## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (186.405 recursos)

Kodai Mathematical Journal

1. #### On combinatorial criteria for non-degenerate singularities

Brzostowski, Szymon; Oleksik, Grzegorz
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.

2. #### Balls in quaternionic hyperbolic manifolds

Cao, Wensheng
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 $\mathcal{M}$ = HHn/Γ. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds.

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

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...

4. #### Douady-Earle extension of the strongly symmetric homeomorphism

Wu, Yan; Qi, Yi
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.

5. #### Tikhonov regularization for Dunkl multiplier operators

Soltani, Fethi
We study some class of Dunkl multiplier operators Tk,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 Tk,m on the Dunkl-type Paley-Wiener spaces Hh.

6. #### On convexity of simple closed frontals

Fukunaga, Tomonori; Takahashi, Masatomo
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.

7. #### A construction of lattices in splittable solvable Lie groups

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

8. #### Linear combinations of harmonic quasiconformal mappings convex in one direction

Sun, Yong; Rasila, Antti; Jiang, Yue-Ping
In this paper, we introduce a new class $\mathcal{S}_{H}$ (k, γ; φ) of harmonic quasiconformal mappings, where k $\in$ [0,1), γ $\in$ [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.

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

Zhang, Jian-Feng; Wang, Yue
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.

10. #### Cohomology formula for obstructions to asymptotic Chow semistability

Suzuki, Yuta
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.

11. #### Some new lower bounds of the first eigenvalue on Finsler manifolds

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

12. #### The asymptotic behavior of holomorphic 1-cochains

Yamaki, Daisuke
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.

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

Kitano, Teruaki
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.

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

Li, Qiang; Li, Yongxiang; Chen, Pengyu
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.

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

Dang, Van Doat; Nguyen, Thi Thao
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].

16. #### Integral inequalities for Lipschitzian mappings between two Banach spaces and applications

Dragomir, Sever S.
In this paper we obtain some inequalities of Ostrowski and Hermite-Hadamard type for Lipschitzian mappings between two Banach spaces. Applications for functions of norms in Banach spaces and functions defined by power series in Banach algebras are provided as well.

17. #### A new form of the generalized complete elliptic integrals

Takeuchi, Shingo
Generalized trigonometric functions are applied to Legendre's form of complete elliptic integrals, and a new form of the generalized complete elliptic integrals of the Borweins is presented. According to the form, it can be easily shown that these integrals have similar properties to the classical ones. In particular, it is possible to establish a computation formula of the generalized π in terms of the arithmetic-geometric mean, in the classical way as the Gauss-Legendre algorithm for π by Brent and Salamin. Moreover, an elementary alternative proof of Ramanujan's cubic transformation is also given.

18. #### Topological triviality of linear deformations with constant Lê numbers

Eyral, Christophe; Ruas, Maria Aparecida Soares
Let f(t,z) = f0(z) + tg(z) be a holomorphic function defined in a neighbourhood of the origin in C × Cn. It is well known that if the one-parameter deformation family {ft} defined by the function f is a μ-constant family of isolated singularities, then {ft} is topologically trivial—a result of A. Parusiński. It is also known that Parusiński's result does not extend to families of non-isolated singularities in the sense that the constancy of the Lê numbers of ft at 0, as t varies, does not imply the topological triviality of the family ft in general—a result of J....

19. #### Congruence of minimal surfaces

Kassabov, Ognian
An interesting problem in classical differential geometry is to find methods to prove that two surfaces defined by different charts actually coincide up to position in space. In a previous paper we proposed a method in this direction for minimal surfaces. Here we explain not only how this method works but also how we can find the correspondence between the minimal surfaces, if they are congruent. We show that two families of minimal surfaces which are proved to be conjugate actually coincide and coincide with their associated surfaces. We also consider another family of minimal polynomial surfaces of degree 6...

20. #### The structure Jacobi operator of three-dimensional real hypersurfaces in non-flat complex space forms

Kaimakamis, George; Panagiotidou, Konstantina; Pérez, Juan de Dios
In this paper new results concerning three dimensional real hypersurfaces in non-flat complex space forms in terms of their stucture Jacobi operator are presented. More precisely, the conditions of 1) the structure Jacobi operator being of Codazzi type with respect to the generalized Tanaka-Webster connection and commuting with the shape operator and 2) η-invariance of the structure Jacobi operator and commutativity of it with the shape operator are studied. Furthermore, results concerning Hopf hypersurfaces and ruled hypersurfaces of dimension greater than three satisfying the previous conditions are also included.

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