A new approach to the problem of minimizing L2sensitivity subject to L2-norm scaling constraints for two-dimensional (2-D) state-space digital filters is proposed. Using linear-algebraic techniques, the problem at hand is converted into an unconstrained optimization problem, and the unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. Computer simulatio...

We consider the nite element approximation of a non-Newtonian ow, where the viscosity obeys a general law including the Carreau or power law. For suuciently regular solutions we prove energy type error bounds for the velocity and pressure. These bounds improve on existing results in the literature. A key step in the analysis is to prove abstract error bounds initially in a quasi-norm, which nat...

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l2-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linearalgebraic techniques. The unconstrained problem obta...

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...

We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show that, depending on the norm for measuring the error, the problems are strongly polynomially or quasi-polynomially tractable even in the model of computation whe...

This paper is concerned with boundary dissipative conditions that guarantee the exponential stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We present a comprehensive review of the results that are available in the literature. The main result of the paper is then to supplement these previous results by showing how a new Lyapunov stability approach can be use...

We provide a new proof of the theorem of Simon and Zhu that in the region |E| < λ for a.e. energies, − d2 dx2 + λ cos(xα), 0 < α < 1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e. E ∈ [−2, 2] for the discrete model with V (j2) = ej , V (n) = 0 if n / ∈ {1, 4, 9, . . . }. The arguments depend on a direct analysis of the eq...

We study an adaptive finite element method for the p-Laplacian like PDE’s using piecewise linear, continuous functions. The error is measured by means of the quasi-norm of Barrett and Liu. We provide residual based error estimators without a gap between the upper and lower bound. We show linear convergence of the algorithm which is similar to the one of Morin, Nochetto, and Siebert. All results...

We give two weak-strong uniqueness results for the weak solutions to the critical dissipative quasi-geostrophic equation when the initial data belongs to Ḣ−1/2. The first one shows that we can construct a unique Ḣ−1/2-solution when the initial data belongs moreover to L∞ with a small L∞ norm. The other one gives the uniqueness of a Ḣ−1/2-solution which belongs to C([0, T ), CMO).

In this work we investigate the numerical solution for two-dimensional Maxwell’s equations on graded meshes. The approach is based on the Hodge decomposition. The solution u of Maxwell’s equations is approximated by solving standard second order elliptic problems. Quasi-optimal error estimates for both u and ∇ × u in the L2 norm are obtained on graded meshes. We prove the uniform convergence of...