# Showing papers in "Kodai Mathematical Journal in 2016"

••

[...]

TL;DR: In this paper, 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, which can be easily shown that these integrals have similar properties to the classical ones.

Abstract: 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.

28 citations

••

[...]

TL;DR: A sufficient and necessary condition for a Kouchnirenko non-degenerate holomorphic function to have an isolated singularity at 0 in terms of its support is given in this paper.

Abstract: 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.

12 citations

••

[...]

Hunan University

^{1}TL;DR: In this paper, the authors introduced a new class of harmonic quasiconformal mappings with analytic functions and proved that the images of linear combinations in this class are convex in a given direction.

Abstract: In this paper, we introduce a new class $\mathscr{S}_{H} (k, γ; \phi)$ of harmonic quasiconformal mappings, where $k \in [0,1), γ \in [0,π)$ and $\phi$ 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 $\phi$, are convex.

12 citations

••

[...]

TL;DR: In this paper, the Ricci curvature of the Reeb vector field is invariant to the Riemannian curvature tensor in a 3D almost co-Kahler manifold.

Abstract: Let M3 be a three-dimensional almost coKahler manifold such that the Ricci curvature of the Reeb vector field is invariant along the Reeb vector field. In this paper, we obtain some classification results of M3 for which the Ricci tensor is η-parallel or the Riemannian curvature tensor is harmonic.

9 citations

••

[...]

TL;DR: In this paper, the authors derived several new results and pose some new conjectures that relate to the yet to be resolved conjecture concerning the quantitative estimates on the zeros of ff(k)-b, for a non-vanishing small function b.

Abstract: Let f denote a transcendental meromorphic function with N(r, f) = S(r, f) and k be an integer. By using methods different from others, we have been able to derive several new results and pose some new conjectures that relate to the yet to be resolved conjecture concerning the quantitative estimates on the zeros of ff(k)-b, for a non-vanishing small function b.

8 citations

••

[...]

Wuhan University

^{1}TL;DR: In this article, the nonexistence result for general p-biharmonic submanifolds was studied and the existence and nonexistence of p-bienergy of general isometric isometric p-bharmonic maps were studied.

Abstract: Let u: (M, g) → (N, h) be a map between Riemannian manifolds (M, g) and (N, h). The p-bienergy of u is τp(u) = ∫M|τ(u)|p dνg, where τ(u) is the tension field of u and p > 1. Critical points of τp are called p-biharmonic maps and isometric p-biharmonic maps are called p-biharmonic submanifolds. When p = 2, p-biharmonic submanifolds are biharmonic submanifolds and in recent years many nonexistence results are found for biharmonic submanifolds in nonpositively curved manifolds. In this paper we will study the nonexistence result for general p-biharmonic submanifolds.

7 citations

••

[...]

TL;DR: In this article, the existence and uniqueness of time periodic solutions for the general periodic parabolic equation boundary problem with nonlocal delay was studied. But the authors only considered the case of the non-local delay version of the problem.

Abstract: 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.

7 citations

••

[...]

TL;DR: In this article, the Reidemeisiter torsion of a 3-manifold obtained by a Dehn-surgery along the figure-eight knot was studied for any SL(2; C)-irreducible representation.

Abstract: 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.

6 citations

••

[...]

TL;DR: In this paper, the basic notions and results of equivariant intersection theory are reviewed, and a generalization of this theory to the theory of schemes is given. But the results are restricted to the case where the diagonal action on the scheme is also free.

Abstract: 2. Equivariant intersectiontheoryEdidin and Graham [5, 6] gave an algebraic construction to equivari-ant intersection theory. In this section, we review the basic notionsand results of this theory. Let Gbe a linear algebraic group and letX be a scheme of ﬁnite type over C endowed with a G-action. Forany non-negative integer i, we can ﬁnd a representation V of Gto-gether with a dense open subset U ⊂ V on which Gacts freely andwhose complement has codimension larger than dimX−isuch that theprincipal bundle quotient U→ U/Gexists in the category of schemes(see [5, Lemma 9]). The diagonal action on X× U is then also free,which implies that under mild assumption, a principal bundle quotientX×U→ (X×U)/Gexists in the category of schemes (see [5, Propo-sition 23]). In what follows, we will tacitly assume that the scheme(X× U)/Gexists and denote it by X

4 citations

••

[...]

TL;DR: In this paper, the authors obtained some inequalities of the Ostrowski and Hermite-Hadamard type for Lipschitzian mappings between two Banach spaces, and applied them to functions of norms in Banach algebras.

Abstract: 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.

4 citations

••

[...]

TL;DR: In this article, it was shown that the Izeki-Nayatani invariance of a graph model on a Bruhat-Tits building associated to a semi-simple algebraic group has a global fixed point.

Abstract: We prove that if a geodesically complete CAT(0) space X admits a proper cocompact isometric action of a group, then the Izeki-Nayatani invariant of X is less than 1. Let G be a finite connected graph, μ1(G) be the linear spectral gap of G, and λ1(G,X) be the nonlinear spectral gap of G with respect to such a CAT(0) space X. Then, the result implies that the ratio λ1(G,X)/μ1(G) is bounded from below by a positive constant which is independent of the graph G. It follows that any isometric action of a random group of the graph model on such X has a global fixed point. In particular, any isometric action of a random group of the graph model on a Bruhat-Tits building associated to a semi-simple algebraic group has a global fixed point.

••

[...]

Wuyi University

^{1}TL;DR: In this paper, a lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifolds was obtained by using the Zassenhaus neighborhood of Sp(n, 1).

Abstract: 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 $\mathscr{M} = \mathbf H_\mathbf H ^n/Γ$. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds.

••

[...]

TL;DR: In this paper, the Tutte polynomial was used to give an explicit formula for the Jones Polynomial of any rational link in terms of the denominators of the canonical continued fraction of its slope.

Abstract: We use the Tutte polynomial to give an explicit formula for the Jones polynomial of any rational link in terms of the denominators of the canonical continued fraction of its slope.

••

[...]

TL;DR: In this article, a self-adjoint dilation of the dissipative singular q-Sturm-Liouville operator is studied in the Hilbert space and completeness of the system of eigenfunctions and associated functions (or root functions) of the operator is proved.

Abstract: In this study, dissipative singular q-Sturm-Liouville operators are studied in the Hilbert space $\mathscr{L}_{r,q}^{2}$(Rq,+), that the extensions of a minimal symmetric operator in limit-point case. We construct a self-adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax-Phillips. Then, we create a functional model of the maximal dissipative operator via the incoming spectral representation and define its characteristic function in terms of the Weyl-Titchmarsh function (or scattering function of the dilation) of a self-adjoint q-Sturm-Liouville operator. Finally, we prove the theorem on completeness of the system of eigenfunctions and associated functions (or root functions) of the dissipative q-Sturm-Liouville operator.

••

[...]

TL;DR: In this article, the existence of a cyclic (q, n)-gonal Riemann surface is studied and the necessary and sufficient conditions for its existence are given for the full automorphism group being G = Z2sn.

Abstract: A compact Riemann surface X of genus g ≥ 2 is called asymmetric or pseudo-real if it admits an anticonformal automorphism but no anticonformal involution. The order d = #(δ) of an anticonformal automorphism δ of such a surface is divisible by 4. In the particular case where d = 4, δ is a pseudo-symmetry and the surface is called pseudo-symmetric. A Riemann surface X is said to be p-hyperelliptic if it admits a conformal involution ρ for which the orbit space X/ has genus p. This notion is the particular case of so called cyclic (q,n)-gonal surface which is defined as the one admitting a conformal automorphism φ of prime order n such that X/φ has genus q. We are interested in possible values of n and q for which an asymmetric surface of given genus g ≥ 2 is (q,n)-gonal, and possible values of p for which the surface is p-hyperelliptic. Up till now, this problem was solved in the case where the surface is asymmetric and pseudo-symmetric. If an asymmetric Riemann surface X is not pseudo-symmetric then any anticonformal automorphism of X has order divisible by 2sn for s ≥ 3 and n = 1 or n being an odd prime. In this paper we give the necessary and sufficient conditions on the existence of an asymmetric Riemann surface with the full automorphism group being G = Z2sn, and we study (q,n)-gonal automorphisms and p-hyperelliptic involutions in G.

••

[...]

TL;DR: The smoothness of a conjugation of a 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 was studied in this paper.

Abstract: 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.

••

[...]

TL;DR: The topology of the moduli spaces of representations of degree 2 for free monoids was studied in this article, and the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations were calculated.

Abstract: In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.

••

[...]

TL;DR: In this paper, a unified constructions of lattices in splittable solvable Lie groups are considered. But they do not consider a unified construction of the lattices of a lattice in polynomial time.

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

••

[...]

TL;DR: In this article, it was shown that Parusinski's result generalizes all the same to families of non-isolated singularities if the Le numbers of the function f itself are defined and constant along the strata of an analytic stratification of C × (f0−1(0) $\cap$ g− 1(0)).

Abstract: 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. Parusinski. It is also known that Parusinski's result does not extend to families of non-isolated singularities in the sense that the constancy of the Le numbers of ft at 0, as t varies, does not imply the topological triviality of the family ft in general—a result of J. Fernandez de Bobadilla. In this paper, we show that Parusinski's result generalizes all the same to families of non-isolated singularities if the Le numbers of the function f itself are defined and constant along the strata of an analytic stratification of C × (f0−1(0) $\cap$ g−1(0)). Actually, it suffices to consider the strata that contain a critical point of f.

••

[...]

••

[...]

TL;DR: In this paper, the p-harmonic map u: M → N is studied, and a theorem of Liouville type is obtained, where n is a weighted Riemannian manifold with non-negative Bakry-Emery-Ricci curvature.

Abstract: Let M be a weighted Riemannian manifold with non-negative Bakry-Emery-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.

••

[...]

TL;DR: In this paper, the authors studied the convexity of simple closed frontals of Legendre curves in the Euclidean plane by using the curvature of the Legendre curve.

Abstract: 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.

••

[...]

TL;DR: In this paper, the Bott residue formula in equivariant cohomology is used to show a formula for the algebraic degree in semidefinite programming, which is the same formula used in this paper.

Abstract: In this paper we use the Bott residue formula in equivariant cohomology to show a formula for the algebraic degree in semidefinite programming.

••

[...]

TL;DR: In this paper, the authors established new sufficient conditions for the polynomial f to be SOS in terms of the Newton polyhedron of f (Theorems 2.6 and 2.12).

Abstract: 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].

••

[...]

TL;DR: It was shown in this paper that the complex dilatation of the Douady-Earle extension of a strongly symmetric homeomorphism induces a vanishing Carleson measure on the unit disk D.

Abstract: 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-Teichmuller space is a subgroup of the universal Teichmuller space.

••

[...]

TL;DR: In this article, the intersection formula for the Donaldson-Futaki invariant was generalized to the case of higher FIFI invariants, which are obstructions to asymptotic Chow semistability.

Abstract: 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.

••

[...]

••

[...]

TL;DR: In this paper, it was shown that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group.

Abstract: Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated by C. Leininger and D. Margalit that any pair of elements of the Torelli group either commute or generate a free group.

••

[...]

Kyoto University

^{1}TL;DR: In this paper, the authors generalize Earle-Li's polydisk theorem and embedding theorem, and study isometries from the unit disk to infinite dimensional Teichmuller spaces.

Abstract: We generalize Earle-Li's polydisk theorem and embedding theorem, and study isometries from the unit disk to infinite dimensional Teichmuller spaces. We also give a simple proof that for any non-Strebel point τ, there exist infinitely many real analytic geodesic disks through τ and the basepoint in infinitely dimensional Teichmuller spaces.