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Kodai Mathematical Journal
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  - No.2 p.253-
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Predecessor

KODAI MATHEMATICAL SEMINAR REPORTS

Kodai Mathematical Journal Vol. 39(2016) No. 2

Sufficient conditions for a real polynomial to be a sum of squares of polynomials

Van Doat Dang, Thi Thao Nguyen

Released: July 14, 2016

p.253-275

In this paper, we establish new sufficient conditions for the polynomial f to be SOS in terms of the Newton polyhedron of f (Theorems 2.6 and 2.12). These new sufficient conditions include results which were proved earlier by Lasserre [13, Theorem 3], Fidalgo and Kovacec [6, Theorem 4.3], Ghasemi and Marshall [7, Theorems 2.1 and 2.3], and Ghasemi and Marshall [8, Theorem 2.3].

Existence and uniqueness of periodic solutions for parabolic equation with nonlocal delay

Qiang Li, Yongxiang Li, Pengyu Chen

Released: July 14, 2016

p.276-289

This paper deals with the existence and uniqueness of time periodic solutions for the general periodic parabolic equation boundary problem with nonlocal delay. We apply operator semigroup theory and monotone iterative technique of lower and upper solutions to obtain the existence and uniqueness of ω-periodic mild solutions of some abstract evolution equation under some quasimonotone conditions. In the end, applying our abstract results to parabolic equation with nonlocal delay, we get the existence and uniqueness of ω-periodic solution, which generalize the recent conclusions on this issue.

Reidemeister torsion of a 3-manifold obtained by an integral Dehn-surgery along the figure-eight knot

Teruaki Kitano

Released: July 14, 2016

p.290-296

Let M be a 3-manifold obtained by a Dehn-surgery along the figure-eight knot. We give a formula of the Reidemeisiter torsion of M for any SL(2; C)-irreducible representation. It has a rational expression of the trace of the image of the meridian.

The asymptotic behavior of holomorphic 1-cochains

Daisuke Yamaki

Released: July 14, 2016

p.297-317

In this paper, we focus on relations between holomorphic 1-forms and holomorphic 1-cochains on a closed Riemann surface. Holomorphic 1-cochains are defined by Wilson in 2008 using a combinatorial Hodge theory. A holomorphic 1-form is characterized by its periods. So is a holomorphic 1-cochain. We consider relations between a holomorphic 1-form and a holomorphic 1-cochain which have the same periods and show that holomorphic 1-cochains provide an approximation of holomorphic 1-forms.

Some new lower bounds of the first eigenvalue on Finsler manifolds

Song-Ting Yin, Qun He, Da-Xiao Zheng

Released: July 14, 2016

p.318-339

We establish some unified lower bounds for the first Neumann and closed eigenvalues of the Finsler-Laplacian on compact Finsler manifolds under the weighted Ricci curvature conditions, which extend some recent theorems on the first eigenvalue of the Riemannian-Laplacian. Moreover, the Lichnerowicz type lower bound for the first Dirichlet eigenvalue of the Finsler-Laplacian is also obtained.

Cohomology formula for obstructions to asymptotic Chow semistability

Yuta Suzuki

Released: July 14, 2016

p.340-353

Odaka [16] and Wang [19] proved the intersection formula for the Donaldson-Futaki invariant. In this paper, we generalize this result for the higher Futaki invariants, which are obstructions to asymptotic Chow semistability.

A theorem of Liouville type for p-harmonic maps in weighted Riemannian manifolds

Jian-Feng Zhang, Yue Wang

Released: July 14, 2016

p.354-365

Let M be a weighted Riemannian manifold with non-negative Bakry-Émery-Ricci curvature and N be a complete Riemannian manifold of non-positive sectional curvature. In this paper, the p-harmonic map u: M → N is studied, and a theorem of Liouville type is obtained.

Linear combinations of harmonic quasiconformal mappings convex in one direction

Yong Sun, Antti Rasila, Yue-Ping Jiang

Released: July 14, 2016

p.366-377

In this paper, we introduce a new class $\mathcal{S}_{H}$ (k, γ; φ) of harmonic quasiconformal mappings, where k ∈ [0,1), γ ∈ [0,π) and φ is an analytic function. Sufficient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of γ and φ, are convex.

A construction of lattices in splittable solvable Lie groups

Takumi Yamada

Released: July 14, 2016

p.378-388

In this paper, we consider a unified constructions of lattices in splittable solvable Lie groups.

On convexity of simple closed frontals

Tomonori Fukunaga, Masatomo Takahashi

Released: July 14, 2016

p.389-398

We study convexity of simple closed frontals of Legendre curves in the Euclidean plane by using the curvature of Legendre curves. We show that for a Legendre curve, the simple closed frontal under conditions is convex if and only if the sign of both functions of the curvature of the Legendre curve does not change. We also give some examples of convex simple closed frontals.

Tikhonov regularization for Dunkl multiplier operators

Fethi Soltani

Released: July 14, 2016

p.399-409

We study some class of Dunkl multiplier operators T_k,m; and we give for them an application of the theory of reproducing kernels to the Tikhonov regularization, which gives the best approximation of the operators T_k,m on the Dunkl-type Paley-Wiener spaces H_h.

Douady-Earle extension of the strongly symmetric homeomorphism

Yan Wu, Yi Qi

Released: July 14, 2016

p.410-424

It is shown that the complex dilatation of the Douady-Earle extension of a strongly symmetric homeomorphism induces a vanishing Carleson measure on the unit disk D. As application, it is proved that the VMO-Teichmüller space is a subgroup of the universal Teichmüller space.

A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms

Abdelhamid Adouani, Habib Marzougui

Released: July 14, 2016

p.425-438

Let f be a class P-homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a sharp estimate for the smoothness of a conjugation of class P-homeomorphism f of the circle satisfying the (D)-property (i.e. the product of f-jumps in the break points contained in a same orbit is trivial), to diffeomorphism. When f does not satisfy the (D)-property the conjugating homeomorphism is never a class P and even more it is not absolutely continuous function when the total product of f-jumps in all the break points is non-trivial.

Balls in quaternionic hyperbolic manifolds

Wensheng Cao

Released: July 14, 2016

p.439-454

By use of the Zassenhaus neighborhood of Sp(n,1), we obtain an explicit lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifold $\mathcal{M}$ = H_Hⁿ/Γ. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds.

On combinatorial criteria for non-degenerate singularities

Szymon Brzostowski, Grzegorz Oleksik

Released: July 14, 2016

p.455-468

In this article we give a sufficient and necessary condition for a Kouchnirenko non-degenerate holomorphic function to have an isolated singularity at 0 in terms of its support. As a corollary we give some useful sufficient conditions for singularity to be isolated.

1 - 15 / 15 Articles.

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Volume And Issue List
Kodai Mathematical Journal

Predecessor

Kodai Mathematical Journal Vol. 39(2016) No. 2

Sufficient conditions for a real polynomial to be a sum of squares of polynomials

Existence and uniqueness of periodic solutions for parabolic equation with nonlocal delay

Reidemeister torsion of a 3-manifold obtained by an integral Dehn-surgery along the figure-eight knot

The asymptotic behavior of holomorphic 1-cochains

Some new lower bounds of the first eigenvalue on Finsler manifolds

Cohomology formula for obstructions to asymptotic Chow semistability

A theorem of Liouville type for p-harmonic maps in weighted Riemannian manifolds

Linear combinations of harmonic quasiconformal mappings convex in one direction

A construction of lattices in splittable solvable Lie groups

On convexity of simple closed frontals

Tikhonov regularization for Dunkl multiplier operators

Douady-Earle extension of the strongly symmetric homeomorphism

A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms

Balls in quaternionic hyperbolic manifolds

On combinatorial criteria for non-degenerate singularities

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Volume And Issue List Kodai Mathematical Journal

Predecessor

Kodai Mathematical Journal Vol. 39(2016) No. 2

System Maintenance

Announcement From J-STAGE

Journal Tools

Share this Title

Volume And Issue List
Kodai Mathematical Journal