Abstract. Let I be a finite interval and r, s ∈ N. Given a set M , of functions defined on I, denote by ∆+M the subset of all functions y ∈ M such that the s-difference ∆τ y(·) is nonnegative on I, ∀τ > 0. Further, denote by ∆+W r p , the class of functions x on I with the seminorm ‖x‖Lp ≤ 1, such that ∆τ x ≥ 0, τ > 0. Let Mn(hk) := Pn i=1 cihk(wit − θi) | ci, wi, θi ∈ R , be a single hidden la...

We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities in the log-concave setting and discuss some examples. 2010 Mathematics Subject Classification. Primary 94A17; Secondary 52A40, 60E15.

In an earlier paper [SIAM J. Matrix Anal. Appl. vol. 30 (2008), 925–938] we gave sufficient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving linear systems whose coefficient matrix is Hermitian and positive semidefinite. In this paper we show in which cases these conditions are also necessary, and show that they are not necessary in others.

In this paper Tikhonov regularization for nonlinear illposed problems is investigated. The regularization term is characterized by a closed linear operator, permitting seminorm regularization in applications. Results for existence, stability, convergence and convergence rates of the solution of the regularized problem in terms of the noise level are given. An illustrating example involving para...

We examine a cell-vertex finite volume method which is applied to a model parabolic convection-diffusion problem. By using techniques from finite element analysis, local errors away from all layers are obtained in a seminorm that is related to, but weaker than, the L2 norm.

We show that the minimal discrepancy of a point set in d-dimensional unit cube with respect to BMO seminorm suffers from curse dimensionality.

We introduce an approximate description of N-qubit state, which contains sufficient information to estimate the expectation value any observable a precision that is upper bounded by ratio suitably-defined seminorm square root number system's identical preparations xmlns:mml="http://www.w3.org/1998/Math/MathML">...

Abstract We establish the mean convergence for multiple ergodic averages with iterates given by distinct fractional powers of primes and related recurrence results. A consequence our main result is that every set integers positive upper density contains patterns form $\{m,m+[p_n^a], m+[p_n^b]\}$ , where $a,b$ are nonintegers $p_n$ denotes n th prime, a property fails if or b natural number. Our...

Abstract We prove residual-type a posteriori error estimates in the maximum norm for linear scalar elliptic convection–diffusion problem that may be singularly perturbed. Similar analysis energy by Verfürth indicates dual of convective derivative must added to natural order residual estimator reliable and efficient. show situation is similar norm. In particular, we define mesh-dependent weighte...