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Kodai Mathematical Journal
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KODAI MATHEMATICAL SEMINAR REPORTS

Kodai Mathematical Journal Vol. 40(2017) No. 1

Complete flat resolutions, Tate homology and the depth formula

Yanping Liu, Zhongkui Liu, Xiaoyan Yang

Released: March 30, 2017

p.1-15

We introduce Tate homology of complexes of finite Gorenstein flat dimension based on complete flat resolutions and give a new method of computing Tate homology in Christensen and Jorgensen's sense. We also investigate the relationship between Tate homology and Tate cohomology. As an application, a more brief proof of the main result on derived depth formula of [Vanishing of Tate homology and depth formula over local rings, J. Pure Appl. Algebra 219 (2015) 464-481] is given.

A number theoretical observation of a resonant interaction of Rossby waves

Nobu Kishimoto, Tsuyoshi Yoneda

Released: March 30, 2017

p.16-20

Rossby waves are generally expected to dominate the β plane dynamics in geophysics, and here in this paper we give a number theoretical observation of the resonant interaction with a Diophantine equation. The set of resonant frequencies does not have any frequency on the horizontal axis.

Centro-affine invariants and the canonical Lorentz metric on the space of centered ellipses

Marcos Salvai

Released: March 30, 2017

p.21-30

We consider smooth plane curves which are convex with respect to the origin. We describe centro-affine invariants (that is, GL₊ (2,R)-invariants), such as centro-affine curvature and arc length, in terms of the canonical Lorentz structure on the three dimensional space of all the ellipses centered at zero, by means of null curves of osculating ellipses. This is the centro-affine analogue of the approach to conformal invariants of curves in the sphere introduced by Langevin and O'Hara, using the canonical pseudo Riemannian metric on the space of circles.

Herz-type Besov spaces of variable smoothness and integrability

Douadi Drihem, Rabah Heraiz

Released: March 30, 2017

p.31-57

In this paper, Herz-type Besov spaces with variable smoothness and integrability are introduced. Our scale contains variable Besov spaces as special cases. We prove several basic properties, especially the Sobolev-type embeddings.

On Faltings' local-global principle of generalized local cohomology modules

Nguyen Van Hoang

Released: March 30, 2017

p.58-62

Let R be a commutative Noetherian ring, I an ideal of R and M, N finitely generated R-modules. Let 0 ≤ n ∈ Z. This note shows that the least integer i such that dim Supp($H^i_I$(M, N)/K) ≥ n for any finitely generated submodule K of $H^i_I$(M, N) equal to the number inf{f_{I_$\frak{p}$} (M_$\frak{p}$,N_$\frak{p}$)|$\frak{p}$ ∈ Supp(N/I_MN), dim R/$\frak{p}$ ≥ n}, where f_{I_$\frak{p}$}(M_$\frak{p}$,N_$\frak{p}$) is the least integer i such that $H^i_{I_{\frak{p}}} (M_$\frak{p}$,N_$\frak{p}$) is not finitely generated, and I_M = ann(M/IM). This extends the main result of Asadollahi-Naghipour [1] and Mehrvarz-Naghipour-Sedghi [8] for generalized local cohomology modules by a short proof.

Global attractors for a Kirchhoff type plate equation with memory

Xiaobin Yao, Qiaozhen Ma, Ling Xu

Released: March 30, 2017

p.63-78

A Kirchhoff type plate equation with memory is investigated. Under the suitable assumptions, we establish the existence of a global attractor by using the contraction function method.

The Euler product for the Riemann zeta-function in the critical strip

Hirotaka Akatsuka

Released: March 30, 2017

p.79-101

In this paper we study a pointwise asymptotic behavior of the partial Euler product for the Riemann zeta-function on the right half of the critical strip. We discuss relations among the behavior of the partial Euler product, the distribution of the prime numbers and the distribution of nontrivial zeros of the Riemann zeta-function.

Unit tangent sphere bundles with the Reeb flow invariant Ricci operator

Jong Taek Cho, Sun Hyang Chun

Released: March 30, 2017

p.102-116

In this paper, we study unit tangent sphere bundles T₁M whose Ricci operator $\bar{S}$ is Reeb flow invariant, that is, L_ξ$\bar{S}$ = 0. We prove that for a 3-dimensional Riemannian manifold M, T₁M satisfies L_ξ$\bar{S}$ = 0 if and only if M is of constant curvature 1. Also, we prove that for a 4-dimensional Riemannian manifold M, T₁M satisfies L_ξ $\bar{S}$ = 0 and ℓ$\bar{S}$ξ = 0 if and only if M is of constant curvature 1 or 2, where ℓ = $\bar{R}$(·,ξ)ξ is the characteristic Jacobi operator.

Global uniqueness results for ground states for a class of quasilinear elliptic equations

Shinji Adachi, Masataka Shibata, Tatsuya Watanabe

Released: March 30, 2017

p.117-142

In this paper, we are concerned with the uniqueness of ground states for a class of quasilinear elliptic equations which arise in the study of plasma physics. We obtain global uniqueness results in the sense that we don't require any assumptions on the parameter.

Effective actions of the general indefinite unitary groups on holomorphically separable manifolds

Yoshikazu Nagata

Released: March 30, 2017

p.143-177

We determine all holomorphically separable complex manifolds of dimension p + q which admit smooth envelopes of holomorphy and effective general indefinite unitary group actions of size p + q. Also we give exact description of the automorphism groups of those complex manifolds. As an application we consider a characterization of those complex manifolds by their automorphism groups.

Relative purity in log étale cohomology

Kazumi Higashiyama, Takashi Kamiya

Released: March 30, 2017

p.178-183

We study log étale cohomology. The goal is to prove relative purity in log étale cohomology.

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Back Issues

Volume And Issue List
Kodai Mathematical Journal

Predecessor

Kodai Mathematical Journal Vol. 40(2017) No. 1

Complete flat resolutions, Tate homology and the depth formula

A number theoretical observation of a resonant interaction of Rossby waves

Centro-affine invariants and the canonical Lorentz metric on the space of centered ellipses

Herz-type Besov spaces of variable smoothness and integrability

On Faltings' local-global principle of generalized local cohomology modules

Global attractors for a Kirchhoff type plate equation with memory

The Euler product for the Riemann zeta-function in the critical strip

Unit tangent sphere bundles with the Reeb flow invariant Ricci operator

Global uniqueness results for ground states for a class of quasilinear elliptic equations

Effective actions of the general indefinite unitary groups on holomorphically separable manifolds

Relative purity in log étale cohomology

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Announcement From J-STAGE

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Volume And Issue List Kodai Mathematical Journal

Predecessor

Kodai Mathematical Journal Vol. 40(2017) No. 1

System Maintenance

Announcement From J-STAGE

Journal Tools

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Volume And Issue List
Kodai Mathematical Journal