Let P be the right-angled hyperbolic dodecahedron or 120-cell, and let W be the group generated by reflections across codimension-one faces of P . We prove that if Γ ⊂ W is a torsion free subgroup of minimal index, then the corresponding hyperbolic manifold Hn/Γ is determined up to homeomorphism by Γ modulo the symmetry group of P .

Let K/Q be a number field with euclidean ring of integers O. Let Γ be a finite-index torsion-free subgroup of the symplectic group Sp2n(O), and let N be the cohomological dimension of Γ. We exhibit a finite, geometrically-defined spanning set of H (Γ;Z) by generalizing the modular symbol algorithm of Ash and Rudolph for SLn(O).

Purpose: This work proposes and compares two 3D global evaluation methods for assessing the alteration of calculated dose distributions when treatment planning system algorithms or irradiation techniques is modified in radiation therapy. Methods: The global analysis is based on gamma index (γ) proposed by Low et al.1 and Chi (χ) index proposed by Bakai et al.2. The γ and χ values are signed in ...

On any surface we give an example of a metric that contains simple closed geodesics with arbitrarily high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrarily high Morse index. Previously, no such examples were known. We also discuss whether or not such bounds should hold for a generic metric and why bumpy does not seem to...

Let Γ be a neat finite-index subgroup of SLn(Z) or GLn(Z), and let ν be the cohomological dimension of Γ. We present an algorithm to compute the eigenvalues of the Hecke operators on H(Γ;Z), for n = 2, 3, and 4. In addition, we describe a modification of the modular symbol algorithm of Ash-Rudolph [9] for computing Hecke eigenvalues on H(Γ;Z).

Let Γ ⊂ X be a smooth curve on a 3-fold which has only index 1 terminal singularities along this curve. In this paper we investigate the existence of extremal terminal divisorial contractions E ⊂ Y −→ Γ ⊂ X , contracting an irreducible surface E to Γ. We consider cases with respect to the singularities of the general hypersurface section S of X through Γ. We completely classify the cases when S...

Every finite group acts as the full isometry group of some compact hyperbolic 3-manifold. In this paper we study those finite groups which act maximally, that is when the ratio |Isom(M)|/vol(M) is maximal among all such manifolds. In two dimensions maximal symmetry groups are called Hurwitz groups, and arise as quotients of the (2,3,7)–triangle group. Here we study quotients of the minimal co-v...

The index of composition of an integer n ≥ 2 is defined as λ(n) = (log n)/(log γ(n)), where γ(n) stands for the largest square-free divisor of n. Let φ stand for the Euler totient function. We show that the index of composition of the k-fold iterate of φ(n) is 1 on a set of density 1 and that an analogous result holds if n runs over the set of shifted primes.

Subjects exposed to non-tuberculous mycobacterium (NTM) species do not always develop an active disease, which likely reflects underlying host susceptibility factors. Recent reports have shown that anti interferon gamma (IFN-γ) neutralizing autoantibodies (IFN-γ Ab) are associated with the development of disseminated NTM in patients without known evidence of immunodeficiency. The purpose of thi...

This paper considers a wavelet analogue of the classical Ginzburg-Landau energy, where the Hseminorm is replaced by the Besov seminorm defined via an arbitrary regular wavelet. We prove that functionals of this type converge, in the Γ-sense, to a weighted analogue of the TV functional on characteristic functions of finite-perimeter sets. The Γ-limiting functional is defined explicitly, in terms...