Introduction: Nowadays, using implants as a choice in patient's treatment plans has become popular. The aim of this study was to determine the prevalence of mandibular lingual and maxillary buccal concavity, mean concavity depth and angle and its relation to age and gender. Materials and Methods: In 200 CBCT, concavity depth and angle were measured in 2 mm superior to the inferior alveolar c...

This short review article discusses the concavity method, one of most effective ways to deal with parabolic equations unbounded solutions in finite time. If solution ceases exist for some time, we say it blows up. The or its derivatives become singular depending on equation. We focus situations where becomes and our objective is key blowup theory papers utilising method.

We present a novel method of decomposing digital binary clumps into constituent convex parts. The algorithm is based on the analysis of concavities to determine where splitting should occur. Two relative concavity measures, concavity degree and concavity weight, are also defined.

A concavity tree is a data structure for hierarchically representing the shape of two-dimensional silhouettes using convex polygons. In this paper, we present a new algorithm for concavity tree extraction. The algorithm is fast, works directly on the pixel grid of the shape, and uses exact convex hull computations. We compare our method to the morphological approach to concavity tree extraction...

A method has been developed for the objective assessment of vertebral 'squaring' based on quantitative morphometric analysis of vertebral 'concavity' in lateral radiographs of the lumbar spine. The reference range for vertebral concavity was defined as greater than 1.0-4.0 mm from measurements of 255 radiologically normal lumbar vertebrae in 51 patients with non-specific back pain. Evidence of ...

In this work, we propose a novel and robust method for the accurate separation of elliptical overlapped nuclei in microscopic images. The method is based on both the information provided by the global boundary of the nuclei cluster and the detection of concavity points along this boundary. The number of the nuclei and the area of each nucleus included in the cluster are estimated automatically ...

we discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of kirchhoff type [ u_{tt}-phi (x)||nabla u(t)||^{2}delta u+delta u_{t}=|u|^{a}u,, x in mathbb{r}^{n} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $n geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $l^{n/2}(mathb...