We study perturbations of the self-adjoint periodic Sturm–Liouville operatorA0=1r0(−ddxp0ddx+q0) and conclude under L1-assumptions on differences coefficients that essential spectrum absolutely continuous remain same. If a finite first moment condition holds for coefficients, then at most finitely many eigenvalues appear in spectral gaps. This observation extends seminal result by Rofe-Beketov ...

A result of Chudnovsky concerning rational approximation to certain algebraic numbers is reworked to provide a quantitative result in which all constants are explicitly given. More particularly, Padé approximants to the function (1 jc)1/3 are employed to show, for certain integers a and b, that |(a/fc) p/q\> cq~* when q > 0. Here, c and k are given as functions of a and b only. In 1964 Baker [1...

Recent climate change has resulted in changes to the phenology and distribution of invertebrates worldwide. Where invertebrates are associated with disease, climate variability and changes in climate may also affect the spatio-temporal dynamics of disease. Due to its significant impact on sheep production and welfare, the recent increase in diagnoses of ovine haemonchosis caused by the nematode...

For an arbitrary real number α with convergents p0 q0 , p1 q1 , p2 q2 , . . . , b(n+ qi)αc − bnαc is equal to pi, and so is independent of n, except at a small specified number of values of n. For fixed n, this relation holds for all or for all except a finite number of values of i.

This paper analyzes transient characteristics of Gaussian queues. More specifically, we determine the logarithmic asymptotics of P(Q0 > pB,QTB > qB), where Qt denotes the workload at time t . For any pair (p, q), three regimes can be distinguished: (A) For small values of T , one of the events {Q0 > pB} and {QTB > qB} will essentially imply the other. (B) Then there is an intermediate range of ...

Molecular dynamics simulations employing reactive potentials were used to determine the activation barriers to the dissolution of the amorphous SiO2 surface in the presence of a 2 nm overlayer of water. The potential of mean force calculations of the reactions of water molecules with 15 different starting Q4 sites (Qi is the Si site with i bridging oxygen neighbors) to eventually form the disso...

An Homogeneous Bright QSO Survey (HBQS) has been carried out in the framework of an ESO Key programme. 327 QSOs (with MB < −23 and 0.3 < z < 2.2) have been selected over an area of 555 deg in the magnitude range 15 < B < 18.75. For magnitudes brighter than B = 16.4 the QSO surface density turns out to be a factor 2.2 higher than what measured by the PG survey, corresponding to a surface density...

For a flat universe presently dominated by static or dynamic vacuum energy, cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymp-totic collapsed mass fraction as function of the present ratio of smooth energy to matter energy R 0 = (1 − Ω m0)/Ω m0. Identifying these collapsed fractions as anthropic probabilities, we find the observed present ratio R 0 ∼ 2 to be likely in ...

Consideration in this present paper is the long-time asymptotics of solutions to derivative nonlinear Schrödinger (DNLS) equation with step-like initial value q(x,0)=q0(x)=A1eiϕe2iBx,x<0,A2e−2iBx,x>0,by Deift-Zhou method. The problem described by a matrix Riemann-Hilbert problem. A crucial ingredient used introduce g-function mechanism for solving entries jump growing exponentially as t→∞. It s...

We investigate the relationship of “physical” parton densities defined by k-factorisation, to those in the minimal subtraction scheme, by comparing their small-x behaviour. We first summarize recent results on the above scheme change derived from the BFKL equation at NLx level, and we then propose a simple extension to the renormalisation-group improved (RGI) equation. In this way we are able t...