Cauchy boundary andb-incompleteness of space-time

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector field and a Riemann metricg ⁺ onM. The Cauchy boundary of the Riemann space (M, g ⁺) consists of endpoints ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.     

Observation of intense stokes and anti-stokes lines in CH4 pumped by 355 nm of a Nd:YAG laser

The stimulated Raman scattering (SRS) and four-wave mixing (FWM) processes have been studied in detail in CH₄ gas pumped by the third-harmonic of Nd:YAG laser at =355 nm. The conversion efficiency and average output energy have been measured for the various Stokes and anti-Stokes lines at different experimental conditions. The threshold input energy at various CH₄ pressures has been calculated for the unguided and capillary waveguide Raman cells. The calculated values for the capillary case have been compared with the measured values at different CH₄ pressures and the two results are in good agreement.     

Reconstructing phase space from PDE simulations

We propose the Karhunen-Loève (K-L) decomposition as a tool to analyze complex spatio-temporal structures in PDE simulations in terms of concepts from dynamical systems theory. Taking the Kuramoto-Sivashinsky equation as a model problem we discuss the K-L decomposition for 4 different values of its bifurcation parameter . We distinguish two modes of using the K-L decomposition: As an analytic and synthetic tool respectively. Using the analytic mode we find unstable fixed points and stable and unstable manifolds in a parameter regime with structurally stable homoclinic orbits (=17.75). Choosing the data for a K-L analysis carefully by restricting them to certain burst events, we can analyze a more complicated intermittent regime at =68. We establish that the spatially localized oscillations around a so called strange fixed point which are considered as fore-runners of spatially concentrated zones of turbulence are in fact created by a very specific limit cycle (=83.75) which, for =87, bifurcates into a modulated traveling wave. Using the K-L decomposition synthetically by determining an optimal Galerkin system, we present evidence that the K-L decomposition systematically destroys dissipation and leads to blow up solutions.We would like to dedicate this paper to Klaus Kirchgässner on the occasion of his 60th birthday     

Asymptotics for Euclidean minimal spanning trees on random points

Summary Asymptotic results for the Euclidean minimal spanning tree onn random vertices inR ^d can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in allR ^d. In particular we prove a conjecture of Robert Bland: the sum of thed'th powers of the edge-lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofR ^d tends to a constant asn.Whether the limit forest is in fact a single tree is a hard open problem, relating to continuum percolation.Research supported by N.S.F. Grants MCS87-11426 and MCS 90-01710Research supported in part by N.S.F. Grant DMS88-12868, A.F.O.S.R. Grant 89-0301, ARO Grant DAAL03-89-G-0092 and NSA Grant MDA-904-H-2034     

Theorems of Stein-Rosenberg type. III. The singular case

In the theory of iterative methods, the classical Stein-Rosenberg theorem can be viewed as giving the simultaneous convergence (or divergence) of the extrapolated Jacobi (JOR) matrix J_ω and the successive overrelaxation (SOR) matrix

, in the case when the Jacobi matrix J₁ is nonnegative. As has been established recently by Buoni and Varga, necessary and sufficient conditions for the simultaneous convergence (or divergence) of J_ω and

have been established which do not depend on the assumption that J₁ is nonnegative. Our aim here is to extend these results to the singular case, using the notion of semiconvergence. In particular, for a real singular matrix A with nonpositive off-diagonal entries, we find conditions (Theorem 3.4) which imply that J_ω and

simultaneously semiconverge for all ω in the real interval [0,1).     

Novel enantioselective strong cation exchangers based on sulfodipeptide selectors: evaluation for enantiomer separation of chiral bases by nonaqueous capillary electrochromatography

Strong cation exchange (SCX)-type chiral stationary phases (CSPs) based on beta-amino sulfonic acid-terminated dipeptide derivatives as chiral selectors, immobilized on thiol-modified silica particles (3.5 microm), were synthesized and applied to enantiomer separations of chiral bases by nonaqueous capillary electrochromatography (CEC). The effect of structural variations of the sulfodipeptide selectors on the separation factors alpha was investigated. These studies included variation of the acid-terminal amino sulfonic acid residue, variation of the configurations, i.e., comparison of the diastereomeric (S,S)- and (R,S)-configurations of the sulfodipeptides, and finally comparison of sulfodipeptide selectors with corresponding beta-amino sulfonic acid analogs. In general, the capillary columns (100 microm ID) packed with the new SCX-type CSPs showed enantioselectivity for an elaborated set of chiral basic drugs in CEC acting by an enantioselective cation-exchange retention mechanism. N-[N-(4-Allyloxy-3,5-dichlorobenzoyl)-leucyl]-2-amino-3,3-dimethylbutane sulfonic acid, in particular with (R,S)-configuration, turned out to be a more effective SCX-type selector than a more rigid analog based on N-[N-(4-Allyloxy-3,5-dichlorobenzoyl)-leucyl]-2-pyrrolidinemethane sulfonic acid. Both of the former diastereomers were capable to baseline-resolve the enantiomers of ca. 40% of the tested basic chiral solutes including sympathomimetics and beta-blockers, while for the latter SCX-type CSPs only 10-20% of the selected solutes afforded resolutions > 1.5.     

Synthesis and characterisation of transition metal halide complexes of the xylyl-distibine, 1,2-bis(dimethylstibanylmethyl)benzene

Complexes of the title ligand with Cu(I), Ag(I), Au(I), Pd(II), Pt(II), Rh(III), and rare examples with Ni(II) and Co(III) have been prepared and characterised by analysis, IR, UV-vis, 1H, 63Cu and 59Co NMR spectroscopy and ES+ mass spectrometry as appropriate. The structures of [Cu[1,2-C6H4(CH2SbMe2)2]2]BF4, [PtCl2[1,2-C6H4(CH2SbMe2)2]], [M[1,2-C6H4(CH2SbMe2)2]2][PF6]2 (M = Pd or Pt), and [NiI[1,2-C6H4(CH2SbMe2)2]2]ClO4 have been determined, and the varying chelate bite and conformations of the xylyl backbone in these structures are discussed. Despite the unfavourable seven-membered chelate ring and the large soft antimony donors, 1,2-C6H4(CH2SbMe2)2 proves to be a surprisingly good ligand for late transition metals in medium oxidation states.     

Photochemistry of artificial photosynthetic reaction centers in liquid crystals probed by multifrequency EPR (9.5 and 95 GHz)

Photoinduced charge separation and recombination in a carotenoid-porphyrin-fullerene triad C-P-C(60)(1) have been followed by multifrequency time-resolved electron paramagnetic resonance (TREPR) at intermediate magnetic field and microwave frequency (X-band) and high field and frequency (W-band). The electron-transfer process has been characterized in the different phases of two uniaxial liquid crystals (E-7 and ZLI-1167). The triad undergoes photoinduced electron transfer, with the generation of a long-lived charge-separated state, and charge recombination to the triplet state, localized in the carotene moiety, mimicking different aspects of the photosynthetic electron-transfer process. Both the photoinduced spin-correlated radical pair and the spin-polarized recombination triplet are observed starting from the crystalline up to the isotropic phase of the liquid crystals. The W-band TREPR radical pair spectrum has allowed unambiguous assignment of the spin-correlated radical pair spectrum to the charge-separated state C(.+)-P-C(60)(.-). The magnetic interaction parameters have been evaluated by simulation of the spin-polarized radical pair spectrum and the spin-selective recombination rates have been derived from the time dependence of the spectrum. The weak exchange interaction parameter (J = +0.5 +/- 0.2 G) provides a direct measure of the dominant electronic coupling matrix element V between the C(.+)-P-C(60)(.-) radical pair state and the recombination triplet state (3)C-P-C(60). The kinetic parameters have been analyzed in terms of the effect of the liquid crystal medium on the electron-transfer process. Effects of orientation of the molecular triad in the liquid crystal are evidenced by simulations of the carotenoid triplet state EPR spectra at different orientations of the external magnetic field with respect to the director of the mesophase. The order parameter (S = 0.5 +/- 0.05) has been evaluated.     

Two new standard reference materials for the determination of drugs of abuse in human hair

Two new standard reference materials (SRM) for drugs of abuse in human hair have been developed. SRM 2379 consists of hair spiked with cocaine, benzoylecgonine, cocaethylene, phencyclidine, amphetamine, and methamphetamine. SRM 2380 consists of hair spiked with codeine, morphine, monoacetylmorphine, and tetrahydrocannabinol (THC). The SRMs were prepared by soaking the hair in a solution of the target analytes in water-dimethylsulfoxide. The concentration of each analyte was determined using two methods, one based upon gas chromatography/mass spectrometry (GC/MS) and one based upon liquid chromatography/mass spectrometry (LC/MS). Both methods used 0.1 M HCl for extraction of all the analytes from the hair, except for THC, which was extracted with 1 M NaOH. For isolation of the analytes from the extracts, the GC/MS-based methods used different clean-up procedures from those used for the LC/MS-based methods. The results from the two methods were in good agreement with mean differences for the analytes ranging from 4% to 16%. These materials will enable laboratories performing analyses of hair for drugs of abuse to test the accuracy of their methods.