We consider the convergence of a volume corrected characteristics-mixed method (VCCMM) for advection-diffusion systems. It is known that, without volume correction, the method is first order convergent, provided there is a nondegenerate diffusion term. We consider the advective part of the system and give some properties of the weak solution. With these properties we prove that the volume corre...

with initial terms u0 ux = ••• = ur_2 = 0, ur_1 1. Then (u) is called a unit sequence with coefficients al5 a25 -.., ar. For a positive integer AT, the primitive period of (u) modulo AT, denoted by K(M), is the least positive integer m such that un + m = un (mod AT) for all nonnegative integers n greater than or equal to some fixed integer n0. It is known that the primitive period modulo M of a...

A rank-r matrix X ∈ Rm×n can be written as a product UV >, where U ∈ Rm×r andV ∈ Rn×r. One could exploit this observation in optimization: e.g., consider the minimizationof a convex function f(X) over rank-r matrices, where the scaffold of rank-r matrices is modeledvia the factorization in U and V variables. Such heuristic has been widely used before forspecific problem inst...

The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of BahadurKiefer-type representation for sample quantiles is established, which yields the rquick limit points of quantile processes. These results are applied to linear functions of order statistics. Some results on r-quick convergence of certain Ga...

We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector field, and the scalar rotation. We develop and analyze a stable family of methods, indexed by an integer r ≥ 2 and with rate of convergence in the L2 norm of ...

K e y w o r d s N o n l i n e a r equations, Iteration method, Root finding, Order of convergence. 1. I N T R O D U C T I O N The problem of finding a real root of the nonlinear equation,

In [C2], Chemin shows that solutions of the Navier-Stokes equations in R for an incompressible fluid whose initial vorticity lies in L ∩ L∞ converge in the zero-viscosity limit in the L–norm to a solution of the Euler equations, convergence being uniform over any finite time interval. In [Y2], Yudovich assumes an initial vorticity lying in L for all p ≥ p0, and establishes the uniqueness of sol...