Contribution of ICP-IDMS to the certification of antimony implanted in a silicon wafer - comparison with RBS and INAA results

A thin-layer reference material for surface and near-surface analytical methods was produced and certified. The surface density of the implanted Sb layer was determined by Rutherford backscattering spectrometry (RBS), instrumental neutron activation analysis (INAA), and inductively coupled plasma isotope dilution mass spectrometry (ICP-IDMS) equipped with a multi-collector. The isotopic abundances of Sb (121Sb and 123Sb) were determined by multi-collector ICP-MS and INAA. ICP-IDMS measurements are discussed in detail in this paper. All methods produced values traceable to the SI and are accompanied by a complete uncertainty budget. The homogeneity of the material was measured with RBS. From these measurements the standard uncertainty due to possible inhomogeneities was estimated to be less than 0.78% for fractions of the area increments down to 0.75 mm2 in size. Excellent agreement between the results of the three different methods was found. For the surface density of implanted Sb atoms the unweighted mean value of the means of four data sets is 4.81 x 10(16) cm(-2) with an expanded uncertainty (coverage factor k = 2) of 0.09 x 10(16) cm(-2). For the isotope amount ratio R (121Sb/123Sb) the unweighted mean value of the means of two data sets is 1.435 with an expanded uncertainty (coverage factor k = 2) of 0.006.     

Four-pion production in e^+e^- annihilation

Abstract. We calculate the processes and to in the low-energy expansion of the standard model. The chiral amplitudes of can be extended via resonance exchange to energies around 1 GeV. Higher-order effects have been included in the form of and double exchange and by performing a resummation of the pion form factor. The predicted cross sections and the branching ratios are in good agreement with the available data. Received: 8 March 2002 / Published online: 14 June 2002     

Reversed geometric programming: A branch-and-bound method involving linear subproblems

The paper proposes a branch-and-bound method to find the global solution of general polynomial programs. The problem is first transformed into a reversed posynomial program. The procedure, which is a combination of a previously developed branch-and-bound method and of a well-known cutting plane algorithm, only requires the solution of linear subproblems.     

Profiling eicosanoids and phospholipids using LC-MS/MS: principles and recent applications

Eicosanoids are potent lipid mediators involved in numerous physiological and pathophysiological processes. Precursors are polyunsaturated fatty acids liberated from membrane phospholipids. Thus, profiling and quantification of these molecules has gained a lot of attention during last years. Eicosanoids and phospholipids are commonly profiled by LC-MS/MSbecause this technique allows accurate quantification within acceptable run-times. This article therefore focuses on liquid chromatography and the ESI-MS/MS analysis of proinflammatory lipid mediators, particularly arachidonic acid (C20:4) derived eicosanoids and their precursors phospholipids. Recent analytical developments for quantification of these compounds are highlighted and analytical challenges are discussed. Furthermore, applications such as the use of these molecules as biomarkers are presented.     

Partial regularity at the first singular time for hypersurfaces evolving by mean curvature

In this paper, we consider smooth, properly immersed hypersurfaces evolving by mean curvature in some open subset of   $\mathbb R ^{n+1}$ on a time interval $(0, t_0)$ . We prove that $p$ -integrability with $p\ge 2$ for the second fundamental form of these hypersurfaces in some space–time region $B_R(y)\times (0, t_0)$ implies that the $\mathcal H ^{n+2-p}$ -measure of the first singular set vanishes inside $B_R(y)$ . For $p=2$ and $n=2$ , this was established by Han and Sun. Our result furthermore generalizes previous work of Xu, Ye and Zhao and of Le and Sesum for $p\ge n+2$ , in which case the singular set was shown to be empty. By a theorem of Ilmanen, our integrability condition is satisfied for $p=2$ and $n=2\,$ if the initial surface has finite genus. Thus, the first singular set has zero $\mathcal H ^2$ -measure in this case. This is the conclusion of Brakke’s main regularity theorem for the special case of surfaces, but derived without having to impose the area continuity and unit density hypothesis. It follows from recent work of Head and of Huisken and Sinestrari that for the flow of closed, $k$ -convex hypersurfaces, that is hypersurfaces whose sum of the smallest $k$ principal curvatures is positive, our integrability criterion holds with exponent $p=n+3-k-\alpha $ for all small $\alpha >0$ as long as $1\le k\le n-1$ . Therefore, the first singular set of such solutions is at most $(k-1)$ -dimensional, which is an optimal estimate in view of some explicit examples.     

Solving nonlinear principal-agent problems using bilevel programming

While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem. The principal must maximize expected utility subject to the agent’s participation and incentive compatibility constraints. Linearity of performance measures is often assumed and the Linear, Exponential, Normal (LEN) model is often used to deal with this complexity. These assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent. In this paper we show how to numerically solve principal-agent problems with nonlinear contracts. In our procedure, we deal directly with the agent’s incentive compatibility constraint. We illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a LEN model. We also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts. A principal-agent problem is a special instance of a bilevel nonlinear programming problem. We show how to solve principal-agent problems by solving bilevel programming problems using the ellipsoid algorithm. The approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort.