Polynomials with graphs of maximum length

In this paper we find the pairs of functionsg, G (g<G) such that the maximum length of the graph of polynomials of given degree contained betweeng andG is attained on one of the two snakes generated by the functionsg andG. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 61–69, January, 1999.     

LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

Color balloon snakes for face segmentation

In this paper, a new color balloon snake model is introduced and used for face segmentation in color images. It is an extension of existing balloon snake models. Based on a coarse detection of facial features, the method combines a skin-tone distribution model and a boundary diffusion model to search for the facial boundary. The skin distribution is a single Gaussian, which is proposed to extract the skin-tone region in the RGB space. The diffusion model, which is invented to diffuse the facial boundary, is a one-dimensional Gauss revolution surface. The parameters are evaluated based on an AdaBoost face detection method. The color snakes are weighted by the distributions, and the external forces evolve dynamically to reach the boundary, which depends on the balance between the internal and external forces. Experiments were conducted, and the results show that the model provides desired segmentation outcomes. It is robust against complex backgrounds and lighting pollution.     

Smallest Limited Vertex-to-vertex Snakes of Unit Triangles

A sequence T=T ₁,T ₂,...,T _n of regular triangles of unit side lengths is called a vertex-to-vertex snake if TT is a common vertex of T and T if |i-j|=1 and is empty if |i-j|<1. A vertex-to-vertex snake of unit triangles is called limited if it is not a proper subset of another vertex-to-vertex snake of unit triangles. We prove that the minimum number of unit triangles which form a limited vertex-to-vertex snake is seven.