Kodai Mathematical Journal Articles (Project Euclid)
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The latest articles from Kodai Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTThu, 31 Mar 2011 09:07 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Remarks on complete non-compact gradient Ricci expanding solitons
http://projecteuclid.org/euclid.kmj/1278076334
<strong>Li Ma</strong>, <strong>Dezhong Chen</strong><p><strong>Source: </strong>Kodai Math. J., Volume 33, Number 2, 173--181.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1278076334_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTA number theoretical observation of a resonant interaction of Rossby waveshttp://projecteuclid.org/euclid.kmj/1490083220<strong>Nobu Kishimoto</strong>, <strong>Tsuyoshi Yoneda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 16--20.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083220_20170321040117Tue, 21 Mar 2017 04:01 EDTCentro-affine invariants and the canonical Lorentz metric on the space of centered ellipseshttp://projecteuclid.org/euclid.kmj/1490083221<strong>Marcos Salvai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 21--30.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083221_20170321040117Tue, 21 Mar 2017 04:01 EDTHerz-type Besov spaces of variable smoothness and integrabilityhttp://projecteuclid.org/euclid.kmj/1490083222<strong>Douadi Drihem</strong>, <strong>Rabah Heraiz</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 31--57.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083222_20170321040117Tue, 21 Mar 2017 04:01 EDTOn Faltings' local-global principle of generalized local cohomology moduleshttp://projecteuclid.org/euclid.kmj/1490083223<strong>Nguyen Van Hoang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 58--62.</p><p><strong>Abstract:</strong><br/> Let R be a commutative Noetherian ring, I an ideal of R and M , N finitely generated R -modules. Let 0 ≤ n $\in$ 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{ $f_{I_\frak{p}}(M_\frak{p},N_\frak{p})$ | $\frak{p}$ $\in$ Supp( N / I M N ), 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. </p>projecteuclid.org/euclid.kmj/1490083223_20170321040117Tue, 21 Mar 2017 04:01 EDTGlobal attractors for a Kirchhoff type plate equation with memoryhttp://projecteuclid.org/euclid.kmj/1490083224<strong>Xiaobin Yao</strong>, <strong>Qiaozhen Ma</strong>, <strong>Ling Xu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 63--78.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083224_20170321040117Tue, 21 Mar 2017 04:01 EDTThe Euler product for the Riemann zeta-function in the critical striphttp://projecteuclid.org/euclid.kmj/1490083225<strong>Hirotaka Akatsuka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 79--101.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083225_20170321040117Tue, 21 Mar 2017 04:01 EDTUnit tangent sphere bundles with the Reeb flow invariant Ricci operatorhttp://projecteuclid.org/euclid.kmj/1490083226<strong>Jong Taek Cho</strong>, <strong>Sun Hyang Chun</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 102--116.</p><p><strong>Abstract:</strong><br/> In this paper, we study unit tangent sphere bundles T 1 M 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 , T 1 M 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 , T 1 M 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. </p>projecteuclid.org/euclid.kmj/1490083226_20170321040117Tue, 21 Mar 2017 04:01 EDTGlobal uniqueness results for ground states for a class of quasilinear elliptic equationshttp://projecteuclid.org/euclid.kmj/1490083227<strong>Shinji Adachi</strong>, <strong>Masataka Shibata</strong>, <strong>Tatsuya Watanabe</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 117--142.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083227_20170321040117Tue, 21 Mar 2017 04:01 EDTEffective actions of the general indefinite unitary groups on holomorphically separable manifoldshttp://projecteuclid.org/euclid.kmj/1490083228<strong>Yoshikazu Nagata</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 143--177.</p><p><strong>Abstract:</strong><br/> 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. </p>projecteuclid.org/euclid.kmj/1490083228_20170321040117Tue, 21 Mar 2017 04:01 EDTRelative purity in log étale cohomologyhttp://projecteuclid.org/euclid.kmj/1490083229<strong>Kazumi Higashiyama</strong>, <strong>Takashi Kamiya</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 1, 178--183.</p><p><strong>Abstract:</strong><br/> We study log étale cohomology. The goal is to prove relative purity in log étale cohomology. </p>projecteuclid.org/euclid.kmj/1490083229_20170321040117Tue, 21 Mar 2017 04:01 EDTA note on "On the appearance of Eisenstein series through degeneration"http://projecteuclid.org/euclid.kmj/1499846592<strong>Thérèse Falliero</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 185--199.</p><p><strong>Abstract:</strong><br/> Let M = Γ $\backslash$ H be a geometrically finite hyperbolic surface, realized as the quotient of the hyperbolic upper half plane H by a geometrically finite discrete group of isometries acting on H . To a parabolic element of the uniformizing group Γ, there is an associated 1-form parabolic Eisenstein series. To a primitive hyperbolic element, then, following ideas due to Kudla-Millson, there is a corresponding 1-form hyperbolic Eisenstein series. In this article, we study the limiting behavior of these hyperbolic Eisenstein series on a degenerating family of hyperbolic Riemann surfaces of finite type, using basically the limiting behavior of counting functions associated to degenerating hyperbolic Riemann surfaces. In this sense, we generalize the results obtained in Garbin, Jorgenson and Munn (Comment Math Helv 83:701-721, 2008) to the case of geometrically finite hyperbolic surfaces of infinite volume and form-valued parabolic and hyperbolic Eisenstein series. </p>projecteuclid.org/euclid.kmj/1499846592_20170712040345Wed, 12 Jul 2017 04:03 EDTCriteria for singularities for mappings from two-manifold to the plane. The number and signs of cuspshttp://projecteuclid.org/euclid.kmj/1499846594<strong>Iwona Krzyżanowska</strong>, <strong>Aleksandra Nowel</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 200--213.</p><p><strong>Abstract:</strong><br/> Let M $subset$ R n +2 be a two-dimensional complete intersection. We show how to check whether a mapping f : M → R 2 is 1-generic with only folds and cusps as singularities. In this case we give an effective method to count the number of positive and negative cusps of a polynomial f , using the signatures of some quadratic forms. </p>projecteuclid.org/euclid.kmj/1499846594_20170712040345Wed, 12 Jul 2017 04:03 EDTLinear Weingarten submanifolds immersed in a space formhttp://projecteuclid.org/euclid.kmj/1499846595<strong>Henrique Fernandes De Lima</strong>, <strong>Fábio Reis Dos Santos</strong>, <strong>Jogli Gidel Da Silva Araújo</strong>, <strong>Marco Antonio Lázaro Velásquez</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 214--228.</p><p><strong>Abstract:</strong><br/> In this paper, we deal with complete linear Weingarten submanifolds M n immersed with parallel normalized mean curvature vector field in a Riemannian space form Q c n + p of constant sectional curvature c . Under an appropriated restriction on the norm of the traceless part of the second fundamental form, we show that such a submanifold M n must be either totally umbilical or isometric to a Clifford torus, if c = 1, a circular cylinder, if c = 0, or a hyperbolic cylinder, if c = −1. We point out that our results are natural generalizations of those ones obtained in [2] and [6]. </p>projecteuclid.org/euclid.kmj/1499846595_20170712040345Wed, 12 Jul 2017 04:03 EDTUniversal inequalities for eigenvalues of a class of operators on Riemannian manifoldhttp://projecteuclid.org/euclid.kmj/1499846596<strong>Jianghai Shi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 229--253.</p><p><strong>Abstract:</strong><br/> In this paper, we investigate the boundary value problem of the following operator $\left\{\begin{array}{l}\Delta^{2}u-a\rm div\it A\nabla{u}+Vu=\rho\lambda{u}\ \ \hbox{in} \ \rm\Omega, \\ u|_{\partial \Omega}=\frac{\partial u}{\partial v}|_{\partial \Omega}=0,\\ \end{array}\right.$$ where Ω is a bounded domain in an n -dimensional complete Riemannian manifold M n , A is a positive semidefinite symmetric (1,1)-tensor on M n , V is a non-negative continuous function on Ω, v denotes the outwards unit normal vector field of ∂Ω and ρ is a weight function which is positive and continuous on Ω. By the Rayleigh-Ritz inequality, we obtain universal inequalities for the eigenvalues of these operators on bounded domain of complete manifolds isometrically immersed in a Euclidean space, and of complete manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to a sphere. </p>projecteuclid.org/euclid.kmj/1499846596_20170712040345Wed, 12 Jul 2017 04:03 EDTOpial and Lyapunov inequalities on time scales and their applications to dynamic equationshttp://projecteuclid.org/euclid.kmj/1499846597<strong>Nguyen Du Vi Nhan</strong>, <strong>Tran Dinh Phung</strong>, <strong>Dinh Thanh Duc</strong>, <strong>Vu Kim Tuan</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 254--277.</p><p><strong>Abstract:</strong><br/> We prove some weighted inequalities for delta derivatives acting on products and compositions of functions on time scales and apply them to obtain generalized dynamic Opial-type inequalities. We also employ these inequalities to establish some new dynamic Lyapunov-type inequalities, which are essential in studying disfocality, disconjugacy, lower bounds of eigenvalues, and distance between generalized zeros for half-linear dynamic equations. In particular, we solve an open problem posed by Saker in [Math. Comput. Modelling 58 (2013), 1777-1790]. Moreover, the results presented in this paper generalize, improve, extend, and unify most of known results not only in the discrete and continuous analysis but also on time scales. </p>projecteuclid.org/euclid.kmj/1499846597_20170712040345Wed, 12 Jul 2017 04:03 EDTA technique of constructing planar harmonic mappings and their propertieshttp://projecteuclid.org/euclid.kmj/1499846598<strong>Om P. Ahuja</strong>, <strong>Sumit Nagpal</strong>, <strong>V. Ravichandran</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 278--288.</p><p><strong>Abstract:</strong><br/> The analytic part of a planar harmonic mapping plays a vital role in shaping its geometric properties. For a normalized analytic function f defined in the unit disk, define an operator Φ[ f ]( z ) = f ( z ) + $\overline{f(z)-z}$ . In this paper, necessary and sufficient conditions on f are determined for the harmonic function Φ[ f ] to be univalent and convex in one direction. Similar results are obtained for Φ[ f ] to be starlike and convex in the unit disk. This results in the coefficient estimates, growth results and convolution properties of Φ[ f ]. In addition, various radii constants associated with Φ[ f ] have been computed. </p>projecteuclid.org/euclid.kmj/1499846598_20170712040345Wed, 12 Jul 2017 04:03 EDTRate functions for random walks on random conductance models and related topicshttp://projecteuclid.org/euclid.kmj/1499846599<strong>Chikara Nakamura</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 289--321.</p><p><strong>Abstract:</strong><br/> We consider laws of the iterated logarithm and the rate function for sample paths of random walks on random conductance models under the assumption that the random walks enjoy long time sub-Gaussian heat kernel estimates. </p>projecteuclid.org/euclid.kmj/1499846599_20170712040345Wed, 12 Jul 2017 04:03 EDTA note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularitieshttp://projecteuclid.org/euclid.kmj/1499846600<strong>Tanran Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 322--342.</p><p><strong>Abstract:</strong><br/> The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity was described up to the second order derivatives by Kraus and Roth, 2008. We refine Kraus and Roth's result for the second order mixed derivatives and give estimates for higher order derivatives near an isolated singularity. We also compute the Minda-type limits for SK-metrics near the singularity. Combining these limits with Ahlfors' lemma, we provide two observations for SK-metrics. </p>projecteuclid.org/euclid.kmj/1499846600_20170712040345Wed, 12 Jul 2017 04:03 EDTp -harmonic functions on complete manifolds with a weighted Poincaré inequalityhttp://projecteuclid.org/euclid.kmj/1499846601<strong>Bui Van Binh</strong>, <strong>Nguyen Thac Dung</strong>, <strong>Nguyen Thi Le Hai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 343--357.</p><p><strong>Abstract:</strong><br/> In this paper, we consider p -harmonic functions on complete Riemannian manifolds and give different proofs of some main theorems by Chang-Chen-Wei, in [3]. Moreover, we are able to refine their results in case of weakly p -harmonic functions. Some applications to study the connectedness at infinity of stable minimal hypersurfaces are also given. </p>projecteuclid.org/euclid.kmj/1499846601_20170712040345Wed, 12 Jul 2017 04:03 EDTApparent contours of stable maps between closed surfaceshttp://projecteuclid.org/euclid.kmj/1499846602<strong>Takahiro Yamamoto</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 358--378.</p><p><strong>Abstract:</strong><br/> Let M and N be connected and orientable, closed surfaces. For a stable map φ : M → N , denote by c (φ) and n (φ) the numbers of cusps and nodes of φ respectively. In this paper, we determine the minimal number c (φ) + n (φ) among the apparent contours of degree d stable maps M → N whose singular points set consists of one component. </p>projecteuclid.org/euclid.kmj/1499846602_20170712040345Wed, 12 Jul 2017 04:03 EDTOn deviations, small functions and strong asymptotic functions of meromorphic functionshttp://projecteuclid.org/euclid.kmj/1499846603<strong>Ewa Ciechanowicz</strong>, <strong>Ivan Ivanovich Marchenko</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 2, 379--404.</p><p><strong>Abstract:</strong><br/> The paper addresses two long-standing problems: of extending the second main theorem of Nevanlinna to the case of small functions, and of finding an upper limit for the number of asymptotic functions of a function of finite lower order. Upper estimates of the sum of deviations and the numbers of strong asymptotic functions and strong functional asymptotic spots of meromorphic functions of finite lower order are presented. The structure of the set of Petrenko's deviations from small functions for meromorphic functions of finite lower order is examined. An analogue of Denjoy's question for strong asymptotic small functions of meromorphic functions of finite lower order is also considered. </p>projecteuclid.org/euclid.kmj/1499846603_20170712040345Wed, 12 Jul 2017 04:03 EDTL 2 continuity of the Calderón type commutator for the Littlewood-Paley operator with rough variable kernelhttps://projecteuclid.org/euclid.kmj/1509415223<strong>Yanping Chen</strong>, <strong>Zhendong Niu</strong>, <strong>Liwei Wang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 405--420.</p><p><strong>Abstract:</strong><br/>
For b $\in$ Lip ( R n ), the Calderón type commutator for the Littlewood-Paley operator with variable kernel is defined by
μ Ω,1; b ( f )( x ) = $\bigg(\int_0^{\infty}\bigg|\frac{1}{t^2}\int_{|x-y|\leq t}\frac{\Omega(x,x-y)}{|x-y|^{n-1}}(b(x)-b(y))f(y)dy\bigg|^2\frac{dt}{t}\bigg)^{1/2}$ .
By giving a method based on Littlewood-Paley theory, Fourier transform and the spherical harmonic development, we prove the L 2 norm inequalities for the rough operators μ Ω,1; b with Ω( x , z ′) $\in$ L ∞ ( R n ) × L q ( S n −1 ) $(q>\frac{2(n-1)}{n})$ satisfying certain cancellation conditions.
</p>projecteuclid.org/euclid.kmj/1509415223_20171030220055Mon, 30 Oct 2017 22:00 EDTOn proper holomorphic self-mappings of generalized complex ellipsoids and generalized Hartogs triangleshttps://projecteuclid.org/euclid.kmj/1509415224<strong>Akio Kodama</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 421--449.</p><p><strong>Abstract:</strong><br/>
In this paper, we study proper holomorphic self-mappings of generalized complex ellipsoids and generalized Hartogs triangles. By making use of our previous result on the holomorphic automorphism group of a generalized complex ellipsoid and Monti-Morbidelli's result on the extendability of a local CR-diffeomorphism between open subsets contained in the strictly pseudoconvex part of the boundary of a generalized complex ellipsoid, we obtain natural generalizations of some results due to Landucci, Chen-Xu and Zapalowski.
</p>projecteuclid.org/euclid.kmj/1509415224_20171030220055Mon, 30 Oct 2017 22:00 EDTInstability of solitary waves for a generalized derivative nonlinear Schrödinger equation in a borderline casehttps://projecteuclid.org/euclid.kmj/1509415227<strong>Noriyoshi Fukaya</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 450--467.</p><p><strong>Abstract:</strong><br/>
We study the orbital instability of solitary waves for a derivative nonlinear Schrödinger equation with a general nonlinearity. We treat a borderline case between stability and instability, which is left as an open problem by Liu, Simpson and Sulem (2013). We give a sufficient condition for instability of a two-parameter family of solitary waves in a degenerate case by extending the results of Ohta (2011), and verify this condition for some cases.
</p>projecteuclid.org/euclid.kmj/1509415227_20171030220055Mon, 30 Oct 2017 22:00 EDTAn addition type formula for the double cotangent functionhttps://projecteuclid.org/euclid.kmj/1509415228<strong>Masaki Kato</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 468--491.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove an addition type formula for the double cotangent function. Furthermore, we see that the addition theorem of the usual cotangent function, the reciprocity laws of (classical and higher) Dedekind sums, Lerch's functional equation and Ramanujan's formula can be deduced from it.
</p>projecteuclid.org/euclid.kmj/1509415228_20171030220055Mon, 30 Oct 2017 22:00 EDTAlmost automorphic solutions of semilinear stochastic hyperbolic differential equations in intermediate spacehttps://projecteuclid.org/euclid.kmj/1509415229<strong>Zhinan Xia</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 492--517.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the existence, uniqueness of almost automorphic in one-dimensional distribution mild solution for semilinear stochastic differential equations driven by Lévy noise. The semigroup theory, fixed point theorem and stochastic analysis technique are the main tools in carrying out proof. Finally, we give one example to illustrate the main findings.
</p>projecteuclid.org/euclid.kmj/1509415229_20171030220055Mon, 30 Oct 2017 22:00 EDTL p p -harmonic 1-forms on locally conformally flat Riemannian manifoldshttps://projecteuclid.org/euclid.kmj/1509415230<strong>Yingbo Han</strong>, <strong>Qianyu Zhang</strong>, <strong>Mingheng Liang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 518--536.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain some vanishing and finiteness theorems for L p p -harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of M is bounded by a suitable constant.
</p>projecteuclid.org/euclid.kmj/1509415230_20171030220055Mon, 30 Oct 2017 22:00 EDTNote on restriction maps of Chow rings to Weyl group invariantshttps://projecteuclid.org/euclid.kmj/1509415231<strong>Nobuaki Yagita</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 537--552.</p><p><strong>Abstract:</strong><br/>
Let G be an algebraic group over C corresponding a compact simply connected Lie group. When H *( G ) has p -torsion, we see ρ* CH : CH *( BG ) → CH *( BT ) W G ( T ) is always not surjective. We also study the algebraic cobordism version ρ* Ω . In particular when G = Spin (7) and p = 2, we see each Griffiths element in CH *( BG ) is detected by an element in Ω*( BT ).
</p>projecteuclid.org/euclid.kmj/1509415231_20171030220055Mon, 30 Oct 2017 22:00 EDTOn infinitesimal Strebel pointshttps://projecteuclid.org/euclid.kmj/1509415232<strong>Alastair Fletcher</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 553--561.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that if X is a Riemann surface of infinite analytic type and [μ] T is any element of Teichmüller space, then there exists μ 1 $\in$ [μ] T so that [μ 1 ] B is an infinitesimal Strebel point.
</p>projecteuclid.org/euclid.kmj/1509415232_20171030220055Mon, 30 Oct 2017 22:00 EDTGround state solutions for asymptotically periodic linearly coupled Schrödinger equations with critical exponenthttps://projecteuclid.org/euclid.kmj/1509415233<strong>Sitong Chen</strong>, <strong>XianHua Tang</strong>, <strong>Jianxiong Li</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 562--576.</p><p><strong>Abstract:</strong><br/>
We consider the following system of coupled nonlinear Schrödinger equations
$$\left\{\begin{array}{ll}-\triangle u+a(x) u=|u|^{p-2}u+\lambda(x) v, x\in \mathbb{R}^N,\\-\triangle v+b(x) v=|v|^{2^*-2}v+\lambda(x) u, x\in \mathbb{R}^N,\\u,v\in H^1(\mathbb{R}^N), \end{array}\right.$$
where N ≥ 3, 2 < p < 2*, 2* = 2 N /( N −2) is the Sobolev critical exponent, a , b , λ $\in$ C ( R N , R ) $\cap$ L ∞ ( R N , R ) and a ( x ), b ( x ) and λ( x ) are asymptotically periodic, and can be sign-changing. By using a new technique, we prove the existence of a ground state of Nehari type solution for the above system under some mild assumptions on a , b and λ. In particular, the common condition that |λ( x )| < $\sqrt{a(x)b(x)}$ for all x $\in$ R N is not required.
</p>projecteuclid.org/euclid.kmj/1509415233_20171030220055Mon, 30 Oct 2017 22:00 EDTA note on Atiyah's Γ-index theorem in Heisenberg calculushttps://projecteuclid.org/euclid.kmj/1509415234<strong>Tatsuki Seto</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 577--583.</p><p><strong>Abstract:</strong><br/>
In this note, we prove an index theorem on Galois coverings for Heisenberg elliptic (but not elliptic) differential operators, which is analogous to Atiyah's Γ-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial Γ-index.
</p>projecteuclid.org/euclid.kmj/1509415234_20171030220055Mon, 30 Oct 2017 22:00 EDTAbsolute zeta functions and the automorphyhttps://projecteuclid.org/euclid.kmj/1509415235<strong>Nobushige Kurokawa</strong>, <strong>Hidekazu Tanaka</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 584--614.</p><p><strong>Abstract:</strong><br/>
</p>projecteuclid.org/euclid.kmj/1509415235_20171030220055Mon, 30 Oct 2017 22:00 EDTOn endomorphisms of hypersurfaceshttps://projecteuclid.org/euclid.kmj/1509415236<strong>Ilya Karzhemanov</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 615--624.</p><p><strong>Abstract:</strong><br/>
For any prime p ≥ 5, we show that generic hypersurface X p $subset$ P p defined over Q admits a non-trivial rational dominant self-map of degree > 1, defined over $\overline{\mathbb{Q}}$ . A simple arithmetic application of this fact is also given.
</p>projecteuclid.org/euclid.kmj/1509415236_20171030220055Mon, 30 Oct 2017 22:00 EDTThe Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus onehttps://projecteuclid.org/euclid.kmj/1509415237<strong>Yuichiro Hoshi</strong>, <strong>Ryo Kinoshita</strong>, <strong>Chikara Nakayama</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 625--637.</p><p><strong>Abstract:</strong><br/>
We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub- p -adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub- p -adic field. We also prove related results in absolute anabelian geometry.
</p>projecteuclid.org/euclid.kmj/1509415237_20171030220055Mon, 30 Oct 2017 22:00 EDTClassification results of quasi Einstein solitonshttps://projecteuclid.org/euclid.kmj/1509415238<strong>Shu Yau Huang</strong>, <strong>Lin Feng Wang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 40, Number 3, 638--647.</p><p><strong>Abstract:</strong><br/>
We classify (ρ,τ)-quasi Einstein solitons with ( a ,τ)-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a (ρ,τ)-quasi Einstein soliton in a Riemannian manifold equipped with an ( a ,τ)-concurrent vector field.
</p>projecteuclid.org/euclid.kmj/1509415238_20171030220055Mon, 30 Oct 2017 22:00 EDTVanishing of Killing vector fields on compact Finsler manifoldshttps://projecteuclid.org/euclid.kmj/1521424815<strong>Bin Shen</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
In this paper, we define a new Ricci curvature on Finsler manifold named the mean Ricci curvature, which is useful in the study of different symmetric fields on manifolds. By presenting a Bochner type formula of Killing vector fields on general Finsler manifolds, we prove the vanishing theorem of the Killing vector fields on any compact Finsler manifold with a negative mean Ricci curvature. This result involves the vanishing theorem of Killing vector fields in the Riemannian case.
</p>projecteuclid.org/euclid.kmj/1521424815_20180320003217Tue, 20 Mar 2018 00:32 EDTDehn twists on Kauffman bracket skein algebrashttps://projecteuclid.org/euclid.kmj/1521424819<strong>Shunsuke Tsuji</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 16--41.</p><p><strong>Abstract:</strong><br/>
We give an explicit formula for the action of the Dehn twist along a simple closed curve in a compact connected oriented surface on the completion of the filtered skein modules of the surface. To do this, we introduce filtrations of the Kauffman bracket skein algebra and the Kauffman bracket skein modules of the surface.
</p>projecteuclid.org/euclid.kmj/1521424819_20180320003217Tue, 20 Mar 2018 00:32 EDTOn 3-dimensional homogeneous generalized $m$-quasi-Einstein manifoldshttps://projecteuclid.org/euclid.kmj/1521424822<strong>Zejun Hu</strong>, <strong>Dehe Li</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 42--51.</p><p><strong>Abstract:</strong><br/>
In this paper, we show that for 3-dimensional homogeneous manifolds only the space form can carry a proper generalized $m$-quasi-Einstein structure.
</p>projecteuclid.org/euclid.kmj/1521424822_20180320003217Tue, 20 Mar 2018 00:32 EDTAn effective Schmidt's subspace theorem for hypersurfaces in subgeneral position in projective varieties over function fieldshttps://projecteuclid.org/euclid.kmj/1521424823<strong>Giang Le</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 52--69.</p><p><strong>Abstract:</strong><br/>
We established an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in $m$-subgeneral position with respect to $\mathcal{X}$.
</p>projecteuclid.org/euclid.kmj/1521424823_20180320003217Tue, 20 Mar 2018 00:32 EDTAn isoperimetric inequality for diffused surfaceshttps://projecteuclid.org/euclid.kmj/1521424824<strong>Ulrich Menne</strong>, <strong>Christian Scharrer</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 70--85.</p><p><strong>Abstract:</strong><br/>
For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.
</p>projecteuclid.org/euclid.kmj/1521424824_20180320003217Tue, 20 Mar 2018 00:32 EDTTwisted Alexander polynomials of genus one two-bridge knotshttps://projecteuclid.org/euclid.kmj/1521424825<strong>Anh T. Tran</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 86--97.</p><p><strong>Abstract:</strong><br/>
Morifuji [14] computed the twisted Alexander polynomial of twist knots for nonabelian representations. In this paper we compute the twisted Alexander polynomial and Reidemeister torsion of genus one two-bridge knots, a class of knots which includes twist knots. As an application, we give a formula for the Reidemeister torsion of the 3-manifold obtained by $\frac{1}{q}$-Dehn surgery on a genus one two-bridge knot.
</p>projecteuclid.org/euclid.kmj/1521424825_20180320003217Tue, 20 Mar 2018 00:32 EDTLinear Weingarten spacelike hypersurfaces in Lorentz space forms with prescribed Gauss maphttps://projecteuclid.org/euclid.kmj/1521424826<strong>Xiaoli Chao</strong>, <strong>Yusha Lv</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 98--114.</p><p><strong>Abstract:</strong><br/>
This paper address the geometry of complete linear Weingarten spacelike hypersurfaces in the Lorentz space forms. First, a divergence lemma concerning linear Weingarten spacelike hypersurfaces is obtained. Then, with the aid of this lemma, by supposing suitable restrictions on the Gauss map, we show that such hypersurfaces must be totally umbilical, which are some extension of the recent results of Aquino, Bezerra and Lima [7] and Aquino, Lima and Velásquez [11].
</p>projecteuclid.org/euclid.kmj/1521424826_20180320003217Tue, 20 Mar 2018 00:32 EDTUniqueness theorem for meromorphic mappings with multiple valueshttps://projecteuclid.org/euclid.kmj/1521424827<strong>Ha Huong Giang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 115--124.</p><p><strong>Abstract:</strong><br/>
In this article, we will prove a uniqueness theorem for meromorphic mappings into complex projective space $\mathbf{P}^n(\mathbf{C})$ with different multiple values and a general condition on the intersections of the inverse images of these hyperplanes.
</p>projecteuclid.org/euclid.kmj/1521424827_20180320003217Tue, 20 Mar 2018 00:32 EDTDegeneration of period matrices of stable curveshttps://projecteuclid.org/euclid.kmj/1521424828<strong>Yu Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 125--153.</p><p><strong>Abstract:</strong><br/>
In the present paper, we study the extent to which linear combinations of period matrices arising from stable curves are degenerate (i.e., as bilinear forms). We give a criterion to determine whether a stable curve admits such a degenerate linear combination of period matrices. In particular, this criterion can be interpreted as a certain analogue of the weight-monodromy conjecture for non-degenerate elements of pro-$\ell$ log étale fundamental groups of certain log points associated to the log stack $\overline{\mathcal{M}}_{g}^{log}$.
</p>projecteuclid.org/euclid.kmj/1521424828_20180320003217Tue, 20 Mar 2018 00:32 EDTGenerators for the mapping class group of a nonorientable surfacehttps://projecteuclid.org/euclid.kmj/1521424829<strong>Susumu Hirose</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 154--159.</p><p><strong>Abstract:</strong><br/>
We show that Szepietowski's system of generators for the mapping class group of a non-orientable surface is a minimal generating set by Dehn twists and $Y$-homemorphisms.
</p>projecteuclid.org/euclid.kmj/1521424829_20180320003217Tue, 20 Mar 2018 00:32 EDTA lower bound for the number of integral solutions of Mordell equationhttps://projecteuclid.org/euclid.kmj/1521424830<strong>Hassan Shabani-Solt</strong>, <strong>Ali S. Janfada</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 160--166.</p><p><strong>Abstract:</strong><br/>
For a nonzero integer $d$, a celebrated Siegel Theorem says that the number $N(d)$ of integral solutions of Mordell equation $y^2+x^3=d$ is finite. We find a lower bound for $N(d)$, showing that the number of solutions of Mordell equation increases dramatically. We also prove that for any positive integer $n$, there is an integer square multiply represented by Mordell equations, i.e., $k^2=y_1^2+x_1^3=y_2^2+x_2^3=\cdots =y_n^2+x_n^3$.
</p>projecteuclid.org/euclid.kmj/1521424830_20180320003217Tue, 20 Mar 2018 00:32 EDTA regulator map for 1-cycles with modulushttps://projecteuclid.org/euclid.kmj/1521424831<strong>Mirai Onoda</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 167--200.</p><p><strong>Abstract:</strong><br/>
Let $k$ be a field of characteristic 0. We define a map from the additive higher Chow group of 1-cycles with strong sup $m$-modulus $CH_1(A_k(m), n)_{ssup}$ to the module of absolute Kähler differentials of $k$ with twisted $k^*$-action $\Omega^{n-2}_k\langle \omega \rangle$ of weight $\omega$. We will call the map a $\emph{regulator map}$, and we show that the regulator map is surjective if $k$ is an algebraically closed field. In case $\omega = m+1$, this map specializes to Park's regulator map. We study a relationship between the cyclic homology and the additive higher Chow group with strong sup modulus by using our regulator map.
</p>projecteuclid.org/euclid.kmj/1521424831_20180320003217Tue, 20 Mar 2018 00:32 EDTOn complex deformations of Kähler-Ricci solitonshttps://projecteuclid.org/euclid.kmj/1521424832<strong>Nefton Pali</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 1, 201--226.</p><p><strong>Abstract:</strong><br/>
We obtain a formal obstruction, i.e. a necessary condition for the existence of polarized complex deformations of Kähler-Ricci solitons. This obstruction is expressed in terms of the harmonic part of the variation of the complex structure.
</p>projecteuclid.org/euclid.kmj/1521424832_20180320003217Tue, 20 Mar 2018 00:32 EDTZeta functions for Kähler graphshttps://projecteuclid.org/euclid.kmj/1530496832<strong>Yaermaimaiti Tuerxunmaimaiti</strong>, <strong>Toshiaki Adachi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 227--239.</p><p><strong>Abstract:</strong><br/>
To create a discrete analogue of magnetic fields on Riemannian manifolds is a challenging problem. The notion of Kähler graphs introduced by the second author is one of trials of this discretization. In this article we study the asymptotic behavior of the weighted number of prime cycles with respect to their lengths by use of a zeta function.
</p>projecteuclid.org/euclid.kmj/1530496832_20180701220050Sun, 01 Jul 2018 22:00 EDTCyclic coverings of the projective line by Mumford curves in positive characteristichttps://projecteuclid.org/euclid.kmj/1530496835<strong>Ryota Mikami</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 240--263.</p><p><strong>Abstract:</strong><br/>
We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of cyclic coverings of degree $p$ of the projective line by Mumford curves over complete discrete valuation fields of positive characteristic $p$. Previously, Bradley studied that of any degree over non-archimedean local fields of characteristic zero.
</p>projecteuclid.org/euclid.kmj/1530496835_20180701220050Sun, 01 Jul 2018 22:00 EDTUltra-discrete equations and tropical counterparts of some complex analysis resultshttps://projecteuclid.org/euclid.kmj/1530496839<strong>Min-Feng Chen</strong>, <strong>Zong-Sheng Gao</strong>, <strong>Ji-Long Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 264--283.</p><p><strong>Abstract:</strong><br/>
A tropical version of Nevanlinna theory describes value distribution of continuous piecewise linear functions of a real variable. In this paper, we present some results on value distribution theory of tropical difference polynomials and uniqueness theory of tropical entire functions. Application to some ultra-discrete equations is also given.
</p>projecteuclid.org/euclid.kmj/1530496839_20180701220050Sun, 01 Jul 2018 22:00 EDTA non-integrated hypersurface defect relation for meromorphic maps over complete Kähler manifolds into projective algebraic varietieshttps://projecteuclid.org/euclid.kmj/1530496842<strong>Wei Chen</strong>, <strong>Qi Han</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 284--300.</p><p><strong>Abstract:</strong><br/>
In this paper, a non-integrated defect relation for meromorphic maps from complete Kähler manifolds $M$ into smooth projective algebraic varieties $V$ intersecting hypersurfaces located in $k$-subgeneral position (see (1.5) below) is proved. The novelty of this result lies in that both the upper bound and the truncation level of our defect relation depend only on $k$, $\dim_{\,\mathbf{C}}(V)$ and the degrees of the hypersurfaces considered; besides, this defect relation recovers Hirotaka Fujimoto [6, Theorem 1.1] when subjected to the same conditions.
</p>projecteuclid.org/euclid.kmj/1530496842_20180701220050Sun, 01 Jul 2018 22:00 EDTThe Hessian of quantized Ding functionals and its asymptotic behaviorhttps://projecteuclid.org/euclid.kmj/1530496843<strong>Ryosuke Takahashi</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 301--314.</p><p><strong>Abstract:</strong><br/>
We compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.
</p>projecteuclid.org/euclid.kmj/1530496843_20180701220050Sun, 01 Jul 2018 22:00 EDTCurvature properties of homogeneous real hypersurfaces in nonflat complex space formshttps://projecteuclid.org/euclid.kmj/1530496844<strong>Sadahiro Maeda</strong>, <strong>Hiroshi Tamaru</strong>, <strong>Hiromasa Tanabe</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 315--331.</p><p><strong>Abstract:</strong><br/>
In this paper, we study curvature properties of all homogeneous real hypersurfaces in nonflat complex space forms, and determine their minimalities and the signs of their sectional curvatures completely. These properties reflect the sign of the constant holomorphic sectional curvature $c$ of the ambient space. Among others, for the case of $c$ < 0 there exist homogeneous real hypersurfaces with positive sectional curvature and also ones with negative sectional curvature, whereas for the case of $c$ > 0 there do not exist any homogeneous real hypersurfaces with nonpositive sectional curvature.
</p>projecteuclid.org/euclid.kmj/1530496844_20180701220050Sun, 01 Jul 2018 22:00 EDTOn Perez Del Pozo's lower bound of Weierstrass weighthttps://projecteuclid.org/euclid.kmj/1530496845<strong>Nan Wangyu</strong>, <strong>Masumi Kawasaki</strong>, <strong>Fumio Sakai</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 332--347.</p><p><strong>Abstract:</strong><br/>
Let $V$ be a smooth projective curve over the complex number field with genus $g \geq 2$, and let $\sigma$ be an automorphism on $V$ such that the quotient curve $V/\langle \sigma \rangle$ has genus 0. We write $d$ (resp., $b$) for the order of $\sigma$ (resp., the number of fixed points of $\sigma$). When $d$ and $b$ are fixed, the lower bound of the (Weierstrass) weights of fixed points of $\sigma$ was obtained by Perez del Pozo [7]. We obtain necessary and sufficient conditions for when the lower bound is attained.
</p>projecteuclid.org/euclid.kmj/1530496845_20180701220050Sun, 01 Jul 2018 22:00 EDTConvexity and the Dirichlet problem of translating mean curvature flowshttps://projecteuclid.org/euclid.kmj/1530496846<strong>Li Ma</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 348--358.</p><p><strong>Abstract:</strong><br/>
In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.
</p>projecteuclid.org/euclid.kmj/1530496846_20180701220050Sun, 01 Jul 2018 22:00 EDTOn the complex Łojasiewicz inequality with parameterhttps://projecteuclid.org/euclid.kmj/1530496847<strong>Maciej P. Denkowski</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 359--374.</p><p><strong>Abstract:</strong><br/>
We prove a continuity property in the sense of currents of a continuous family of holomorphic functions which allows us to obtain a Łojasiewicz inequality with an effective exponent independent of the parameter.
</p>projecteuclid.org/euclid.kmj/1530496847_20180701220050Sun, 01 Jul 2018 22:00 EDTBased chord diagrams of spherical curveshttps://projecteuclid.org/euclid.kmj/1530496848<strong>Noboru Ito</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 375--396.</p><p><strong>Abstract:</strong><br/>
This paper demonstrates an approach for developing a framework to produce invariants of base-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based chord diagrams. Our invariants not only contain Arnold's classical generic spherical curve invariant but also new invariants.
</p>projecteuclid.org/euclid.kmj/1530496848_20180701220050Sun, 01 Jul 2018 22:00 EDTFoxby equivalences associated to strongly Gorenstein moduleshttps://projecteuclid.org/euclid.kmj/1530496849<strong>Wanru Zhang</strong>, <strong>Zhongkui Liu</strong>, <strong>Xiaoyan Yang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 397--412.</p><p><strong>Abstract:</strong><br/>
In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly $\mathcal{W}_P$-Gorenstein, $\mathcal{W}_I$-Gorenstein and $\mathcal{W}_F$-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left $R$-modules in the left Auslander class and the subcategory of strongly $\mathcal{W}_P$-Gorenstein left $S$-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.
</p>projecteuclid.org/euclid.kmj/1530496849_20180701220050Sun, 01 Jul 2018 22:00 EDTOn Terai's conjecturehttps://projecteuclid.org/euclid.kmj/1530496850<strong>Xin Zhang</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 413--420.</p><p><strong>Abstract:</strong><br/>
Let $p$ be an odd prime such that $b^r+1=2p^t$, where $r$, $t$ are positive integers and $b \equiv$ 3,5 (mod 8). We show that the Diophantine equation $x^2+b^m=p^n$ has only the positive integer solution $(x,m,n)=(p^t-1,r,2t)$. We also prove that if $b$ is a prime and $r=t=2$, then the above equation has only one solution for the case $b \equiv$ 3,5,7 (mod 8) and the case $d$ is not an odd integer greater than 1 if $b \equiv$ 1 (mod 8), where $d$ is the order of prime divisor of ideal ($p$) in the ideal class group of $\mathbf{Q}$ ($\sqrt {-q}$).
</p>projecteuclid.org/euclid.kmj/1530496850_20180701220050Sun, 01 Jul 2018 22:00 EDTThe effect of Fenchel-Nielsen coordinates under elementary moveshttps://projecteuclid.org/euclid.kmj/1530496851<strong>Dong Tan</strong>, <strong>Peijia Liu</strong>, <strong>Xuewen Liu</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 421--439.</p><p><strong>Abstract:</strong><br/>
We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.
</p>projecteuclid.org/euclid.kmj/1530496851_20180701220050Sun, 01 Jul 2018 22:00 EDTA prime geodesic theorem for higher rank buildingshttps://projecteuclid.org/euclid.kmj/1530496852<strong>Anton Deitmar</strong>, <strong>Rupert McCallum</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 440--455.</p><p><strong>Abstract:</strong><br/>
We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.
</p>projecteuclid.org/euclid.kmj/1530496852_20180701220050Sun, 01 Jul 2018 22:00 EDTA note on families of monogenic number fieldshttps://projecteuclid.org/euclid.kmj/1530496853<strong>Joachim König</strong>. <p><strong>Source: </strong>Kodai Mathematical Journal, Volume 41, Number 2, 456--464.</p><p><strong>Abstract:</strong><br/>
We give a sufficient criterion for specializations of certain families of polynomials to yield monogenic number fields. This generalizes constructions in several earlier papers. As applications we give new infinite families of monogenic number fields for several prescribed Galois groups.
</p>projecteuclid.org/euclid.kmj/1530496853_20180701220050Sun, 01 Jul 2018 22:00 EDT