Average prime-pair counting formula

Taking $r>0$, let $\pi_{2r}(x)$ denote the number of prime pairs $(p, p+2r)$ with $p\le x$. The prime-pair conjecture of Hardy and Littlewood (1923) asserts that $\pi_{2r}(x)\sim 2C_{2r} {\rm li}_2(x)$ with an explicit constant $C_{2r}>0$. There seems to be no good conjecture for the remainders $\omega_{2r}(x)=\pi_{2r}(x)- 2C_{2r} {\rm li}_2(x)$ that corresponds to Riemann's formula for $\pi(x)-{\rm li}(x)$. However, there is a heuristic approximate formula for averages of the remainders $\omega_{2r}(x)$ which is supported by numerical results.Comment: 26 pages, 6 figure

The hexagonal versus the square lattice

We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p. 201), motivated by considerations from hyperbolic geometry, conjectured that in dimensions 2 to 8 the best known lattice sphere packings have `maximal lengths' and goes on to write: "In dimension 2 the conjecture means in particular that the hexagonal lattice is `better' than the square lattice. More precisely, let 0<h_1<h_2<... be the positive integers, listed in ascending order, which can be written as h_i=x^2+3y^2 for integers x and y. Let 0<q_1<q_2<... be the positive integers, listed in ascending order, which can be written as q_i=x^2+y^2 for integers x and y. Then the conjecture is that q_i<=h_i for i=1,2,3,..." Our proof requires computational prime number theory in combination with methods from a preprint of the first author (to appear in Math. Comp.), arXiv:math.NT/0112100.Comment: 24 pages, 6 figures, 2 table

Direct patterning of complex oxides by pulsed laser deposition through stencils

The possibilities to grow isolated structures of complex oxides by pulsed laser\ud deposition through stencils were investigated. A stencil consisting of a SiN membrane with apertures of several hundred nanometers embedded in a Si chip is placed in front of a heated substrate (up to 750 degrees Celsius). Deposition through these apertures results in resistless, direct patterning by local deposition of complex oxides like ferroelectric Lead Zirconate Titanate. The created isolated structures were analyzed by AFM imaging. Under-deposition, in this work called broadening, is inevitable during stencil deposition and is depending on deposition parameters, especially pressure. Different causes of broadening are mapped and discussed

From Controlling to Constructive: Youth unemployment policy in Australia and The Netherlands

Youth unemployment is an issue that has increasingly troubledwestern countries since the 1970s. This paper provides data on youth unemployment in Australia and the Netherlands, and discusses government policy in both countries. The rate of youth unemployment was similar in both countries in the mid 1980s, but since then it has declined dramatically in the Netherlands, while changing little in Australia. Youth unemployment policy in Australia has been driven by the concept of obligation, while in the Netherlands youth unemployment policy has been organised around the principle of a guarantee for youth. The Dutch labour market programme offers more continuity and coherence than the rather ad hoc Australian programmes.However, the paper argues that youth labour market policy in both countries is of a controlling nature, and does not serve marginalised youth. Moreover, policy in neither country meets OECD criteria for effective labour market programs. The paper concludes with the description of a Dutch program which, to a large extent, does meet the OECD criteria, and demonstrates that a more constructive approach to youth unemployment is possible

Direct patterning of oxides by pulsed laser stencil deposition

This thesis describes a detailed study of the application of stencil technology in the patterning of epitaxial oxide thin films by pulsed laser deposition (PLD). Stencil patterning has been applied in thin film sub-micron patterning of metals successfully for decades since it has several advantages over lithography techniques. It is a single processing step technique which can be applied to many different types of surfaces. The stencil patterning process does not utilize any solvents which makes it a favored technique for patterning metals on fragile and/or organic materials. However, for successful stencil patterning and unlimited (re)use of stencils, several issues need to be solved. The main issues that limit the re-usability of stencils are clogging of the apertures and deformation of the stencil caused by stress induced by the deposited material