Kodai Mathematical Journal Articles (Project Euclid)

Remarks on complete non-compact gradient Ricci expanding solitons

Thu, 05 Aug 2010 15:41 EDT

Li Ma, Dezhong Chen

Source: Kodai Math. J., Volume 33, Number 2, 173--181.

Abstract:
In this paper, we study gradient Ricci expanding solitons ( X,g ) satisfying Rc = cg + D 2 f , where Rc is the Ricci curvature, c < 0 is a constant, and D 2 f is the Hessian of the potential function f on X . We show that for a gradient expanding soliton ( X,g ) with non-negative Ricci curvature, the scalar curvature R has at most one maximum point on X , which is the only minimum point of the potential function f . Furthermore, R > 0 on X unless ( X,g ) is Ricci flat. We also show that there is exponentially decay for scalar curvature on a complete non-compact expanding soliton with its Ricci curvature being ε-pinched.

Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel shape operator

Thu, 10 Nov 2011 09:33 EST

Imsoon Jeong, Hyunjin Lee, Young Jin Suh

Source: Kodai Math. J., Volume 34, Number 3, 352--366.

Abstract:
We introduce the notion of generalized Tanaka-Webster connection for hypersurfaces in complex two-plane Grassmannians G 2 ( C m +2 ) and give a non-existence theorem for Hopf hypersurfaces in G 2 ( C m +2 ) with parallel shape operator in this connection.

Dehn twists combined with pseudo-Anosov maps

Thu, 10 Nov 2011 09:33 EST

Chaohui Zhang

Source: Kodai Math. J., Volume 34, Number 3, 367--382.

Abstract:
Let S be a Riemann surface of type ( p , n ) with 3 p + n > 4 and n ≥ 1. Let a be a puncture of S . We show that for any Dehn twist t c along a simple closed geodesic c on S , there exists a sequence { f m } of pseudo-Anosov maps of S such that for sufficiently large integers m , the products f m $\circ$ t c k are pseudo-Anosov for all integers k . As a corollary, we prove that for a multi-twist M 2 on $\tilde{S}$ along two disjoint simple closed geodesics, there are infinitely many pseudo-Anosov maps of S that are isotopic to M 2 as a is filled in.

An inequality of Frank, Steinmetz and Weissenborn

Thu, 10 Nov 2011 09:33 EST

James K. Langley

Source: Kodai Math. J., Volume 34, Number 3, 383--389.

Abstract:
An inequality proved by Frank, Steinmetz and Weissenborn relates the frequency of poles of a function meromorphic in the plane to the frequency of zeros of a linear differential polynomial in that function with small coefficients. A version of this inequality is established in terms of the frequency of distinct zeros of the linear differential polynomial.

A 2 -singularities of hypersurfaces with non-negative sectional curvature in Euclidean space

Thu, 10 Nov 2011 09:33 EST

Kentaro Saji, Masaaki Umehara, Kotaro Yamada

Source: Kodai Math. J., Volume 34, Number 3, 390--409.

Abstract:
In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. As an application, we investigate the behavior of principal singular curvatures along A 2 -singularities of hypersurfaces with non-negative sectional curvature in Euclidean space.

Lifting monogenic cubic fields to monogenic sextic fields

Thu, 10 Nov 2011 09:33 EST

Melisa J. Lavallee, Blair K. Spearman, Kenneth S. Williams

Source: Kodai Math. J., Volume 34, Number 3, 410--425.

Abstract:
Let e $\in$ {-1, +1}. Let a,b $\in$ Z be such that x 6 + ax 4 + bx 2 + e is irreducible in Z [ x ]. The cubic field C = Q (α), where α 3 + a α 2 + b α + e = 0, is said to lift to the sextic field K = Q (θ), where θ 6 + a θ 4 + b θ 2 + e = 0. The field K is called the lift of C . If {1, α, α 2 } is an integral basis for C (so that C is monogenic), we investigate conditions on a and b so that {1, θ, θ 2 , θ 3 , θ 4 , θ 5 } is an integral basis for the lift K of C (so that K is monogenic). As the sextic field K contains a cubic subfield (namely C ), there are eight possibilities for the Galois group of K . For five of these Galois groups, we show that infinitely many monogenic sextic fields can be obtained in this way, and for the remaining three Galois groups, we show that only finitely many monogenic fields can arise in this way, when e $\in$ {-1, +1}.

A classification of certain almost α-Kenmotsu manifolds

Thu, 10 Nov 2011 09:33 EST

Giulia Dileo

Source: Kodai Math. J., Volume 34, Number 3, 426--445.

Abstract:
We study $\mathcal{D}$ -homothetic deformations of almost α-Kenmotsu structures. We characterize almost contact metric manifolds which are CR -integrable almost α-Kenmotsu manifolds, through the existence of a canonical linear connection, invariant under $\mathcal{D}$ -homothetic deformations. If the canonical connection associated to the structure (φ, ξ, η, g ) has parallel torsion and curvature, then the local geometry is completely determined by the dimension of the manifold and the spectrum of the operator h ′ defined by 2α h ′ = ( $\mathcal{L}$ ξ φ) $\circ$ φ. In particular, the manifold is locally equivalent to a Lie group endowed with a left invariant almost α-Kenmotsu structure. In the case of almost α-Kenmotsu (κ, μ)′-spaces, this classification gives rise to a scalar invariant depending on the real numbers κ and α.

Note on Chow rings of nontrivial G -torsors over a field

Thu, 10 Nov 2011 09:33 EST

Nobuaki Yagita

Source: Kodai Math. J., Volume 34, Number 3, 446--463.

Abstract:
Let G k be a split reductive group over a field k corresponding to a compact Lie group G . Let G k be a nontrivial G k -torsor over a field k . In this paper we study the Chow ring of G k . For example when ( G , p ) = ( G 2 , 2), we have the isomorphism CH * ( G k ) (2) $\cong$ Z (2) .

A generalization of Michael finite dimensional selection theorem

Thu, 10 Nov 2011 09:33 EST

Adel A. George Michael

Source: Kodai Math. J., Volume 34, Number 3, 464--473.

Abstract:
In this paper we generalize the classical finite dimensional selection theorem due to Michael [12, theorem 1.2] to the case where the target space is only a Hausdorff uniform space. This also generalizes the zero-dimensional selection theorem of Fakhoury-Gieler [7, 8]. The proof of this generalization utilizes an elegant construction due to Ageev.

The Tanaka-Webster connection and real hypersurfaces in a complex space form

Thu, 10 Nov 2011 09:33 EST

Jong Taek Cho, Mayuko Kon

Source: Kodai Math. J., Volume 34, Number 3, 474--484.

Abstract:
We classify parallel real hypersurfaces in a complex space form for the generalized Tanaka-Webster connection.

Behaviors of circular trajectories on hypersurfaces of type ( A 1 ) in a complex hyperbolic space

Thu, 10 Nov 2011 09:33 EST

Tuya Bao, Toshiaki Adachi

Source: Kodai Math. J., Volume 34, Number 3, 485--504.

Abstract:
We study circular trajectories for Sasakian magnetic fields on geodesic spheres, horospheres and tubes around totally geodesic complex hypersurfaces in a complex hyperbolic space. Investigating their extrinsic shapes in the ambient complex hyperbolic space, we give conditions for them to be bounded and to be closed. By use of information on lengths of circles in complex space forms, we give expressions of lengths of circular trajectories on those real hypersurfaces and show that their length spectrum is a discrete subset of a real line.

Local properties on the remainders of the topological groups

Thu, 10 Nov 2011 09:33 EST

Fucai Lin

Source: Kodai Math. J., Volume 34, Number 3, 505--518.

Abstract:
When does a topological group G have a Hausdorff compactification bG with a remainder belonging to a given class of spaces? In this paper, we mainly improve some results of A. V. Arhangel'skiĭ and C. Liu's. Let G be a non-locally compact topological group and bG be a compactification of G . The following facts are established: (1) If bG $\backslash$ G has locally a k -space with a point-countable k -network and π-character of bG $\backslash$ G is countable, then G and bG are separable and metrizable; (2) If bG $\backslash$ G has locally a δθ-base, then G and bG are separable and metrizable; (3) If bG $\backslash$ G has locally a quasi- G δ -diagonal, then G and bG are separable and metrizable. Finally, we give a partial answer for a question, which was posed by C. Liu in [16].

Torus invariant special Lagrangian submanifolds in the canonical bundle of toric positive Kähler Einstein manifolds

Thu, 10 Nov 2011 09:33 EST

Kotaro Kawai

Source: Kodai Math. J., Volume 34, Number 3, 519--535.

Abstract:
In this paper we construct torus invariant special Lagrangian submanifolds in the canonical bundle K M of the toric positive Kähler Einstein manifold M . We construct a Ricci-flat metric on K M using the Calabi ansatz to show that K M is a Calabi-Yau manifold. Then, using moment map techniques developed in [6], we construct special Lagrangian submanifolds in K M .

f -cohomology and motives over number rings

Thu, 29 Mar 2012 09:21 EDT

Jakob Scholbach

Source: Kodai Math. J., Volume 35, Number 1, 1--32.

Abstract:
This paper is concerned with an interpretation of f -cohomology, a modification of motivic cohomology of motives over number fields, in terms of motives over number rings. Under standard assumptions on mixed motives over finite fields, number fields and number rings, we show that the two extant definitions of f -cohomology of mixed motives M η over a number field F —one via ramification conditions on ℓ-adic realizations, another one via the K -theory of proper regular models—both agree with motivic cohomology of η !* M η [1]. Here η !* is constructed by a limiting process in terms of intermediate extension functors j !* defined in analogy to perverse sheaves.

On Heisenberg's inequality and Bell's inequality

Thu, 29 Mar 2012 09:21 EDT

Masao Nagasawa

Source: Kodai Math. J., Volume 35, Number 1, 33--51.

Abstract:

Schatten class Toeplitz operators on the parabolic Bergman space II

Thu, 29 Mar 2012 09:21 EDT

Masaharu Nishio, Noriaki Suzuki, Masahiro Yamada

Source: Kodai Math. J., Volume 35, Number 1, 52--77.

Abstract:
Let 0 < α ≤ 1 and let $\boldsymbol{b}_\alpha^{2}$ be a Hilbert space of all square integrable solutions of a parabolic equation (∂ t + (−Δ) α ) u = 0 on the upper half space. We study the Toeplitz operators on $\boldsymbol{b}_\alpha^{2}$ , which we characterize to be of Schatten class whose exponent is smaller than 1. For the proof, we use an atomic decomposition theorem of parabolic Bergman functions. Generalizations to Schatten class operators for Orlicz type and Herz type are also discussed.

Some sections on rational elliptic surfaces and certain special conic-quartic configurations

Thu, 29 Mar 2012 09:21 EDT

Hiro-o Tokunaga

Source: Kodai Math. J., Volume 35, Number 1, 78--104.

Abstract:

A normality criterion for meromorphic functions

Thu, 29 Mar 2012 09:21 EDT

Shanpeng Zeng, Indrajit Lahiri

Source: Kodai Math. J., Volume 35, Number 1, 105--114.

Abstract:
In the paper we prove a normality criterion for a family of meromorphic functions which involves sharing of a non-zero finite value by certain differential polynomials generated by the members of the family.

Derivatives of rotation number of one parameter families of circle diffeomorphisms

Thu, 29 Mar 2012 09:21 EDT

Shigenori Matsumoto

Source: Kodai Math. J., Volume 35, Number 1, 115--125.

Abstract:
We consider the rotation number ρ( t ) of a diffeomorphism f t = R t $\circ$ f , where R t is the rotation by t and f is an orientation preserving C ∞ diffeomorphism of the circle S 1 . We shall show that if ρ( t ) is irrational $\limsup_{t'\to t}$ (ρ( t ′) − ρ( t )) / ( t ′ − t ) ≥ 1.

Asymptotic behaviors of nonlinear neutral impulsive delay differential equations with forced term

Thu, 29 Mar 2012 09:21 EDT

Fangfang Jiang, Jianhua Shen

Source: Kodai Math. J., Volume 35, Number 1, 126--137.

Abstract:
In this paper, we study the asymptotic behavior of solutions of a class of nonlinear neutral impulsive delay differential equations with forced term of the form $\left\{\begin{array}{lll}[x(t)+c(t)x(t-\tau)]' +p(t)f(x(t-\delta))=q(t),\hspace{3zw}t\geq t_0, t\neq t_k,\\ x(t_k)=b_kx(t_k^-)+(1-b_k)\int_{t_k-\delta}^{t_k}p(s+\delta)f(x(s))ds+(b_k-1)\int_{t_k}^\infty q(s)ds,\hspace{3zw}k\in{\mathbf{Z_+}},\end{array}\right.$ Sufficient conditions are obtained for every solution of the equations that tends to a constant as t → ∞.

Teichmüller space of genus two based on Schmutz Schaller's hyperbolic polygons

Thu, 29 Mar 2012 09:21 EDT

Gou Nakamura

Source: Kodai Math. J., Volume 35, Number 1, 138--156.

Abstract:
Following the idea of P. Schmutz Schaller, we shall consider a parametrization of the Teichmüller space $\mathcal{T}_2$ of compact Riemann surfaces of genus two. In the first part of this paper, we calculate the coordinates of 4 kinds of surface uniformized by Fuchsian groups whose fundamental regions can be the regular octagon. In the second part, we give a characterization of $\mathcal{T}_2$ in R 7 .

An embedding theorem on reducing subspace frame multiresolution analysis

Thu, 29 Mar 2012 09:21 EDT

Yun-Zhang Li, Lin Zhang

Source: Kodai Math. J., Volume 35, Number 1, 157--172.

Abstract:
This paper addresses FMRA and MRA in the setting of reducing subspaces of L 2 ( R d ). We prove that an FMRA must be contained in some MRA , and obtain a sufficient condition for an MRA to contain no FMRA other than itself.

The Nash problem of arcs and the rational double point E 6

Thu, 29 Mar 2012 09:21 EDT

Camille Plénat, Mark Spivakovsky

Source: Kodai Math. J., Volume 35, Number 1, 173--213.

Abstract:
This paper deals with the Nash problem, which consists in proving that the number of families of arcs on a germ of a normal isolated singularity coincides with the number of essential components of the exceptional set in any resolution of this singularity. We propose a program for an affirmative solution of the Nash problem for special types of normal isolated hypersurface singularities. We illustrate this program by giving an affirmative solution of the Nash problem for the rational double point E 6 . We also prove some results on the algebraic structure of the space of k -jets of an arbitrary hypersurface singularity and apply them to the specific case of E 6 .

Unstable subsystems cause Turing instability

Wed, 04 Jul 2012 07:25 EDT

Atsushi Anma, Kunimochi Sakamoto, Tohru Yoneda

Source: Kodai Math. J., Volume 35, Number 2, 215--247.

Abstract:
We study Turing instabilities in 3-component reaction-diffusion systems. The existence of a complementary pair of stable-unstable subsystems always gives rise to Turing instability for suitable diagonal diffusion matrices. There are two types of Turing instability, one called steady instability and the other wave instability . To determine which of the two types of instability actually occurs, easily verifiable conditions on unstable subsystems are given. A complementary pair of unstable-unstable subsystems in a stable full system also leads to steady instability. Our results give a perspective to the rich variety and complexity of pattern dynamics in 3-component systems of reaction-diffusion equations at the onset.

Intersection theory on mixed curves

Wed, 04 Jul 2012 07:25 EDT

Mutsuo Oka

Source: Kodai Math. J., Volume 35, Number 2, 248--267.

Abstract:
We consider two mixed curves C , C ′ $subset$ C 2 which are defined by mixed functions of two variables z = ( z 1 , z 2 ). We have shown in [4], that they have canonical orientations. If C and C ′ are smooth and intersect transversely at P , the intersection number I top ( C , C ′; P ) is topologically defined. We will generalize this definition to the case when the intersection is not necessarily transversal or either C or C ′ may be singular at P using the defining mixed polynomials.

Some rigidity theorems in semi-Riemannian warped products

Wed, 04 Jul 2012 07:25 EDT

Antonio Gervasio Colares, Henrique Fernandes de Lima

Source: Kodai Math. J., Volume 35, Number 2, 268--282.

Abstract:
We study the problem of uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product whose warping function has convex logarithm. By applying a maximum principle at the infinity due to S. T. Yau and supposing a natural comparison inequality between the mean curvature of the hypersurface and that of the slices of the region where the hypersurface is contained, we obtain rigidity theorems in such ambient spaces. Applications to the hyperbolic and the steady state spaces are given.

Creating limit functions by the Pang-Zalcman lemma

Wed, 04 Jul 2012 07:25 EDT

Shai Gul, Shahar Nevo

Source: Kodai Math. J., Volume 35, Number 2, 283--310.

Abstract:
In this paper we calculate the collection of limit functions obtained by applying an extension of Zalcman's Lemma, due to X. C. Pang to the non-normal family { f ( nz ): n $in$ N } in C , where f = Re P . Here R and P are an arbitrary rational function and a polynomial, respectively, where P is a non-constant polynomial.

An explicit bound for the Łojasiewicz exponent of real polynomials

Wed, 04 Jul 2012 07:25 EDT

Tien Son Pham

Source: Kodai Math. J., Volume 35, Number 2, 311--319.

Abstract:
Let f : R n → R be a polynomial function of degree d with f (0) = 0. The classical Łojasiewiz inequality states that there exist c > 0 and α > 0 such that | f ( x )| ≥ cd ( x , f –1 (0)) α in a neighbourhod of the origin 0 $in$ R n , where d ( x , f –1 (0)) denotes the distance from x to the set f –1 (0). We prove that the smallest such exponent α is not greater than R ( n , d ) with R ( n , d ) := max{ d (3 d – 4) n –1 , 2 d (3 d – 3) n –2 }.

Invariants of ample line bundles on projective varieties and their applications, III

Wed, 04 Jul 2012 07:25 EDT

Yoshiaki Fukuma

Source: Kodai Math. J., Volume 35, Number 2, 320--344.

Abstract:
Let X be a smooth complex projective variety of dimension n and let L 1 , ..., L n – i be ample line bundles on X , where i is an integer with 0 ≤ i ≤ n – 1. In the first part, we defined the i th sectional geometric genus g i ( X , L 1 , ..., L n – i ) and the i th sectional H-arithmetic genus χ i H ( X , L 1 , ..., L n – i ) of ( X , L 1 , ..., L n – i ). In this third part, we will investigate g 2 ( X , L 1 , ..., L n –2 ) and χ 2 H ( X , L 1 , ..., L n –2 ). Moreover we will give some applications of the sectional invariants of multi-polarized manifolds.

Fiberwise Green functions of skew products semiconjugate to some polynomial products on C 2

Wed, 04 Jul 2012 07:25 EDT

Kohei Ueno

Source: Kodai Math. J., Volume 35, Number 2, 345--357.

Abstract:
We consider the dynamics of polynomial skew products that are semiconjugate to some polynomial products on C 2 . We show that the fiberwise Green functions exist outside thin sets, whose upper semicontinuous regularizations are defined, continuous and plurisubharmonic on C 2 . This result is obtained from the existence of Green functions of polynomials outside thin sets.

A solution to an Ambarzumyan problem on trees

Wed, 04 Jul 2012 07:25 EDT

Chun-Kong Law, Eiji Yanagida

Source: Kodai Math. J., Volume 35, Number 2, 358--373.

Abstract:
We consider the Neumann Sturm-Liouville problem defined on trees such that the ratios of lengths of edges are not necessarily rational. It is shown that the potential function of the Sturm-Liouville operator must be zero if the spectrum is equal to that for zero potential. This extends previous results and gives an Ambarzumyan theorem for the Neumann Sturm-Liouville problem on trees. To prove this, we compute approximated eigenvalues for zero potential by using a generalized pigeon hole argument, and make use of recursive formulas for characteristic functions.

Nonexistence of nontrivial quasi-Einstein metrics

Wed, 04 Jul 2012 07:25 EDT

Yawei Chu

Source: Kodai Math. J., Volume 35, Number 2, 374--381.

Abstract:
Let ( M n , g , e – f dvol g ) be a smooth metric measure space of dimension n . In this note, we first prove a nonexistence result for M n with the Bakry-Émery Ricci tensor is bounded from below. Then we show that f $in$ L ∞ ( M n , e – f dvol ) and |∇ f | $in$ L ∞ ( M n , e – f dvol ) are equivalent for complete gradient shrinking Ricci solitons. Furthermore, we prove that there is no non-Einstein shrinking soliton when the normalized function $\tilde f$ is non-positive.

δ(2)-ideal null 2-type hypersurfaces of Euclidean space are spherical cylinders

Wed, 04 Jul 2012 07:25 EDT

Bang-Yen Chen, Oscar J. Garay

Source: Kodai Math. J., Volume 35, Number 2, 382--391.

Abstract:
We prove that a null 2-type hypersurface in the Euclidean ( n + 1)-space is an open portion of a spherical cylinder S n –1 × R if and only if it is δ(2)-ideal.

A note on countably bi-quotient mappings

Wed, 04 Jul 2012 07:25 EDT

Shou Lin, Zhongjing Zhu

Source: Kodai Math. J., Volume 35, Number 2, 392--402.

Abstract:
In this paper some properties of weakly first countable spaces and sequence-covering images of metric spaces are studied. Strictly Fréchet spaces are characterized as the spaces in which every sequence-covering mapping onto them is strictly countably bi-quotient. Strict accessibility spaces are introduced, in which a T 1 -space X is strict accessibility if and only if every quotient mapping onto X is strictly countably bi-quotient. For a T 2 , k -space X every quotient mapping onto X is strictly countably bi-quotient or bi-quotient if and only if X is discrete. They partially answer some questions posed by F. Siwiec in [16, 17].

A discriminant criterion of irreducibility

Wed, 04 Jul 2012 07:25 EDT

Evelia R. García Barroso, Janusz Gwoździewicz

Source: Kodai Math. J., Volume 35, Number 2, 403--414.

Abstract:
In this paper we give a criterion of irreducibility for a complex power series in two variables, using the notion of jacobian Newton diagrams, defined with respect to any direction. Then we apply our method to study the branches of plane algebraic curves. For an affine plane curve with one point at infinity, we also obtain a criterion for an analytical irreducibility in terms of the Newton diagram of a discriminant, without using coordinates centered at the point at infinity.

A gluing theorem for quasiconformal mappings

Thu, 15 Nov 2012 08:18 EST

Yunping Jiang, Yi Qi

Source: Kodai Math. J., Volume 35, Number 3, 415--424.

Abstract:
We prove, by using the main inequality of Reich and Strebel, that any n K -quasiconformal germs defined on n disjoint domains in the Riemann sphere can be glued by one ( K + ε)-quasiconformal homeomorphism, where ε is a positive number which can go to zero as the domains of germs shrinking to n points. This generalizes a result in [8] where only the case K = 1 has been considered.

On Fano manifolds with an unsplit dominating family of rational curves

Thu, 15 Nov 2012 08:18 EST

Carla Novelli

Source: Kodai Math. J., Volume 35, Number 3, 425--438.

Abstract:
We study Fano manifolds X admitting an unsplit dominating family of rational curves and we prove that the Generalized Mukai Conjecture holds if X has pseudoindex i X = (dim X )/3 or dimension dim X = 6. We also show that this conjecture is true for all Fano manifolds with i X > (dim X )/3.

The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator

Thu, 15 Nov 2012 08:18 EST

Erhan Deniz, Murat Çağlar, Halit Orhan

Source: Kodai Math. J., Volume 35, Number 3, 439--462.

Abstract:
By using Dziok-Srivastava operator a new subclass of analytic functions generalized k -parabolic starlike functions, denoted by k – SP l , m (α 1 ;γ), is introduced. For this class the Fekete-Szegö problem is completely solved. Various known or new special cases of our results are also point out.

A finiteness theorem for meromorphic mappings sharing few hyperplanes

Thu, 15 Nov 2012 08:18 EST

Duc Quang Si

Source: Kodai Math. J., Volume 35, Number 3, 463--484.

Abstract:
In this article, we prove a finiteness theorem for meromorphic mappings of C m into P n ( C ) sharing 2 n + 2 hyperplanes without counting multiplicity.

The uniqueness problem for meromorphic mappings with truncated multiplicities

Thu, 15 Nov 2012 08:18 EST

Feng Lü

Source: Kodai Math. J., Volume 35, Number 3, 485--499.

Abstract:
The purpose of this work is twofold. The first is to solve a uniqueness problem of meromorphic mappings posed by T. Cao and H. Yi in [1]. The second is to generalize several previous uniqueness theorems of meromorphic mappings "partially" sharing a few moving targets, which were given by Z. Chen and M. Ru [2], Z. Chen and Q. Yan [3], D. Thai and S. Quang [13].

Forced hyperbolic mean curvature flow

Thu, 15 Nov 2012 08:18 EST

Jing Mao

Source: Kodai Math. J., Volume 35, Number 3, 500--522.

Abstract:
In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in [5, 8]. For the first hyperbolic flow, as in [8], by using support function, we reduce it to a hyperbolic Monge-Ampère equation successfully, leading to the short-time existence of the flow by the standard theory of hyperbolic partial differential equation. If the initial velocity is non-negative and the coefficient function of the forcing term is non-positive, we also show that there exists a class of initial velocities such that the solution of the flow exists only on a finite time interval [0, T max ), and the solution converges to a point or shocks and other propagating discontinuities are generated when t → T max . These generalize the corresponding results in [8]. For the second hyperbolic flow, as in [5], we can prove the system of partial differential equations related to the flow is strictly hyperbolic, which leads to the short-time existence of the smooth solution of the flow, and also the uniqueness. We also derive nonlinear wave equations satisfied by some intrinsic geometric quantities of the evolving hypersurface under this hyperbolic flow. These generalize the corresponding results in [5].

Deforming two-dimensional graphs in R 4 by forced mean curvature flow

Thu, 15 Nov 2012 08:18 EST

Jing Mao

Source: Kodai Math. J., Volume 35, Number 3, 523--531.

Abstract:
A surface Σ 0 is a graph in R 4 if there is a unit constant 2-form w in R 4 such that ‹ e 1 ∧ e 2 , w › ≥ v 0 > 0, where { e 1 , e 2 } is an orthonormal frame on Σ 0 . In this paper, we investigate a 2-dimensional surface Σ evolving along a mean curvature flow with a forcing term in direction of the position vector. If v 0 ≥ ${1 \over \sqrt {2}}$ holds on the initial graph Σ 0 which is the immersion of the surface Σ, and the coefficient function of the forcing vector is nonnegative, then the forced mean curvature flow has a global solution, which generalizes part of the results of Chen-Li-Tian in [2].

Bundle decomposition and infinitesimal CR automorphism approaches to CR automorphism group of generalized ellipsoids

Thu, 15 Nov 2012 08:18 EST

Atsushi Hayashimoto

Source: Kodai Math. J., Volume 35, Number 3, 532--559.

Abstract:
Two types of elementary and direct proofs of the classification theorem for CR automorphisms of generalized ellipsoids by [MM10] are given. The first proof is to use an invariant decomposition of holomorphic tangent bundle, and the second is to use infinitesimal CR automorphisms. The advantages of our proofs are: (1) The conditions on the number n j of the variables and the exponents m j in the defining equation are weakened, (2) the proofs are more direct than [MM10], (3) our proofs may be applicable to wider class of hypersurfaces.

Large deviations for simple random walk on supercritical percolation clusters

Thu, 15 Nov 2012 08:18 EST

Naoki Kubota

Source: Kodai Math. J., Volume 35, Number 3, 560--575.

Abstract:
We prove quenched large deviation principles governing the position of the random walk on a supercritical site percolation on the integer lattice. A feature of this model is non-ellipticity of transition probabilities. Our analysis is based on the consideration of so-called Lyapunov exponents for the Laplace transform of the first passage time. The rate function is given by the Legendre transform of the Lyapunov exponents.

Asymptotic behaviour of good systems of parameters of sequentially generalized Cohen-Macaulay modules

Thu, 15 Nov 2012 08:18 EST

Quy Pham Hung

Source: Kodai Math. J., Volume 35, Number 3, 576--588.

Abstract:
Let ( R , $\mathfrak{m}$ ) be a commutative Noetherian local ring. A finitely generated R -module M is called sequentially generalized Cohen-Macaulay module if there is a filtration M 0 $\subseteq$ M 1 $\subseteq$ ··· $\subseteq$ M t = M of submodules of M such that 0 = dim M 0 < dim M 1 < ··· < dim M t and each M i / M i –1 is a generalized Cohen-Macaulay module. In this paper we study the asymptotic behavior of good systems of parameters, introduced in [N. T. Cuong, D. T. Cuong, On sequentially Cohen-Macaulay modules, Kodai Math. J. 30 (2007), 409-428], of sequentially generalized Cohen-Macaulay modules.

A mathematical theory for double-slit experiments of Walborn et al

Thu, 15 Nov 2012 08:18 EST

Masao Nagasawa

Source: Kodai Math. J., Volume 35, Number 3, 589--612.

Abstract:

Emden equation involving the critical Sobolev exponent with the third-kind boundary condition in S 3

Thu, 15 Nov 2012 08:18 EST

Atsushi Kosaka

Source: Kodai Math. J., Volume 35, Number 3, 613--628.

Abstract:
We consider a positive solution of the Emden equation with the critical Sobolev exponent on a geodesic ball in S 3 . In the case of the Dirichlet boundary condition, Bandle and Peletier [2] proved the precise result on the existence of a positive radial solution. We investigate the same equation with the third kind boundary condition and obtain a more general result. Namely we prove that the existence and the nonexistence of solutions depend on the geodesic radius and the boundary condition. Moreover the set of solutions consists of a unique radial classical solution and a continuum of singular solutions.

Limiting distribution of the maximum of a null recurrent diffusion process

Thu, 15 Nov 2012 08:18 EST

Yuji Kasahara, Genki Tahara

Source: Kodai Math. J., Volume 35, Number 3, 629--641.

Abstract:
A limit theorem for the maximum processes of a class of null recurrent linear diffusions is proved. The limiting distribution is a mixture of the Mittag-Leffler distribution.

On the linear independence of the set of Dirichlet exponents

Thu, 15 Nov 2012 08:18 EST

Artūras Dubickas

Source: Kodai Math. J., Volume 35, Number 3, 642--651.

Abstract:
Given k ≥ 2 let α 1 , ..., α k be transcendental numbers such that α 1 , ..., α k –1 are algebraically independent over Q and α k $\in$ Q (α 1 , ..., α k –1 ), but α k , ≠ ( a α i + c )/ b for some i $\in$ {1, ..., k – 1} and some a, b $\in$ N , c $\in$ Z satisfying gcd( a,b ) = 1. We prove that then there exists a nonnegative integer q such that the set of so-called Dirichlet exponents log( n + α j , where n runs through the set of all nonnegative integers for j = 1, ..., k – 1 and n = q, q + 1, q + 2, ... for j = k , is linearly independent over Q . As an application we obtain a joint universality theorem for corresponding Hurwitz zeta functions ζ( s , α 1 ), ..., ζ( s , α k ) in the strip { s $\in$ C : 1/2 < $\Re$ ( s ) < 1}. In our approach we follow a recent result of Mishou who analyzed the case k = 2.

A finite generating set for the level 2 mapping class group of a nonorientable surface

Fri, 29 Mar 2013 09:12 EDT

Błażej Szepietowski

Source: Kodai Math. J., Volume 36, Number 1, 1--14.

Abstract:
We obtain a finite set of generators for the level 2 mapping class group of a closed nonorientable surface of genus g ≥ 3. This set consists of isotopy classes of Lickorish's Y-homeomorphisms also called crosscap slides.

Banach spaces of bounded Dirichlet finite harmonic functions on Riemann surfaces

Fri, 29 Mar 2013 09:12 EDT

Mitsuru Nakai

Source: Kodai Math. J., Volume 36, Number 1, 15--37.

Abstract:
The Banach space of bounded Dirichlet finite harmonic functions on an open Riemann surface will be seen to be reflexive and also separable if and only if the underlying Riemann surface does not carry any unbounded Dirichlet finite harmonic function.

Positive Toeplitz operators of finite rank on the parabolic Bergman spaces

Fri, 29 Mar 2013 09:12 EDT

Masaharu Nishio, Noriaki Suzuki, Masahiro Yamada

Source: Kodai Math. J., Volume 36, Number 1, 38--49.

Abstract:
We define the Toeplitz operators on the parabolic Bergman spaces by using a positive bilinear form. In this setting we characterize finite rank Toeplitz operators. A relation with the Carleson inclusion is also discussed.

On Hermitian modular forms of small weight over imaginary quadratic fields

Fri, 29 Mar 2013 09:12 EDT

Hisashi Kojima, Yasuhide Miura, Hiroshi Sakata, Yasushi Tokuno

Source: Kodai Math. J., Volume 36, Number 1, 50--55.

Abstract:
In this paper, we prove that an Hermitian modular form with small weight over the quadratic field with class number one is a linear combination of theta series associated with Hermitian quadratic forms.

On meromorphic functions sharing a one-point set and three two-point sets CM

Fri, 29 Mar 2013 09:12 EDT

Manabu Shirosaki

Source: Kodai Math. J., Volume 36, Number 1, 56--68.

Abstract:
We show that if two meromorphic functions sharing a one-point set and three two-point sets CM, then one of them is a Möbius transform of the other.

Another improvement of Montel's criterion

Fri, 29 Mar 2013 09:12 EDT

Yan Xu

Source: Kodai Math. J., Volume 36, Number 1, 69--76.

Abstract:
Let $\cal F$ be a family of meromorphic functions defined in a domain D $subset$ C , let ψ 1 , ψ 2 and ψ 3 be three meromorphic functions such that ψ i ( z ) \not\equiv ψ j ( z ) ( i ≠ j ) in D , one of which may be ∞ identically, and let l 1 , l 2 and l 3 be positive integers or ∞ with 1/ l 1 + 1/ l 2 + 1/ l 3 < 1. Suppose that, for each f $in$ $\cal F$ and z $in$ D , (1) all zeros of f – ψ i have multiplicity at least l i for i = 1,2,3; (2) f ( z 0 ) ≠ ψ i ( z 0 ) if there exist i , j $in$ {1,2,3} ( i ≠ j ) and z 0 $in$ D such that ψ i ( z 0 ) = ψ j ( z 0 ). Then $\cal F$ is normal in D . This improves and generalizes Montel's criterion.

Bifurcation set, M-tameness, asymptotic critical values and Newton polyhedrons

Fri, 29 Mar 2013 09:12 EDT

Tat Thang Nguyen

Source: Kodai Math. J., Volume 36, Number 1, 77--90.

Abstract:
Let F = ( F 1 , F 2 , ..., F m ): C n → C m be a polynomial dominant mapping with n > m . In this paper we give the relations between the bifurcation set of F and the set of values where F is not M-tame as well as the set of generalized critical values of F . We also construct explicitly a proper subset of C m in terms of the Newton polyhedrons of F 1 , F 2 , ..., F m and show that it contains the bifurcation set of F . In the case m = n – 1 we show that F is a locally C ∞ -trivial fibration if and only if it is a locally C 0 -trivial fibration.

Leaf-wise intersections in coisotropic submanifolds

Fri, 29 Mar 2013 09:12 EDT

Satoshi Ueki

Source: Kodai Math. J., Volume 36, Number 1, 91--98.

Abstract:
The leaf-wise intersection on a coisotropic submanifold of a symplectic manifold is a generalization of the Lagrangian intersection investigated by Weinstein. In a similar way as Weinstein's argument, we replace the leaf-wise intersections by zero points of some closed 1-form, and show the same result as Moser's on the existence of leaf-wise intersections under different conditions.

On vanishing Fermat quotients and a bound of the Ihara sum

Fri, 29 Mar 2013 09:12 EDT

Igor E. Shparlinski

Source: Kodai Math. J., Volume 36, Number 1, 99--108.

Abstract:
We improve an estimate of A. Granville (1987) on the number of vanishing Fermat quotients q p ( ℓ ) modulo a prime p when ℓ runs through primes ℓ ≤ N . We use this bound to obtain an unconditional improvement of the conditional (under the Generalised Riemann Hypothesis) estimate of Y. Ihara (2006) on a certain sum, related to vanishing Fermat quotients. In turn this sum appears in the study of the index of certain subfields of cyclotomic fields Q (exp(2π i / p 2 )).

Formal group laws for multiple sine functions and applications

Fri, 29 Mar 2013 09:12 EDT

Shin-ya Koyama, Nobushige Kurokawa

Source: Kodai Math. J., Volume 36, Number 1, 109--118.

Abstract:
We investigate addition relations for multiple sine functions from the view point of formal group laws. We find that the functions which appear in the coefficients are related to classical Eisenstein serires. As application we obtain a limit formula for automorphic forms.

Recurrence relations for Super-Halley's method with Hölder continuous second derivative in Banach spaces

Fri, 29 Mar 2013 09:12 EDT

Maroju Prashanth, Dharmendra K. Gupta

Source: Kodai Math. J., Volume 36, Number 1, 119--136.

Abstract:
The aim of this paper is to study the semilocal convergence of the Super-Halley's method used for solving nonlinear equations in Banach spaces by using the recurrence relations. This convergence is established under the assumption that the second Frëchet derivative of the involved operator satisfies the Hölder continuity condition which is milder than the Lipschitz continuity condition. A new family of recurrence relations are defined based on two constants which depend on the operator. An existence-uniqueness theorem and a proori error estimates are provided for the solution x *. The R -order of the method equals to (2 + p ) for p $in$ (0,1] is also established. Three numerical examples are worked out to demonstrate the efficacy of our approach. On comparison with the results obtained for the Super-Halley's method in [3] by using majorizing sequence, we observed improved existence and uniqueness regions for the solution x * by our approach.

A notion of Δ-multigenus for certain rank two ample vector bundles

Fri, 29 Mar 2013 09:12 EDT

Enrique Arrondo, Antonio Lanteri, Carla Novelli

Source: Kodai Math. J., Volume 36, Number 1, 137--153.

Abstract:
A notion of "delta-genus" for ample vector bundles $\mathcal{E}$ of rank two on a smooth projective threefold X is defined as a couple of integers (δ 1 , δ 2 ). This extends the classical definition holding for ample line bundles. Then pairs ( X , $\mathcal{E}$ ) with low δ 1 and δ 2 are classified under suitable additional assumptions on $\mathcal{E}$ .

Contact metric structures on S 3

Fri, 29 Mar 2013 09:12 EDT

Michael Markellos, Charalambos Tsichlias

Source: Kodai Math. J., Volume 36, Number 1, 154--166.

Abstract:
In this paper, we construct a new family of contact metric structures on the unit sphere S 3 . Especially, the above family has the property that ∇ ξ τ = 2ατφ.

Conformally natural extensions in view of dynamics

Fri, 29 Mar 2013 09:12 EDT

Yunping Jiang, Sudeb Mitra, Zhe Wang

Source: Kodai Math. J., Volume 36, Number 1, 167--173.

Abstract:
We give an easy description of the barycentric extension of a map of the unit circle to the closed unit disk using some ideas from dynamical systems. We then prove that every circle endomorphism of the unit circle of degree d ≥ 2 (with a topological expansion condition) has a conformally natural extension to the closed unit disk which is real analytic on the open unit disk. If the endomorphism is uniformly quasisymmetric, then the extension is quasiconformal.

Chern classes and the Rost cohomological invariant

Fri, 29 Mar 2013 09:12 EDT

Nobuaki Yagita

Source: Kodai Math. J., Volume 36, Number 1, 174--178.

Abstract:

Extensions of the Euler-Satake characteristic determine point singularities of orientable 3-orbifolds

Fri, 29 Mar 2013 09:12 EDT

Ryan Carroll, Christopher Seaton

Source: Kodai Math. J., Volume 36, Number 1, 179--188.

Abstract:
We compute the extensions of the Euler-Satake characteristic of a closed, effective, orientable 3-orbifold corresponding to free and free abelian groups in terms of the number and type of point singularities of the orbifold. Using these computations, we show that the free Euler-Satake characteristics determine the number and type of point singularities, and that it takes an infinite collection of free Euler-Satake characteristics to do so. Additionally, we show that the stringy orbifold Euler characteristic determines all of the free abelian Euler-Satake characteristics for an orbifold in this class.