For a function φ in L(0, 1), extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates φ(nx), n = 1, 2, 3, . . . , constitutes a Riesz basis or a complete sequence in L(0, 1). The problem translates into a question concerning multipliers and cyclic vectors in the Hilbert space H of Dirichlet series f(s) = ∑ n ann, where the coefficients an ar...

Functional central limit theorems in L(0, 1) for logarithmic combinatorial assemblies are presented. The random elements argued in this paper are viewed as elements taking values in L(0, 1) whereas the Skorokhod space is argued as a framework of weak convergences in functional central limit theorems for random combinatorial structures in the literature. It enables us to treat other standardized...

The paper improves the classical uniqueness result for the Euler system in the n dimensional case assuming that ∇u E ∈ L 1 (0, T ; BM O(Ω)), only. Moreover the rate of the convergence for the inviscid limit of solutions to the Navier-Stokes equations is obtained, provided the same regularity of the limit Eulerian flow. A key element of the proof is a logarithmic inequality between the Hardy and...

Let M k be the moduli space of based (anti-self-dual) instantons on CP 2 of charge k and rank n. There is a natural inclusion M k →֒ M n+1 k . We show that the direct limit space M∞ k is homotopy equivalent to BU(k)× BU(k). Let l∞ be a line in the complex projective plane and let C̃P 2 be the blow-up at a point away from l∞. Mnk can be alternatively described as the moduli space of rank n holomor...

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established. 0. Introduction Quant...

The convergence properties of some LOD schemes are considered. New stability estimates with respect to boundary conditions are proved. These results are used to investigate the accuracy of LOD schemes when no special boundary correction technique is used for the realization of LOD schemes. The accuracy of LOD schemes with corrected boundary conditions is also investigated. Results of the comput...

The limit of detection (LOD) for any analytical procedure, the point at which analysis is just feasible, may be determined by a statistical approach based on measuring replicate blank (negative) samples or by an empirical approach, consisting of measuring progressively more dilute concentrations of analyte. The limit of quantitation (LOQ), or concentration at which quantitative results can be r...

A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing \stable" L evy processes. This model can be understood as a continuum limit of discrete state-space, two allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitable large space and tim...