We establish an asymptotic formula with a power savings in the error term for traces of CM values of a family of Maass-Poincaré series which contains the modular j-function as a special case. By work of Borcherds [B], Zagier [Za], and Bringmann and Ono [BO], these traces are Fourier coefficients of half-integral weight weakly holomorphic modular forms and Maass forms.

In this note, we bound the inverse of nonsingular diagonal dominant matrices under the infinity norm. This bound is always sharper than the one in [P.N. Shivakumar, et al., On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital dynamics, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 298–312]. c © 2008 Published by Elsevier Ltd

Excitons in a quantum well depend on the interfacial roughness resulting from its growth. The interface is characterized by islands of size j separated by one monolayer steps across which the confining potential decreases by V0 for wider wells. A natural length is the localization length j05p\/A2MV0 characterizing the minimum size island to confine an exciton. For small islands (j,j0), the abso...

A. Appendix. We repeatedly use the notation for empirical measures and processes introduced in Section 2 following [2]. The fundamental idea of [2] is to view Gξj,Nj as the exchangeably weighted bootstrap empirical process corresponding to Gj,Nj ≡ √ Nj ( Pj,Nj − P0|j ) for j = 1, . . . , J . The processes Gξj,Nj converge weakly to √ pj(1− pj)Gj for independent P0|jBrownian bridge processes Gj ,...

1. J. F. Berglund and K. H. Hofmann, Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math., vol. 42, Springer-Verlag, Berlin and New York, 1967. MR 36 #6531. 2. Mary Katherine Bennett, Review of "Distributive Lattices by R. Balbes and P. Dwinger," Bull. Amer. Math. Soc. 82 (1976), 246-249. 3. R. Burckel, Weakly almost periodic functions on semigroups, G...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.