A case of Herpes zoster of the mandibular nerve in an 80 year old man is reported. Herpes zoster infection affecting only the mandibular branch of the trigeminal nerve is rare. It is proposed that the distribution of lesions is a consequence of a unique latent site of the virus within neurons of the gasserian ganglion innervating the mandibular division of the trigeminal nerve.

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.

This case report highlights an unusual presentation of herpes zoster mandibularis in immunocompromised patient with previous head and neck surgery, relative sparing the cheek. It demonstrates importance critically considering past medical surgical history clinical diagnosis management disease.

Twenty new species of Scolytidae from the Mount Kinabalu area in northern Borneo (Sabah) are described: Acanthotomicus explanatus, Cyrtogenius abruptodeclivis, C. cavifrons, C. glabrata, C. kadazanus, C. lowi, C. mandibularis, C. mediosetosus, C. nodulosus, C. obesus, C. piceus, C. prinavorus, C. quercicolens, C. smetanai, C. tanae, C. tikaludus, Dryocoetes conspicuus, Scolytoplatypus carinatus...

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 ...