We introduce an exponentially confining potential well that can be used as a model to describe the structure of strongly localized system. obtain approximate partial solution Schrödinger equation with this where we find lowest energy spectrum and corresponding wavefunctions. use tridiagonal representation approach method for obtaining finite series square-integrable functions written in terms B...

Abstract We discuss Meyers-Serrin’s type results for smooth approximations of functions $$b=b(t,x): \mathbb {R}\times {R}^n\rightarrow {R}^m$$ b = ( t , x ) : R <m...

Newey and Smith (2001) have recently shown that Empirical Likelihood (EL) exhibits desirable higher-order asymptotic properties, namely, that its O ¡ n−1 ¢ bias is particularly small and that biascorrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that the asymptotic variance of EL in the presence of model misspe...

Starting with general hyperbolic systems of conservation laws, a special sub{class is extracted in which classical solutions can be expressed in terms of a linear transport equation. A characterizing property of this sub{class which contains, for example, all linear systems and non{linear scalar equations, is the existence of so called exponentially exact entropies.

d|en d denote the number and the sum of exponential divisors of n, respectively. Properties of these functions were investigated by several authors, see [1], [2], [3], [5], [6], [8]. Two integers n,m > 1 have common exponential divisors iff they have the same prime factors and for n = ∏r i=1 p ai i , m = ∏r i=1 p bi i , ai, bi ≥ 1 (1 ≤ i ≤ r), the greatest common exponential divisor of n and m is

The amalgamation of leaf-labelled trees into a single supertree that displays each of the input trees is an important problem in classification. Clearly, there can be more than one (super) tree for a given set of input trees, in particular if a highly unresolved supertree exists. Here, we show (by explicit construction) that even if every supertree of a given collection of input trees is binary...

For any oblique incidence and arbitrarily high order, lattice sums for one-dimensional gratings can be expressed in terms of exponentially convergent series. The scattering Green's function can be efficiently evaluated also in the grating plane. Numerical implementation of the method is 200 times faster than for the previous best result.

This thesis deals with questions relating to the maximum density of rank-n matroids in a minor-closed class. Consider a minor-closed class M of matroids that does not contain a given rank-2 uniform matroid. The growth rate function is defined by hM(n) = max (|M | : M ∈M simple, r(M) ≤ n) . The Growth Rate Theorem, due to Geelen, Kabell, Kung, and Whittle, shows that the growth rate function is ...

We show that when a suitable entanglement-generating unitary operator depending on a parameter is applied on N qubits in parallel, a precision of the order of 2(-N) in estimating the parameter may be achieved. This exponentially improves the precision achievable in classical and in quantum nonentangling strategies.