In this paper we prove that any multi-resolution analysis of L2(R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the an...

We consider the complexity of a Lenstra Lenstra Lovász lattice reduction algorithm ([LLL]) in which the vectors are allowed to be linearly dependent and in which one also asks for the matrix of the transformation from the given generators to the reduced basis. The main problem will be to show that the entries of the transformation matrix remain bounded through the algorithm, with a reasonable b...

(6 x ~}R30°-Xe/Pd(lil) and the dilute phase of Xe/Pd(li I) were investigated with spin-polarized low-energy electron diffraction (SPLEED). In the experiment spin-polarized electrons from a GaAs source were scattered and the spin-dependent intensities were measured. Comparative calculations were carried out by means of a relativistic LEED program. The structure determination of (6 x fi)R30”-Xe/P...

The potential dependence in the surlace second hannonic response from hydrogen terminated n-Si(111) i(l l and oxidized n-Si(1l1) ll surfaces has been examined in aqueous NH4F and H2S04 4 solutions. The relative phase of the nonlinear response as measured by rotational anisotropy experiments is found to be highly sensitive to the presence of the oxide and the field applied across Si(ll I)/mdde/e...

25 years ago, Lenstra, Lenstra and Lovász presented their celebrated LLL lattice reduction algorithm. Among the various applications of the LLL algorithm is a method due to Coppersmith for finding small roots of polynomial equations. We give a survey of the applications of this root finding method to the problem of inverting the RSA function and the factorization problem. As we will see, most o...

25 years ago, Lenstra, Lenstra and Lovasz presented their celebrated LLL lattice reduction algorithm. Among the various applications of the LLL algorithm is a method due to Coppersmith for finding small roots of polynomial equations. We give a survey of the applications of this root finding method to the problem of inverting the RSA function and the factorization problem. As we will see, most o...

Light Linear Logic (LLL) of [Gir95] characterizes the polytime functions through a careful handling of structural inference rules of logic. Based on this purely logical approach, we give a characterization of the polyspace functions. Our logical system is an extension of Intuitionistic Light A ne Logic (ILAL) of [Asp98], a variant of LLL with full (unrestricted) weakening. We introduce the noti...

In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi–Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically ...