We say that a class of finite structures for a finite signature is r-compressible if each structure G in the class has a first-order description of size at most O(r(|G|)). We show that the class of finite simple groups is log-compressible, and the class of all finite groups is log-compressible. The result relies on the classification of finite simple groups, the bi-interpretability of the small...

Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar...

by, for example, a finite difference method in the computational (μ, χ, φ) space. The above standard dipole coordinates is convenient and certainly appropriate for analytical studies in which the Earth’s dipolar field plays central roles. It also works as a base coordinates for the node and cell generation of the finite element method in the dipole geometry [2, 3]. However, when one tries to us...

We present a finite element analogue to the second-order, finite difference scheme for the solution of the heat diffusion equation in strongly magnetised plasmas given in Günter et al. [S. Günter et al., J. Comp. Phys. 209 (2005) 354]. Compared to standard finite element or finite difference formulations it strongly reduces the pollution of perpendicular heat fluxes by parallel ones even withou...

1 STATEMENT OF THE PROBLEM Our goal is to introduce how derivatives can be approximated by using difference quotients. Suppose we have an interval [a,b] ⊂ R. Let a = x0 < x1 < ·· · < xN−1 < xN = b be a partition. We call {x1, . . . , xN−1} the interior points, and {x0, xN } the boundary. Given a function f : [a,b] → R, we want to approximate the derivative f ′ using our partition. 2 DIFFERENCE ...

By B(X), we also denote the set of all bounded linear operators on X into itself. If X is any Banach space and T ∈ B(X), then the adjoint T∗ of T is a bounded linear operator on the dual X∗ of X defined by (T∗ f )(x)= f (Tx) for all f ∈ X∗ and x ∈ X . LetX = {θ} be a nontrivial complex normed space and T : (T)→ X a linear operator defined on a subspace (T)⊆ X . We do not assume thatD(T) is dens...

0. Introduction. In this paper we consider factorizations of finite rank operators through finite-dimensional C∗-algebras. We are interested in factorization norms involving either the completely bounded norm ‖ ‖cb or Haagerup’s decomposable norm ‖ ‖dec (see [11]). Let us denote byMn the C∗-algebra of all n×n matrices with complex entries. Let A and B be two C∗-algebras, and let us consider a f...

(Here and everywhere else in the paper, the expectation E[·] is with respect to the uniform probability distribution on {−1, 1}.) The Parseval’s identity is the fact that ∑ S⊆[n] f̂(S) 2 = E[f(x)]. In particular, if f is boolean-valued then this implies that ∑ S⊆[n] f̂(S) 2 = 1. Given f : {−1, 1} → R and i ∈ [n], we define the discrete derivative ∂if : {−1, 1} → R by ∂if(x) = f(x1, x2, · · · , 1,...