In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

In the paper, we analyze the L norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the f...

In 7 experiments, undergraduates judged the force exerted by a videotaped standing puller, a computer-generated (stick-figure) puller, or a computer-generated inverted pendulum. Single and stepwise multiple regression analyses determined the kinematic variables exploited by the participants. Results show that (a) judgments correlated highly with force and improved with feedback; (b) judgments c...

In this paper, we study the differential equation with the periodic boundary value u′′(t) = f(t, u(t), u′(t)), t ∈ [0, 2π] u(0) = u(2π), u′(0) = u′(2π). The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.

The main goal of this paper is to present new robust and scalable preconditioned conjugate gradient algorithms for solving Stokes equations with large viscosities jumps across subregion interfaces and discretized on non-structured meshes. The proposed algorithms do not require the construction of a coarse mesh and avoid expensive communications between coarse and fine levels. The algorithms bel...