We show that a natural hybridation construction of lattices in SU(n, 1) to produce (non-arithmetic) lattices in SU(n + 1, 1) fails when n = 1 for most triangle groups in SU(1, 1).

We study Euler’s problem of determination of a triangle from its circumcenter, orthocenter, and incenter as a problem of geometric construction. While it cannot be solved using ruler and compass, we construct the vertices by intersecting a circle with a rectangular hyperbola, both easily constructed from the given triangle centers.

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. We interprete some of the so-called Lyapunov exponents of the Kontsevich–Zorich cocycle as normalize...

The studies on cochlear implants have been conducted in the United States, Austria, Brasil, France, Finland, and some other countries. Up to now, this technique does not seem to have a wide spread application. Indeed it can only apply cases of deafness still presenting sufficient neural remnants to transmit the message. Moreover, the patient must be totally deaf( quasi­ complete loss of har cel...

The SQuad data structure represents the connectivity of a triangle mesh by its “S table” of about 2 rpt (integer references per triangle). Yet it allows for a simple implementation of expected constant-time, random-access operators for traversing the mesh, including in-order traversal of the triangles incident upon a vertex. SQuad is more compact than the Corner Table (CT), which stores 6 rpt, ...

Most of the previous multiresolution models use exclusively the triangle graphic primitive both in the data structure and in the rendering stage. Only a few models use another graphic primitive in this rendering process and just one uses the triangle fan as the basic primitive of the model. In this paper we present the first multiresolution model, Multiresolution Triangle Strips, that uses the ...

i ntroduction: bisphosphonates are  widely used  for  various bone  diseases including osteoporosis and bone tumors. one of the complications associated with these pharmaceutical agents is bisphosphonate-related osteonecrosis of the jaw. this condition may be triggered by placement of dental implants. in turn,  osteonecrosis  of  the  jaw  may  cause  failure  in  osseointegration  of implants....

in this article, three techniques for maxillo-mandibular relationship for replace-select implants are described. the use of healing abutments, planning abutments, and impression copings are presented, and the advantages and disadvantages are discussed.

screw-retained implant restorations have an advantage of predictable retention as well as retrievability, and obviate the risk of excessive sub-gingival cement commonly associated with cement retained implant restorations. screw-retained restorations generally have screw access holes, which can compromise esthetics and weaken the porcelain around the holes. the purpose of this study is to descr...