A fast $$(2 + \frac{2}{7})$$ ( 2 + 2 7 ) -approximation algorithm for capacitated cycle covering

Mathematical Programming - We consider the capacitated cycle covering problem: given an undirected, complete graph G with metric edge lengths and demands on the vertices, we want to cover the...     

Optimal radius of convergence of interpolatory iterations for operator equations

The convergence of the class of direct interpolatory iterationsI _n for a simple zero of a non-linear operatorF in a Banach space of finite or infinite dimension is studied.A general convergence result is established and used to show that ifF is entire the radius of convergence goes to infinity withn while ifF is analytic in a ball of radiusR the radius of convergence increases to at leastR/2 withn.The research was supported in part by the National Science Foundation under Grant MCS 75-222-55 and the office of Naval Research under Contract N00014-76-C-0370, NR 044-422.     

Trends in single-cell analysis by use of ICP-MS

The analysis of single cells is a growing research field in many disciplines such as toxicology, medical diagnosis, drug and cancer research or metallomics, and different methods based on microscopic, mass spectrometric, and spectroscopic techniques are under investigation. This review focuses on the most recent trends in which inductively coupled plasma mass spectrometry (ICP-MS) and ICP optical emission spectrometry (ICP-OES) are applied for single-cell analysis using metal atoms being intrinsically present in cells, taken up by cells (e.g., nanoparticles), or which are artificially bound to a cell. For the latter, especially element tagged antibodies are of high interest and are discussed in the review. The application of different sample introduction systems for liquid analysis (pneumatic nebulization, droplet generation) and elemental imaging by laser ablation ICP-MS (LA-ICP-MS) of single cells are highlighted. Because of the high complexity of biological systems and for a better understanding of processes and dynamics of biologically or medically relevant cells, the authors discuss the idea of “multimodal spectroscopies.”     

Über Dicarbonylderivate von Phenolen

Ohne ZusammenfassungAls I. Mitteilung zählen wir die Arbeit: Dialdehyde des Phloroglucins und seiner Homologen in Ber. dtsch. chem. Ges.75, 29 (1942).     

Ueber die Zusammensetzung des Cacao?les

Ohne Zusammenfassung     

Aetherische Oele

Ohne Zusammenfassung     

A three-stage variable-shift iteration for polynomial zeros and its relation to generalized rayleigh iteration

Summary We introduce a new three-stage process for calculating the zeros of a polynomial with complex coefficients. The algorithm is similar in spirit to the two stage algorithms studied by Traub in a series of papers. We prove that the mathematical algorithm always converges and show that the rate of convergence of the third stage is faster than second order. To obtain additional insight we recast the problem and algorithm into matrix form. The third stage is inverse iteration with the companion matrix, followed by generalized Rayleigh iteration.This work was supported in part by the National Science Foundation and the Office of Naval Research.