## Recursos de colección

1. #### Hyperbolic Knots with a Large Number of Disjoint Minimal Genus Seifert Surfaces

TSUTSUMI, Yukihiro
It is known that any genus one hyperbolic knot in the 3-dimensional sphere admits at most seven mutually disjoint and mutually non-parallel genus one Seifert surfaces. In this note, it is shown that for any integers $g>1$ and $n>0$, there is a hyperbolic knot of genus $g$ in the 3-dimensional sphere which bounds $n$ mutually disjoint and mutually non-parallel genus $g$ Seifert surfaces.

2. #### Duality of Weights, Mirror Symmetry and Arnold's Strange Duality

KOBAYASHI, Masanori
A duality of weight systems which corresponds to Batyrev's toric mirror symmetry is given. It is shown that Arnold's strange duality for exceptional unimodal singularities reduces to this duality.

3. #### Latent Quaternionic Geometry

GAMBIOLI, Andrea
We discuss the interaction between the geometry of a quaternion-K\"{a}hler manifold $M$ and that of the Grassmannian $\mathbb{G}_3(\mathfrak{g})$ of oriented $3$-dimensional subspaces of a compact Lie algebra $\mathfrak{g}$. This interplay is described mainly through the moment mapping induced by the action of a group $G$ of quaternionic isometries on $M$. We give an alternative expression for the imaginary quaternionic endomorphisms $I,J,K$ in terms of the structure of the Grassmannian's tangent space. This relies on a correspondence between the solutions of respective twistor-type equations on $M$ and $\mathbb{G}_3(\mathfrak{g})$.

4. #### A Sharp Form of the Uniqueness of the Solution to Nonlinear Totally Characteristic Partial Differential Equations

TAHARA, Hidetoshi
The paper deals with the following nonlinear partial differential equation $(t \partial/\partial t)^m u = F (t,x, \{(t \partial/\partial t)^j (\partial/\partial x)^{\alpha} u\}_{j+\alpha \leq m, j 5. #### Geometric Morita Equivalence for Twisted Poisson Manifolds HIROTA, Yuji We introduce notions of Morita equivalence for both twisted symplectic groupoids and integrable twisted Poisson manifolds without terms of groupoids. We show that two integrable twisted Poisson manifolds are Morita equivalent if and only if their associated groupoids are Morita equivalent as twisted symplectic groupoids. 6. #### Integral Points and the Rank of Elliptic Curves over Imaginary Quadratic Fields KOJIMA, Michitaka One of Silverman's results gives a relationship between the number of integral points and the rank of elliptic curves over$\mathbb{Q}$. This paper generalizes this result for all imaginary quadratic fields. 7. #### The spectra of Jacobi operators for Constant Mean Curvature Tori of Revolution in the$3$-sphere ROSSMAN, Wayne; SULTANA, Nahid We prove a theorem about elliptic operators with symmetric potential functions, defined on a function space over a closed loop. The result is similar to a known result for a function space on an interval with Dirichlet boundary conditions. These theorems provide accurate numerical methods for finding the spectra of those operators over either type of function space. As an application, we numerically compute the Morse index of constant mean curvature tori of revolution in the unit$3$-sphere$\mathbb{S}^3$, confirming that every such torus has Morse index at least five, and showing that other known lower bounds for this Morse index are close to optimal. 8. #### On the Moduli Space of Pointed Algebraic Curves of Low Genus II ---Rationality--- NAKANO, Tetsuo We show that the moduli space$\mathcal{M}_{g,1}^N$of pointed algebraic curves of genus$g$with a given numerical semigroup$N$is an irreducible rational variety if$N$is generated by less than five elements for low genus ($ g \leq 6$) except one case. As a corollary to this result, we get a computational proof of the rationality of the moduli space$\mathcal{M}_{g,1}$of pointed algebraic curves of genus$g$for$1 \leq g \leq 3$. If$g \leq 5$, we also have that$\mathcal{M}_{g,1}^N$is an irreducible rational variety for any semigroup$N$except two cases. It is known that such a moduli space$\mathcal{M}_{g,1}^N$is... 9. #### Uncertainty Principles for the Jacobi Transform KAWAZOE, Takeshi We obtain some uncertainty inequalities for the Jacobi transform$\hat f_{\alpha,\beta}(\lambda)$, where we suppose$\alpha, \beta\in\mathbb{R}$and$\rho=\alpha+\beta+1\geq 0$. As in the Euclidean case, analogues of the local and global uncertainty principles hold for$\hat f_{\alpha,\beta}$. In this paper, we shall obtain a new type of an uncertainty inequality and its equality condition: When$\beta\leq 0$or$\beta\leq\alpha$, the$L^2$-norm of$\hat f_{\alpha,\beta}(\lambda)\lambda$is estimated below by the$L^2$-norm of$\rho f(x)(\cosh x)^{-1}$. Otherwise, a similar inequality holds. Especially, when$\beta>\alpha+1$, the discrete part of$f$appears in the Parseval formula and it influences the inequality. We also apply these uncertainty principles to the spherical Fourier transform on$SU(1,1)$.... 10. ####$M$-matrices of the Ternary Golay Code and the Mathieu Group$M_{12}$KIMIZUKA, Maro; SASAKI, Ryuji In this article, we define$M$-matrices of the ternary Golay code and build fundamental properties of the ternary Golay code on$M$-matrices. Moreover, using four$M$-matrices of the ternary Golay code, we give order three elements, in the Mathieu group$M_{12}$, which generate$M_{11}$and$M_{12}$. 11. #### A Remark on the Breuer's Conjecture Related to the Maillet's Matrix KURIBAYASHI, Izumi 12. #### Counting Points of the Curve$y^2=x^{12}+a$over a Finite Field NIITSUMA, Yasuhiro We give explicit formulas of the number of rational points and those of the congruence zeta functions for the hyperelliptic curves over a finite field defined by affine equations$y^2=x^6+a$,$y^2=x^{12}+a$and$y^2=x(x^6+a)$. 13. #### Generalized$(\kappa,\mu)$-contact Metric Manifolds with$\xi\mu=0$KOUFOGIORGOS, Themis; TSICHLIAS, Charalambos This paper analytically describes the local geometry of a generalized$(\kappa,\mu )$-manifold$M(\eta,\xi,\phi,g)$with$\kappa<1$which satisfies the condition the function$\mu$is constant along the integral curves of the characteristic vector field$\xi$''. This class of manifolds is especially rich, since it is possible to construct in$R^3$two families of such manifolds, for any smooth function$\kappa$($\kappa<1$) of one variable. Every family is determined by two arbitrary functions of one variable. 14. #### The Addition Law Attached to a Stratification of a Hyperelliptic Jacobian Variety ENOLSKII, Victor; MATSUTANI, Shigeki; ÔNISHI, Yoshihiro This article shows explicit relations between fractional expressions of Schottky-Klein type for hyperelliptic$\sigma$-functions and a product of differences of the algebraic coordinates on each stratum of a natural stratification in a hyperelliptic Jacobian. 15. #### Symplectic Volumes of Certain Symplectic Quotients Associated with the Special Unitary Group of Degree Three SUZUKI, Taro; TAKAKURA, Tatsuru We consider the symplectic quotient for a direct product of several integral coadjoint orbits of$SU(3)$and investigate its symplectic volume. According to a fundamental theorem for symplectic quotients, it is equivalent to studying the dimension of the trivial part in a tensor product of several irreducible representations for$SU(3)$, and its asymptotic behavior. We assume that either all of coadjoint orbits are flag manifolds of$SU(3)$, or all are complex projective planes. As main results, we obtain an explicit formula for the symplectic volume in each case. 16. #### Global Solutions of IBVP to Nonlinear Equation of Suspended String WONGSAWASDI, Jaipong; YAMAGUCHI, Masaru We shall consider IBVP to a nonlinear equation of suspended string with uniform density to which a nonlinear time-independent outer force works. We shall show the existence of time-global weak solutions of IBVP. To prove our result we shall use the function spaces defined by [Ya1], and apply the method due to Sattinger [Sat] based on the potential-well and the Galerkin method. 17. #### Monodromy on the Central Hyperbolic Component of Polynomials with Just Two Distinct Critical Points YAZAWA, Hikaru For any given integers$d_0, d_1 \ge 1$, let$\mathcal{F}$be the family of polynomial maps$f$such that$f$has a fixed point at the origin, and moreover has just two distinct critical points 1 and$c_f\neq 1$of multiplicies$d_0$and$d_1$, respectively. For the central hyperbolic component$\mathcal{H}$of$\mathcal{F}$, a monodromy map on$\mathcal{H}$is obtained by Branner-Hubbard deformations. We show that for any given$\lambda$with$0 < |\lambda| < 1$and for any given integer$n \ge 1$, the monodromy map transitively acts on the family of all polynomial maps$f\in \mathcal{H}$with$f^{\prime}(0) = \lambda$and$f^{\circ n}(c_f) = 1$. 18. #### Bicomplex Polygamma Function GOYAL, Ritu The aim of this paper is to extend the domain of polygamma function from the set of complex numbers to the set of bicomplex numbers. We also discuss integral representation, recurrence relation, multiplication formula and reflection formula for this function. 19. #### The Turaev-Viro Invariants of All Orientable Closed Seifert Fibered Manifolds TANIGUCHI, Taiji The Turaev-Viro invariants are topological invariants of closed 3-manifolds. In this paper, we give a formula of the Turaev-Viro invariants of all orientable closed Seifert fibered manifolds. Our formula is based on a new construction of special spines of all orientable closed Seifert fibered manifolds and thegluing lemma'' of topological quantum field theory. By using our formula, we get sufficient conditions of coincidence of the Turaev-Viro invariants of orientable closed Seifert fibered manifolds. 20. #### Singular Distance Powers of Circuits SANDER, Torsten In this work a precise condition for the singularity of a circuit distance power$C_n^{(d)}$is derived. Namely, either$n$and$d$are not relatively prime or the order of 2 in$d+1$is strictly smaller than in$n$. It is also shown that the simple eigenvalues of circuit distance powers are contained in$\{-2,0,2d\}$, generalizing a well-known result for circuits. Further, the nullity of$C_n^{(d)}\$ is calculated.

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