We investigate the electronic confinement in bilayer graphene by topological loops of different shapes. These are created lateral gates acting via gap inversion on two sheets. For large-area spectrum is well described a quantization rule depending only loop perimeter. small sizes, depends shape. find that zero-energy states exhibit characteristic pattern strongly spatial symmetry. show this con...

A rectangular drawing of a planar graph G is in which vertices are mapped to grid points, edges horizontal and vertical straight-line segments, faces drawn as rectangles. Sometimes this latter constraint relaxed for the outer face. In paper, we study drawings have unit length. We show complexity dichotomy problem deciding existence unit-length drawing, depending on whether face must also be rec...

We show that a square-tiling of a p × q rectangle, where p and q are relatively prime integers, has at least log2 p squares. If q > p we construct a square-tiling with less than q/p+C log p squares of integer size, for some universal constant C.

The study of the variations in the superficial veins of head and neck and their draining pattern is very important due to the complexity in their developmental pattern. A total of 32 cadavers of both sexes were used for the study and the head and neck region were dissected carefully and photographed in the department of anatomy, Vinayaka Mission Kirupananda Variyar Medical College & Hospital, S...

recently, design of cropping pattern based on water resources is getting a high priority. this scheme is complicated, and affected by multiple factors. for investigation, designer must gather a huge data, and classify them. the method of processing and analyzing of the information is important. the method of linear programming based on lingo software for hendijan irrigation and drainage network...

We study the problem of packing a set of n rectangles with weights into a dedicated rectangle so that the weight of the packed rectangles is maximized. We consider the case of large resources, that is, the side length of all rectangles is at most 1 and the side lengths of the dedicated rectangle differ by a factor of at least 1="4, for a fixed positive " > 0. We present an algorithm which finds...

We consider the fabrication of high-quality interferogram-type diffractive optical elements with conventional photolithographic techniques and compare the results with those achievable with electron-beam lithography. The fringes associated with the phase transfer function of the binary phase holographic interferogram are approximated with rectangles, which can be realized at submicron accuracy ...