The popularity of medial axis in shape modeling and analysis comes from several of its well known fundamental properties. For example, medial axis captures the connectivity of the domain, has a lower dimension than the space itself, and is closely related to the distance function constructed over the same domain. We formally define the new concept of a medial zone of an n-dimensional semi-analy...

The prevention of periodontal disease is a key factor in oral health. It has also become evident that periodontal health is associated with systemic health. Nonsurgical scaling and root planing is the standard of care for periodontitis. Supragingival plaque removal influences the bacterial environment in pockets up to 3 mm in depth, while subgingival scaling and root planing is essential in poc...

aims and objectives: the present study was carried to evaluate the adjunctive effect of the local application of hyaluronan gel to scaling and root planing in the treatment of chronic periodontitis. materials and methods: twelve patients with chronic periodontitis participated in the study with a split mouth design. plaque formation and bleeding on probing (bop) were evaluated pre-treatment (ba...

We report a case of generalized chronic periodontitis requiring periodontal regenerative therapy. The patient was 53-year-old woman who presented with the chief complaint gingival swelling. An initial examination revealed 31.5% sites probing depth ≥4 mm and 46.3% bleeding on probing. Radiographic showed vertical bone resorption in tooth #33. Horizontal adsorption also observed other areas. Base...

Periodontitis is a common oral infection and inflammatory condition. Following treatment, residual or persistent periodontal inflammation is associated with disease progression and tooth loss. Cumulative evidence from clinical trials and meta-analyses support a complementary medical-mechanical model that combines locally delivered antimicrobials with scaling and root planing for the treatment o...

Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems [7, 8], motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite nu...