We investigate convergence properties in weighted spaces of distributions D′ Lp and their test spaces DLq , 1 p + 1 q = 1. Also we give characterization of weak limits of weakly convergent sequences of L-distributions. AMS Mathematics Subject Classification (2010): 46F05

2. Cycles and their terminology. Let L be an n Xn Latin square or, alternatively, let Q be a quasigroup of order n. Let M be the set of n2 ordered triplets ijk, where k is the entry in the ith row and jth column of L. If 5 is the set of n2 ordered pairs ij, and if 7r,:Af—>S is the projection parallel to the ith coordinate (for example, ir2(ijk) = ik), then for each i, l^i^3, t< is onto S (or eq...

The QR-algorithm is a renowned method for computing all eigenvalues of an arbitrary matrix. A preliminary unitary similarity transformation to Hessenberg form is indispensible for keeping the computational complexity of the QRalgorithm applied on the resulting Hessenberg matrix under control. The unitary factor Q in the QR-factorization of the Hessenberg matrix H = QR is composed of n − 1 rotat...

Interlayer exchange coupling in ordered Fe nanocluster arrays grown on Al2O3/Ni3Al(111) S. Vlaic,1,* L. Gragnaniello,1,† S. Rusponi,1 A. Cavallin,1,‡ F. Donati,1 Q. Dubout,1 C. Piamonteze,2 J. Dreiser,2 F. Nolting,2 and H. Brune1,§ 1Institute of Condensed Matter Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland 2Swiss Light Source, Paul Scherrer Institut, CH-5232 ...

We consider Tikhonov and sparsity-promoting regularization in Banach spaces for inverse scattering from penetrable anisotropic media. To this end, we equip an admissible set of material parameters with the L-topology and use Meyers’ gradient estimate for solutions of elliptic equations to analyze the dependence of scattered fields and their Fréchet derivatives on the material parameter. This al...

Let G be a transitive permutation group on a set ? and let m be a positive integer. If no element of G moves any subset of ? by more than m points, then |? | [2mp I (p-1)] wherep is the least odd primedividing |G |. When the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n....

ing from the embeddability relation between order types, define a quasi-order to be a reflexive, transitive relation. Throughout this paper, the letters Q and R will range over quasi-ordered sets and classes. Various quasi-ordered spaces will be defined; in each case we will use the symbol < (perhaps with subscripts) to denote the quasi-order under consideration. If q1, q2 E Q, write ql < q2 to...