1.
Extensions of the Euler-Satake characteristic determine point singularities of orientable 3-orbifolds - Carroll, Ryan; Seaton, Christopher
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.
3.
Conformally natural extensions in view of dynamics - Jiang, Yunping; Mitra, Sudeb; Wang, Zhe
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.
4.
Contact metric structures on S3 - Markellos, Michael; Tsichlias, Charalambos
In this paper, we construct a new family of contact metric structures on the unit sphere S3. Especially, the above family has the property that ∇ξτ = 2ατφ.
5.
A notion of Δ-multigenus for certain rank two ample vector bundles - Arrondo, Enrique; Lanteri, Antonio; Novelli, Carla
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 (δ1, δ2). This extends the classical definition holding for ample line bundles. Then pairs (X, $\mathcal{E}$ ) with low δ1 and δ2 are classified under suitable additional assumptions on $\mathcal{E}$ .
6.
Recurrence relations for Super-Halley's method with Hölder continuous second derivative in Banach spaces - Prashanth, Maroju; Gupta, Dharmendra K.
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...
7.
Formal group laws for multiple sine functions and applications - Koyama, Shin-ya; Kurokawa, Nobushige
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.
8.
On vanishing Fermat quotients and a bound of the Ihara sum - Shparlinski, Igor E.
We improve an estimate of A. Granville (1987) on the number of vanishing Fermat quotients qp (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(2πi/p2)).
9.
Leaf-wise intersections in coisotropic submanifolds - Ueki, Satoshi
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.
10.
Bifurcation set, M-tameness, asymptotic critical values and Newton polyhedrons - Nguyen, Tat Thang
Let F = (F1, F2, ..., Fm): Cn → Cm 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 Cm in terms of the Newton polyhedrons of F1, F2, ..., Fm 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...
11.
Another improvement of Montel's criterion - Xu, Yan
Let $\cal F$ be a family of meromorphic functions defined in a domain D $subset$ C, let ψ1, ψ2 and ψ3 be three meromorphic functions such that ψi(z) \not\equiv ψj(z) (i ≠ j) in D, one of which may be ∞ identically, and let l1, l2 and l3 be positive integers or ∞ with 1/l1 + 1/l2 + 1/l3 < 1. Suppose that, for each f $in$ $\cal F$ and z $in$ D, (1) all zeros of f – ψi have multiplicity at least li for i = 1,2,3; (2) f(z0) ≠ ψi(z0) if there exist i, j $in$ {1,2,3}...
13.
On Hermitian modular forms of small weight over imaginary quadratic fields - Kojima, Hisashi; Miura, Yasuhide; Sakata, Hiroshi; Tokuno, Yasushi
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.
14.
Positive Toeplitz operators of finite rank on the parabolic Bergman spaces - Nishio, Masaharu; Suzuki, Noriaki; Yamada, Masahiro
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.
15.
Banach spaces of bounded Dirichlet finite harmonic functions on Riemann surfaces - Nakai, Mitsuru
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.
17.
On the linear independence of the set of Dirichlet exponents - Dubickas, Artūras
Given k ≥ 2 let α1, ..., αk be transcendental numbers such that α1, ..., αk–1 are algebraically independent over Q and αk $\in$ Q(α1, ..., αk–1), but αk, ≠ (aαi + 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 + αj, where n runs through the set of all nonnegative integers for j = 1, ..., k – 1 and n = q, q +...
19.
Emden equation involving the critical Sobolev exponent with the third-kind boundary condition in S3 - Kosaka, Atsushi
We consider a positive solution of the Emden equation with the critical Sobolev exponent on a geodesic ball in S3. 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.
1.
