Let a, b and c be positive integers and consider a hexagon with side lengths a,b,c,a,b,c whose angles are 120◦ (see Figure 1). The subject of our interest is rhombus tilings of such a hexagon using rhombi with all sides of length 1 and angles 60◦ and 120◦. Figure 2 shows an example of a rhombus tiling of a hexagon with a = 3, b = 5 and c = 4. A first natural question to be asked is how many rho...

This study is interested in whether there exists a predictable relationship between the midsagittal tongue contour and its related 3D tongue surface shape during speech. The assumption is that for any single language, a limited set of phonemically based 3D tongue shapes are used. If these shapes can be delineated and mapped to specific midsagittal displacements and cross-sectional (coronal) sha...

The recent technological progress contributes to a huge increase of 3D models available in digital forms. Numerous applications were developed to deal with this amount of information, especially for 3D shape retrieval. One of the main issues is to break the semantic gap between shapes desired by users and shapes returned by retrieval methods. In this paper, we propose an algorithm to address th...

A new method for determining skeletons of 3D shapes is described. It is a combination of the approach based on the ”grass-fire” technique and Zhu’s approach based on first finding portions of the shape where its width is approximately constant. The method specifically does not require presmoothing of the shape and is robust in the presence of noise. In an appendix, a method based on variational...

Many modeling techniques for geometric objects have been developed; they allow the user to create, deform, animate objects and produce complex ones from simple primitives. This paper presents a new technique which composes two 2D or 3D interpenetrating shapes by creating another one including them and having a smooth aspect. By moving into each other, composed objects fuse smoothly and naturall...

Cadmium oxide rhombus-shaped nanostructure was synthesized using hydrothermal process followed by heating treatment. Clearly, X-ray diffraction pattern demonstrated the formation of CdO crystalline phase. Scanning electron microscopy (SEM) showed that the obtained rhombus-like structure is composed of nanoparticles with the average size of 29 nm. In addition, we evaluated adsorption of org...

We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N , which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M .

hydro-forming is a fabrication process that uses a fluid medium to form a piece by using high internal pressure. in tube hydro-forming, a tubular blank is placed between two dies, sealed and pressurized water injected, deforming the tube walls in the cavity form of the dies. exist several typical hydro-forming processes such as t- shapes, cross-shapes and y- shapes. successful hydro-forming dep...

cadmium oxide rhombus-shaped nanostructure was synthesized using hydrothermal process followed by heating treatment. clearly, x-ray diffraction pattern demonstrated the formation of cdo crystalline phase. scanning electron microscopy (sem) showed that the obtained rhombus-like structure is composed of nanoparticles with the average size of 29 nm. in addition, we evaluated adsorption of organic ...