Painlevé analysis and hamiltonian structure of a new space-dependent KdV equation

We deduce the Lax pair for a new space-dependent KdV equation, , via the technique of Painlevé analysis. From it, infinitely many conservation laws are deduced and the symplectic structure is obtained.     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Diffusion coefficient measurement in a microfluidic analyzer using dual-beam microscale-refractive index gradient detection. Application to on-chip molecular size determination

We report a microchip-based detection scheme to determine the diffusion coefficient and molecular mass (to the extent correlated to molecular size) of analytes of interest. The device works by simultaneously measuring the refractive index gradient (RIG) between adjacent laminar flows at two different positions along a microchannel. The device, referred to as a microscale molecular mass sensor (micro-MMS), takes advantage of laminar flow conditions where the mixing of two streams occurs essentially by diffusion across the boundary between the two streams. Two flows merge on the microchip, one containing solvent only, referred to as the mobile phase stream and one which contains the analyte(s) of interest in the solvent, i.e. the sample stream. As these two streams merge and flow parallel to each other down the microchannel a RIG is created by the concentration gradient. The RIG is further influenced by analyte diffusion from the sample stream into the mobile phase stream. Measuring the RIG at a position close to the merging point (upstream signal) and simultaneously a selected distance further down the microchannel (downstream signal) provides real-time data related to the extent a given analyte has diffused, which can be readily correlated to analyte molecular mass by taking the ratio of the downstream-to-upstream signals. For the dual-beam RIG measurements, a diode laser output is coupled to a single mode fiber optic splitter with two output fibers. Light from each fiber passes through a graded refractive index (GRIN) lens forming a collimated beam that then passes through the microchannel and then on to a position sensitive detector (PSD). The RIG at both detection positions deflects the two collimated probe beams. The deflection angle of each beam is then measured on two separate PSDs. The micro-MMS was evaluated using polyethylene glycols (PEGs), sugars, and as a detector for size-exclusion chromatography (SEC). Peak purity can be readily identified using the micro-MMS with SEC. The limit of detection was 0.9 ppm (PEG at 11 840 g/mol) at the upstream detection position corresponding to a RI limit of detection (LOD) (3sigma) of 7-10(-8) RI. The pathlength for the RIG measurement was 200 microm and the angular LOD was 0.23 micro(rad) with a detection volume of 8 nl at both positions. The average molecular mass resolution was 9% (relative standard deviation) for a series of PEGs ranging in molecular mass from 106 to 22 800 g/mol. With this excellent mass resolution, small molecules such as monosaccharides, disaccharides, and so on, are readily distinguished. The sensor is demonstrated to readily determine unknown diffusion coefficients.     

Application of the least-squares method in the matrix form: simultaneous spectrophotometric determination of rifampicin and isoniazid in binary pharmaceutical formulations

A least-squares method in the matrix form is described for the simultaneous determination of rifampicin and isoniazid in a mixture. The method allows the rapid analysis of binary pharmaceutical formulations with minimum error. The concentration of each component in the mixture has been determined spectrophotometrically by measuring the absorbance of the mixture at 5-nm intervals from 230 to 290 nm. To calculate the matrix of the proportionality constant a standard mixture was used for each component. All data analyses were performed on a personal computer.