A family of new discrete nonlinear equations associated with the Lotka–Volterra lattice is constructed by defining a novel algebraic system X. Moreover, some properties of the hierarchy are discussed. Furthermore, nonlinear integrable couplings of the resulting hierarchy are derived from an extended algebraic system [Formula: see text]. Finally, an example is given.

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This paper introduces a new method of surface simplification based on calculating changing rate of surface. We apply the adapted Butterfly subdivision method to determine the new vertex positions of simplified mesh, making the new vertices lie on an optimized limiting surface. We test our method on the rabbit mesh, and it is very effective to hold geometric features.

In this paper we present a new adaptive hybrid surfaces mesh subdivision scheme. Designers often want more flexibility in dealing with both triangles and polygons in their models. With the new subdivision scheme, Catmull-Clark subdivision and Loop subdivision results can be generated, as well as other more flexible surface shapes, by tuning the control parameters we designed. A theorem of C 1 is drawn from the scheme analysis. This scheme can optimize the resulting mesh and reduce useless space and running time.

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