We analyze a posteriori error estimators for finite element discretizations of convec-tion-dominated stationary convection-diffusion equations using locally refined, isotropic meshes. The estimators are based on either the evaluation of local residuals or the solution of discrete local problems with Dirichlet or Neumann boundary conditions. All estimators yield global upper and lower bounds for...

We present conditions, some necessary and some suucient, valid under weak assumptions , for robust stability and uniform robust stability of uncertain linear time-invariant systems with linear time-invariant uncertainties that are block-diagonal, with known frequency-dependent norm bounds on the diagonal blocks. Small-theorems with frequency-independent uncertainty bounds are recovered as speci...

We give uniform upper and lower bounds for the L norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.

In this paper, we define the modular space Z σ (s, p) by using the Zweier operator and a modular. Then, we consider it equipped with the Luxemburg norm and also examine the uniform Opial property and property β. Finally, we show that this space has the fixed point property.

We prove new global Hölder-logarithmic stability estimates for the Gel’fand inverse problem at fixed energy in dimension d ≥ 3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. Comparisons with preceeding results in this direction are given.

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

We present a (random) polynomial-time algorithm to generate a randomGaussian integer with the uniform distribution among those with norm at most N , along with its prime factorization. The method generalizes to finding a random ideal in the ring of integers of a quadratic number field together with its prime ideal factorization. We also discuss the analogous problem for higher degree number fie...

We consider spectral semi-Galerkin approximations for the strong solutions of the nonhomogeneous Navier-Stokes equations. We derive an optimal uniform in time error bound in the H 1 norm for approximations of the velocity. We also derive an error estimate for approximations of the density in some spaces L r .

We consider the nonparametric regression model with random design. We study the estimation of a regression function f in the uniform norm assuming that f belongs to a Hölder class. We determine the minimax exact constant and an asymptotically exact estimator. They depend on the minimum value of the design density.

We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimension d ≥ 3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension d = 2 is also gi...