We prove the mean curvature flow of the graph of a symplectomorphism between Riemann surfaces converges smoothly as time approaches infinity.

In this paper, we propose the generalized B divided difference, with which the $(k−1)$th derivative of B-spline curves of order $k$ can be obtained directly without the need to compute the first $(k−2)$ derivatives as before. Based on the generalized B divided difference, the necessary and sufficient condition for degree-reducible B-spline curves is presented. Algorithms for degree reduction of B-spline curves are proposed using the constrained optimization methods.

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We study inhomogeneous random graphs in the subcritical case. Among other results, we derive an exact formula for the size of the largest connected component scaled by log$n$, with$n$being the size of the graph. This generalizes a result for the “rank-1 case”. We also investigate branching processes associated with these graphs. In particular, we discover that the same well-known equation for the survival probability, whose positive solution determines the asymptotics of the size of the largest component in the supercritical case, also plays a crucial role in the subcritical case. However, now it is the$negative$solutions that come into play. We disclose their relationship to the distribution of the progeny of the branching process.