Three-dimensional packings with rotations

We present approximation algorithms for the three-dimensional strip packing problem, and the three-dimensional bin packing problem. We consider orthogonal packings where 90 degrees rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 2.64, and 4.89, respectively. These algorithms are for the more general case in which the bounded dimensions of the bin given in the input are not necessarily equal (that is, we consider bins for which the length. the width and the height are not necessarily equal). Moreover, we show that these problems-in the general version-are as hard to approximate as the corresponding oriented version. (C) 2009 Elsevier Ltd. All rights reserved.

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

Simultaneous analysis of five antidepressant drugs using direct injection of biofluids in a capillary restricted-access media-liquid chromatography-tandem mass spectrometry system

Direct analysis, with minimal sample pretreatment, of antidepressant drugs, fluoxetine, imipramine, desipramine, amitriptyline, and nortriptyline in biofluids was developed with a total run time of 8 min. The setup consists of two HPLC pumps, injection valve, capillary RAM-ADS-C18 pre-column and a capillary analytical C 18 column connected by means of a six-port valve in backflush mode. Detection was performed with ESI-MS/MS and only 1 mu m of sample was injected. Validation was adequately carried out using FLU-d(5) as internal standard. Calibration curves were constructed under a linear range of 1-250 ng mL(-1) in plasma, being the limit of quantification (LOQ), determined as 1 ng mL(-1), for all the analytes. With the described approach it was possible to reach a quantified mass sensitivity of 0.3 pg for each analyte (equivalent to 1.1-1.3 fmol), translating to a lower sample consumption (in the order of 103 less sample than using conventional methods). (C) 2008 Elsevier B.V. All rights reserved.