It is well known that for the Hilbert space H the minimum value of the functional Fμ(f) = ∫ H ‖f−g‖2dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H. We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner pro...

The Kreiss matrix theorem asserts that a family of N X N matrices is L,-stable if and only if either a resolvent condition (R) or a Hennitian norm condition (H) is satisfied. We give a direct, considerahly shorter proof of the power-houndedness of an N X N matrix satisfying (R), sharpening former results by showing that powerhoundedness depends, at most, linearly on the dimension M. We also sho...

We consider traces and discrete harmonic extensions on thin boundary layers. We introduce sharp estimates on how to control the H − or H 00 − boundary norm of a finite element function by its energy in a thin layer and vice versa, how to control the energy of a discrete harmonic function in a layer by the H 1/2 or H 00 norm on the boundary. Such results play an important role in the analysis of...

In this paper we analyze several first-order systems of Oseen-type equations that are obtained from the time-dependent incompressible NavierStokes equations after introducing the additional vorticity and possibly total pressure variables, time-discretizing the time derivative and linearizing the nonlinear terms. We apply the [L, L, L] least-squares finite element scheme to approximate the solut...

We consider the problem of recovering a low-rank tensor from its noisy observation. Previous work has shown a recovery guarantee with signal to noise ratio O(ndK/2e/2) for recovering a Kth order rank one tensor of size n × · · · × n by recursive unfolding. In this paper, we first improve this bound to O(n) by a much simpler approach, but with a more careful analysis. Then we propose a new norm ...

Abstract We consider a singularly perturbed reaction diffusion problem as first order two-by-two system. Using piecewise discontinuous polynomials for the component and $$H_{{{\,\mathrm{{div}}\,}}}$$ Hdiv -conforming elements...

We obtain some ”universal” estimates for L2-norm of the solution of a parabolic equation via a weighted version of H-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation of the equation by adding a constant to the zero order coefficient. The inverse matrix of the higher order coefficients of the parabolic equation is included into the w...

We introduce nearly Frank t-norms as t-norms which are generated from Frank t-norms by means of a negation-preserving automorphism. We state basic properties of nearly Frank t-norms and we show their speci c role in the characterization of T -measures. 1 Basic facts about T -norms A t-norm (fuzzy conjunction) is a binary operation T : [0; 1]2 ! [0; 1] which is commutative, associative, nondecre...

This paper proposes a new approach to solve the problem of designing optimal proportional-integral-derivative (PID) controllers that minimize an H2-norm associated with the set-point response while subjecting to an H∞-norm on the load disturbance rejection. The proposed design approach consists of constructing the feasible domain in the controller gain space and searching over the domain the op...

It is well known that for multipliers f of the Drury-Arveson space H n, ‖f‖∞ does not dominate the operator norm of Mf . We show that in general ‖f‖∞ does not even dominate the essential norm of Mf . A consequence of this is that there exist multipliers f of H n for which Mf fails to be essentially hyponormal, i.e., if K is any compact, self-adjoint operator, then the inequality M∗ f Mf −MfM f ...