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Two necessary and sufficient conditions are presented for Hamiltonian cycle problem in simple undirected graph using linear Diophantine equation systems with cycle vector. The first one is based on the incidence matrix and the second one is based on edge-adjacency matrix. It is proven that the solution set of the cycle vector correspond to the edges of Hamiltonian cycle in a given graph. Based on...
In this research, we developed a real-time fluid simulator for a haptic interface to display a virtual environment including 3-dimensional fluid by using smoothed particles hydrodynamics (SPH). SPH is a type of particle method and is suitable for a fast computation; however, it is difficult to incorporate sufficient fluid incompressibility in SPH for simulating a real-time process. This is because...
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