the prevalence of Torus palatinus and Torus Mandibularis is widely different in various populations and races.this descriptive study was performed in 1999,to investigate the the prevalence of Torus Mandibularis and Torus palatinus in patients referring to Rafsanjan dental school.584 patients(268 men and 316 women) which were over 18 years old were examined.the information recorded in the questi...

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...

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.

New stable decagonal quasicrystal in the system Al–Ir–Os S. Katrych a, Th. Weber a, M. Kobas b, L. Massüger a, L. Palatinus c,1, G. Chapuis c, W. Steurer a,∗ a Laboratory of Crystallography, Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland b SLS Detector Group, Swiss Light Source, Paul-Scherrer-Institut, CH-5232 Villigen-PSI, Switzerland c Laboratory of C...

The category of exploded torus fibrations is an extension of the category of smooth manifolds in which some adiabatic limits look smooth. (For example, the type of limits considered in tropical geometry appear smooth.) In this paper, we prove a compactness theorem for (pseudo)holomorphic curves in exploded torus fibrations. In the case of smooth manifolds, this is just a version of Gromov’s com...

In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus. Keywords—Cut locus, flat torus, geodesics.

Given a compact manifold M, we prove that every critical Riemannian metric g for the functional “first eigenvalue of the Laplacian” is λ1-minimal (i.e., (M, g) can be immersed isometrically in a sphere by its first eigenfunctions) and give a sufficient condition for a λ1-minimal metric to be critical. In the second part, we consider the case where M is the 2dimensional torus and prove that the ...