The uniform norm of the differential of the n-th iteration of a diffeomorphism is called the growth sequence of the diffeomorphism. In this paper we show that there is no lower universal growth bound for volume preserving diffeomorphisms on manifolds with an effective T2 action by constructing a set of volume-preserving diffeomorphisms with arbitrarily slow growth.

In this paper we study a sixth order Cahn-Hilliard type equation that arises as a model for the faceting of a growing surface. We show global in time existence of weak solutions and uniform in time a priori estimates in the H3 norm. These bounds enable us to show the uniqueness of weak solutions.

In this paper, under the framework of Banach space with uniformly Gateaux differentiable norm and uniform normal structure, we use the existence theorem of fixed points of Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive mappings. We get the convergence theorems.

Imposing structure on the Smith form of an (integer) periodicity matrix N = U V leads to e cient m-D DFT implementations. For resampling matrices, i.e. non-singular rational matrices, we introduce Smith form decomposition algorithms to generate matrices whose diagonal elements exhibit minimum variance and U matrices with minimum norm. Such structure simpli es non-uniform m-D lter bank design.

Solutions of two slightly more general problems than those posed by Kenneth B. Stolarsky in [10] are presented. The latter deal with a shape preserving approximation, in the uniform norm, of two functions (1/x) log coshx and (1/x) log(sinhx/x), x ≥ 0, by ratios of exponomials. The main mathematical tools employed include Gini means and the Stolarski means.

We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauß–Seidel method in which the blocks correspond to restrictions of the IIPG method to suitably constructed subspaces. Numerical tests are included, showing the uniform convergence of the iterative meth...

In this paper, under the framework of Banach space with uniformly Gateauxdifferentiable norm and uniform normal structure, we use the existence theorem of fixed points of Gang Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive semigroup. We get the convergence theorems.

We present a pair of sharp lower and upper bounds on the 2-norm of the aliasing error in general multiband sampling representationsfor not necessarily bandlimited multidimensional functions. These boundsimprove and generalize previous bounds. They also complement a recentuniform upper bound due to Higgins. multiband, Poisson summation, error energy.Index TermShannon sampling...

Let X be a non-reflexive real Banach space. Then for each norm | · | from a dense set of equivalent norms on X (in the metric of uniform convergence on the unit ball of X), there exists a three-point set that has no Chebyshev center in (X, | · |). This result strengthens theorems by Davis and Johnson, van Dulst and Singer, and Konyagin.

Abstract. We prove approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy with incomplete data in dimension d ≥ 2. Our estimates are given in uniform norm for coefficient difference and related stability precision efficiently increases with increasing energy and coefficient difference regularity. In addition, our estimates are rather optimal even in the Born a...