We generalize McShane’s identity for the length series of simple closed geodesics on a cusped hyperbolic surface [17] to hyperbolic cone-surfaces (with all cone angles ≤ π), possibly with cusps and/or geodesic boundary. In particular, by applying the generalized identity to the orbifolds obtained from taking the quotient of the one-holed torus by its elliptic involution, and the closed genus tw...

in this paper rst we dene the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.

The aims of this study were to determine the prevalence, size, shape, and location of torus palatinus (TP) and torus mandibularis (TM), and to investigate their sexand age-related differences in a Thai population. One thousand two hundred subjects were examined for the presence of both tori at the Faculty of Dentistry, Chulalongkorn University. The prevalence for TP and TM in the subjects was 5...

A map is constructed from the moduli of hyper-KK ahler tori to hyper-KK ahler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial rst Stiefel-Whitney class and rst Pontrjagin class equal to-4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our ...

Classical differential geometry can be encoded in spectral data, such as Connes’ spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes’ non-commutative spin geometry encompassing noncommutative Riemannian, symplectic, complex-Hermitian and (Hyper-) Kähler geometry...

Within a four-dimensional, toroidally compactified heterotic string, we identify (quantized) charge vectors of electrically charged BPS-saturated states (along with the tower of SL(2, Z) related dyonic states), which preserve 1 2 of N = 4 supersymmetry and become massless along the hyper-surfaces of enhanced gauge symmetry of the two-torus moduli sub-space. In addition, we identify charge vecto...

We study the interplay between following types of special non-Kähler Hermitian metrics on compact complex manifolds (locally conformally Kähler, k-Gauduchon, balanced, and locally balanced) prove that a Kähler nilmanifold carrying balanced or left-invariant k-Gauduchon metric is necessarily torus. Combined with main result in [FV16], this leads to fact 2-step endowed whichever two metrics—balan...

The category of exploded torus fibrations is an extension of the smooth category related to tropical geometry in which some adiabatic limits appear as smooth families. This paper contains regularity results for families of holomorphic curves in this category. The main result is a local model for the moduli space of holomorphic curves, which in the case of transversality of the ∂̄ equation implie...

Let n ≥ 2 and Tn be the space of n × n real skew-symmetric matrices. For each θ ∈ Tn the corresponding n-dimensional noncommutative torus Aθ is defined as the universal C-algebra generated by unitaries U1, · · · , Un satisfying the relation UkUj = e(θkj)UjUk, where e(t) = e. Noncommutative tori are one of the canonical examples in noncommutative differential geometry [12, 2]. One may also consi...

Bragg peaks in point set diffraction show up as eigenvalues of a dynamical system. Topological Bragg peaks arrise from topological eigenvalues and determine the torus parametrisation of the point set. We will discuss how qualitative properties of the torus parametrisation characterise the point set.