = S5 or SL(2, 5).
{"title":"SPHERES NOT ADMITTING SMOOTH ODD-FIXED-POINT ACTIONS OF S_5 AND SL(2, 5)","authors":"M. Morimoto, S. Tamura","doi":"10.18910/73733","DOIUrl":"https://doi.org/10.18910/73733","url":null,"abstract":"Let G be a finite group and Σ a homology sphere with smooth G-action. If the G-fixed-point set of Σ consists of odd-number points then the dimension of Σ could be restrictive. In this article we confirm the claim in the cases where G = S5 or SL(2, 5).","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67914315","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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