Finding minimal spanning trees in a euclidean coordinate space

The minimal spanning tree problem of a point set in ak-dimensional Euclidean space is considered and a new version of the multifragmentMST-algorithm of Bentley and Friedman is given. The minimal spanning tree is found by repeatedly joining the minimal subtree with the closest subtree. Ak-d tree is used for choosing the connecting edges. Computation time of the algorithm depends on the configuration of the point set: for normally distributed random points the algorithm is very fast. Two extreme cases demandingO(n logn) andO(n ²) operations,n being the cardinality of the point set, are also given.     

Identification of some nerve agent homologues and dialkyl methylphosphonates by gas chromatography/Fourier transform infrared spectrometry

GC-FTIR spectra of 55 nerve agent homologues and dialkyl methylphosphonates have been analyzed. Infrared spectral library searches together with retention index searches have been used for identification of nerve agent homologues and dialkyl methylphosphonates.     

Planar chromatographic analysis and quantification of short-lived radioactive metabolites from microdialysis fractions

A sensitive radiochromatographic method for the quantitative determination of compounds labelled with short-lived beta-emitting radionuclides in microdialysates is described. The method is well suited for microdialysis (MD) samples, which have small volumes and low concentrations of compounds. An 18F-labelled (beta+; T(1/2)=109.8 min) radiopharmaceutical, (1R,2S)-4-[18F]fluorometaraminol (FMR), was injected intravenously into rats, and microdialysis fractions were then collected from the blood at 15 min intervals. Fractions were analyzed for FMR and its radioactive metabolites by planar chromatography combined with digital photostimulated luminescence autoradiography. The lowest detectable 18F-radioactivity was 0.24 Bq/application and the limit of quantification was 0.31 Bq/application with 4-16 h exposure. The method was found to be highly sensitive and linear in the range of 0.1 Bq-2 kBq. This method thus allows the quantification of beta-emitting radiopharmaceuticals in sequential microdialysis fractions with good time-resolution.     

Electron ionization mass spectra and tautomerism of 2-phenacylpyridines

The electron ionization mass spectra of 2-phenacylpyridine (ketimine form) and its 13 derivatives substituted in the benzene ring (1an: a R = H, b 3-Me, c 4-Me, d 4-NH(2), e 3-F, f 4-F, g 4-OMe, h 4-Cl,i 4-N(CH(3))(2),j 4-NO(2), k 4-CF(3), l 4-N(CH(2))(4), m 4- Br, n 3-Br) were recorded at 70 eV to determine the fragmentation routes and to screen the presence of their enolimine tautomers, (Z-)-2-(2-hydroxy-2-phenylvinyl)pyridines in the gas phase. The total ion currents (TIC) of the ions [MH](+), [MHCO](+), 2-PyCH(2)O(+), and RC(6)H(4)CO(+) (= ArCO(+) ) showed a fair or good correlation with the Hammett s constants (R = 0.859, 0.876, 0.912, and 0.926, respectively). The relative abundances (RA) of both the [MCO](+.) and the [MHCO](+) ion increased with the decreasing electron donating ability of the substituents and also correlated relatively well with the Hammett constants (R = 0.834 and 0.907, respectively). These observations, in comparison to the NMR results, show that the relative contribution of the ketimine tautomer also increases in the gas phase with the increasing electron donating ability of the phenyl substituent, i.e. the TIC of the ArCO(+) ion decreases whereas that of [MH](+) ion increases.     

Novel water-soluble quaternary piperazine derivatives of chitosan: synthesis and characterization

Novel synthesis methods for the preparation of quaternary piperazine derivatives of chitosan were developed. Quaternary ammonium moiety can be selectively inserted into either one or both of the piperazine nitrogens, yielding structurally uniform chitosan derivative structures. Water-soluble end products were thoroughly characterized with FT-IR, 1H NMR, 13C NMR and 2D 1H-13C HSQC NMR. The molecular weights of the end products were determined by GPC with triple detection.     

A three-dimensional backward-wave network matched with free space

A backward-wave slab based on a capacitively and inductively loaded three-dimensional transmission-line network is designed in such a way that impedance-matching with free space is obtained. To enable field propagation from free space to the network and vice versa, the use of a transition layer is proposed. Matching of the designed network with free space and negative refraction occurring at the slab interfaces are confirmed with full-wave simulations.     

Characteristics of multivariate distributions and the invariant coordinate system

We consider a semiparametric multivariate location–scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main example. The four functionals yield in a natural way the corresponding skewness, kurtosis and unmixing matrix functionals. Affine transformation based on the unmixing matrix transforms the variable to an invariant coordinate system. The limiting properties of the skewness, kurtosis, and unmixing matrix estimates are derived under general conditions. We discuss related statistical inference problems, the role of the sample statistics in testing for normality and ellipticity, and connections to invariant coordinate selection and independent component analysis.     

Boundary Accessibility of a Domain Quasiconformally Equivalent to a Ball

A boundary point of a domain D in Rⁿ is said to be broadly accessibleif it ‘almost lies’ on the boundary of a round ballcontained in D. If f is a quasiconformal mapping of the unitball Bⁿ onto D, then it is shown that broadly accessible boundarypoints on D correspond under f to a set of full measure on Bⁿ.2000 Mathematics Subject Classification 30C65.