We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily highorder discontinuous Galerkin temporal discretizations. Using equilibrated flux reconstructions, we present a posteriori error estimates for a norm composed of the L2(H1)∩H1(H−1)norm of the error and the temporal jumps...

In this paper we obtain upper and lower bounds for the H 1 norm of the Kalman lter and RLS algorithm, with respect to prediction and ltered errors. These bounds can be used to study the robustness properties of such estimators. One main conclusion is that, unlike H 1-optimal estimators which do not allow for any ampliication of the disturbances, the least-squares estimators do allow for such am...

The convergence of the bivariate spline solution to the solution of the second order elliptic PDE in non-divergence form in the maximum norm is presented in this paper. Mainly, the L∞ norm of the spline projection in the Sobolev space H 0 (Ω) ∩H 0 (Ω) is shown to be bounded, where Ω is a polygonal domain. With the boundedness of the projection, one can establish the error of the spline solution...

We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, norm of derivative, and Hofer/spectral norm. obtain as consequence that sufficiently fast convergence in metric forces convergence. The second theme our paper is study pseudo-rotations arise from Anosov-Katok method. As an application inequality, we rigidity result such pseudo-rotations.

For first-order discretizations of the integral fractional Laplacian, we provide sharp local error estimates on proper subdomains in both $H^1$-norm and localized energy norm. Our have form a best approximation plus global measured weaker

Let H be an ultraspherical hypergroup associated to a locally compact group G and let A(H) the Fourier algebra of H. For left Banach A(H)-submodule X VN(H), define QX norm closure linear span set {u f : u ?A(H), ? X} in BA(H)(A(H),X

We determined the effect of muscle glycogen concentration and postexercise nutrition on anabolic signaling and rates of myofibrillar protein synthesis after resistance exercise (REX). Sixteen young, healthy men matched for age, body mass, peak oxygen uptake (Vo(2peak)) and strength (one repetition maximum; 1RM) were randomly assigned to either a nutrient or placebo group. After 48 h diet and ex...

When using Neural Networks as trial functions to numerically solve PDEs, a key choice be made is the loss function minimised, which should ideally correspond norm of error. In multiple problems, this error coincides with – or equivalent H−1-norm residual; however, it often difficult accurately compute it. This work assumes rectangular domains and proposes use Discrete Sine/Cosine Transform effi...

We provide a direct proof that the Haagerup estimate on the completely bounded norm of elementary operators is best possible in the case of B(H) via a generalisation of a theorem of Stampfli. We show that for an elementary operator T of length `, the completely bounded norm is equal to the k-norm for k = `. A C*-algebra A has the property that the completely bounded norm of every elementary ope...