The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations In this paper, we consider the Cauchy problem $$\begin{cases} u_{t}=\Delta(u^{m}), &x\in{}\mathbb{R}^{N}, t>0, N\geq3, \\ % ^^----- here u(x,0)=u_{0}(x), &x\in{}\mathbb{R}^{N}. \end{cases}$$ We will prove that: (i) for $m_{c} Keywords:fast diffusion equations, Cauchy problem, continuous dependence on nonlinearityCategories:35K05, 35K10, 35K15 2. CMB 1999 (vol 42 pp. 169) Ding, Hongming  Heat Kernels of Lorentz Cones We obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of time$t\$ and two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones. Keywords:Lorentz cone, symmetric cone, Jordan algebra, heat kernel, heat equation, Laplace-Beltrami operator, eigenvaluesCategories:35K05, 43A85, 35K15, 80A20