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Volume 65 (2013)
- Issue 4 Pages 467-
- Issue 3 Pages 313-
- Issue 2 Pages 159-
- Issue 1 Pages 1-
Predecessor
Volume 65, Issue 4
Displaying 1-8 of 8 articles from this issue
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YASUHITO NISHIMORI2013 Volume 65 Issue 4 Pages 467-494
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSLet $\nu$ and $\mu$ be positive Radon measures on $\boldsymbol{R}^d$ in Green-tight Kato class associated with a symmetric $\alpha$-stable process $(X_t, P_x)$ on $\boldsymbol{R}^d$, and $A_t^{\nu}$ and $A_t^{\mu}$ the positive continuous additive functionals under the Revuz correspondence to $\nu$ and $\mu$. For a non-negative $\beta$, let $P_{x,t} ^{\beta \mu}$ be the law $X_t$ weighted by the Feynman-Kac functional $\exp(\beta A_t ^{\mu})$, i.e., $P_{x,t} ^{\mu} =(Z_{x,t} ^{\mu})^{-1}\exp(\beta A_t ^{\mu})P_x$, where $Z_{x, t} ^{\mu}$ is a normalizing constant. We show that $A_t ^{\nu} /t$ obeys the large deviation principle under $P_{x, t}^{\beta \mu}$. We apply it to a polymer model to identify the critical value $\beta _{\mathrm{cr}}$ such that the polymer is pinned under the law $P^{\beta \mu} _{x, t} $ if and only if $\beta$ is greater than $\beta_{\mathrm{cr}}$. The value $\beta _{\mathrm{cr}} $ is characterized by the rate function.View full abstractDownload PDF (217K) -
SATORU SHIMIZU2013 Volume 65 Issue 4 Pages 495-514
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSIn this paper, we discuss some algebraic criterion on the completeness of holomorphic vector fields on a tube domain $T_\varOmega$. Our objects of consideration are polynomial vector fields on $T_\varOmega$. We give a method of determining the higher degree complete polynomial vector fields from the data on the lower degree complete polynomial vector fields, which we call prolongation. Furthermore, we give its applications to the holomorphic equivalence problem for tube domains.View full abstractDownload PDF (179K) -
MATTHIAS SCHÜTT2013 Volume 65 Issue 4 Pages 515-522
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSThis paper concerns K3 surfaces with automorphisms of order 11 in arbitrary characteristic. Specifically we study the wild case and prove that a generic such surface in characteristic 11 has Picard number 2. We also construct K3 surfaces with an automorphism of order 11 in every characteristic, and supersingular K3 surfaces whenever possible.View full abstractDownload PDF (90K) -
TORU KAJIGAYA2013 Volume 65 Issue 4 Pages 523-543
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSIn this paper, we investigate compact Legendrian submanifolds $L$ in Sasakian manifolds $M$, which have extremal volume under Legendrian deformations. We call such a submanifold L-minimal Legendrian submanifold. We derive the second variational formula for the volume of $L$ under Legendrian deformations in $M$. Applying this formula, we investigate the stability of L-minimal Legendrian curves in Sasakian space forms, and show the L-instability of L-minimal Legendrian submanifolds in $S^{2n+1}(1)$. Moreover, we give a construction of L-minimal Legendrian submanifolds in $\boldsymbol{R}^{2n+1}(-3)$.View full abstractDownload PDF (172K) -
MASATOSHI SATO2013 Volume 65 Issue 4 Pages 545-568
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSLet $p$ be a finite regular covering on a 2-sphere with at least three branch points. In this paper, we construct a local signature for the class of fibered 4-manifolds whose general fibers are isomorphic to the covering $p$.View full abstractDownload PDF (258K) -
NIKO MAROLA, MATHIAS MASSON2013 Volume 65 Issue 4 Pages 569-589
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSIn this note we consider problems related to parabolic partial differential equations in geodesic metric measure spaces, that are equipped with a doubling measure and a Poincaré inequality. We prove a location and scale invariant Harnack inequality for a minimizer of a variational problem related to a doubly non-linear parabolic equation involving the $p$-Laplacian. Moreover, we prove the sufficiency of the Grigor'yan–Saloff-Coste theorem for general $p>1$ in geodesic metric spaces. The approach used is strictly variational, and hence we are able to carry out the argument in the metric setting.View full abstractDownload PDF (218K) -
SHUN SHIMOMURA2013 Volume 65 Issue 4 Pages 591-605
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSFor the fifth Painlevé transcendents in a sector, under the condition that the values taken along some curve tending to infinity are bounded away from 1 and another specified complex number, we present new upper estimates for the number of $a$-points including poles and for the growth order. As far as we are concerned with the known asymptotic solutions of the fifth Painlevé equation, this condition is easily checked, and our results are applicable to almost all of them. About concrete examples we discuss the frequency of $a$-points, the equi-distribution property and the growth order. Our method works on the third Painlevé transcendents as well, yielding an analogous result.View full abstractDownload PDF (150K) -
MARCO BRUNELLA2013 Volume 65 Issue 4 Pages 607-608
Published: December 30, 2013
Released on J-STAGE: April 09, 2017
JOURNAL FREE ACCESSIn this note we correct a mistake in author's paper Tohoku Mathematical Journal Vol. 63, No. 3 (2011), 441–460.View full abstractDownload PDF (44K)
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