Sommerfeld-Watson representation for double-spectral functions

We demonstrate the existence of a solution of the nonlinear pion-pion equations that incorporate crossing symmetry, unitarity andl-plane meromorphy. In particular, we show how to guarantee the boundedness of the partial waves ass, even when some Regge trajectories rise beyond unity.     

Method development for simultaneous analysis of HBCD,TBBPA, and dimethyl-TBBPA in marine biota from Greenland and the Faroe Islands

The brominated flame retardants hexabromocyclododecane (HBCD) and tetrabromobisphenol A (TBBPA) are high-production-volume chemicals. In recent years, their presence has been reported in sediment and biota from the marine environment. In this study, an analytical method was developed for the simultaneous determination of HBCD, TBBPA, and the possible metabolite dimethyl-TBBPA. The method was applied in a preliminary screening of egg, liver, and adipose tissue of marine biota from Greenland and the Faroe Islands. α-HBCD was detected in 35 of 36 analysed samples from the Arctic, indicating a ubiquitous presence of α-HBCD in the environment. β- and γ-HBCD were found in 10 and 14 samples, respectively. TBBPA and dimethyl-TBBPA were not detected in any of the samples indicating limited or no transport of these compounds to remote areas.     

Bayesian ensemble approach to error estimation of interatomic potentials

Using a Bayesian approach a general method is developed to assess error bars on predictions made by models fitted to data. The error bars are estimated from fluctuations in ensembles of models sampling the model-parameter space with a probability density set by the minimum cost. The method is applied to the development of interatomic potentials for molybdenum using various potential forms and databases based on atomic forces. The calculated error bars on elastic constants, gamma-surface energies, structural energies, and dislocation properties are shown to provide realistic estimates of the actual errors for the potentials.     

Chemometric quality control of chromatographic purity

It is common practice in chromatographic purity analysis of pharmaceutical manufacturing processes to assess the quality of peak integration combined by visual investigation of the chromatogram. This traditional method of visual chromatographic comparison is simple, but is very subjective, laborious and seldom very quantitative. For high-purity drugs it would be particularly difficult to detect the occurrence of an unknown impurity co-eluting with the target compound, which is present in excess compared to any impurity. We hypothesize that this can be achieved through Multivariate Statistical Process Control (MSPC) based on principal component analysis (PCA) modeling. In order to obtain the lowest detection limit, different chromatographic data preprocessing methods such as time alignment, baseline correction and scaling are applied. Historical high performance liquid chromatography (HPLC) chromatograms from a biopharmaceutical in-process analysis are used to build a normal operation condition (NOC) PCA model. Chromatograms added simulated 0.1% impurities with varied resolutions are exposed to the NOC model and monitored with MSPC charts. This study demonstrates that MSPC based on PCA applied on chromatographic purity analysis is a powerful tool for monitoring subtle changes in the chromatographic pattern, providing clear diagnostics of subtly deviating chromatograms. The procedure described in this study can be implemented and operated as the HPLC analysis runs according to the process analytical technology (PAT) concept aiming for real-time release.     

Dynamic TCP acknowledgment in the LogP model

When messages, which are to be sent point-to-point in a network, become available at irregular intervals, a decision must be made each time a new message becomes available as to whether it should be sent immediately or if it is better to wait for more messages and send them all together. Because of physical properties of the networks, a certain minimum amount of time must elapse in between the transmission of two packets. Thus, whereas waiting delays the transmission of the current data, sending immediately may delay the transmission of the next data to become available even more. We propose a new quality measure and derive optimal deterministic and randomized algorithms for this on-line problem.     

Two-photon photosensitized production of singlet oxygen: optical and optoacoustic characterization of absolute two-photon absorption cross sections for standard sensitizers in different solvents

Singlet molecular oxygen, O2(a1Deltag), can be produced upon resonant two-photon excitation of a photosensitizer. In the present study, two molecules that have received recent attention in studies of nonlinear organic materials were characterized for use as standard two-photon sensitizers: 2,5-dicyano-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene, CNPhVB, and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene, BrPhVB. Absolute two-photon absorption cross sections, delta, were independently determined for these molecules using two techniques that have heretofore not been applied to this problem: an optical technique (time-resolved detection of O2(a1Deltag) phosphorescence) and a nonoptical technique (a time-resolved laser-induced optoacoustic experiment). For experiments performed in toluene, a solvent commonly used for such nonlinear optical studies, appreciable absorption by the solvent itself complicates the measurements. In cyclohexane, however, delta values could be obtained without the interfering effects of solvent absorption. On the basis of these results, we discuss key aspects of the respective techniques used to quantify values of delta. The information reported herein provides some explanation for the lack of consensus that is routinely observed in published values of delta, certainly for experiments performed in aromatic solvents such as toluene and benzene.     

Efficient synthesis of [2'-18O]uridine and its incorporation into oligonucleotides: a new tool for mechanistic study of nucleotidyl transfer reactions by isotope effect analysis

Lack of sufficient quantities of isotopically labeled materials has precluded the use of heavy atom isotope effects to investigate mechanisms of nucleotidyl transfer reactions in nucleic acids. Here we achieve regioselective opening of 2,2'-cyclouridine with [(18)O2]benzoic acid/potassium hydride, allowing an efficient "one-pot" synthesis of [2'-18O]uridine in 88% yield. Conversion to the corresponding phosphoramidite enables solid-phase synthesis of [2'-(18)O] RNA substrates for isotope effect studies with nucleotidyl transferases and hydrolases.     

Resonance-behavior of non-linear one-dimensional gas vibrations analyzed by the Ritz-Galerkin method

Summary The present paper concerns an approximate analysis of damped resonance vibrations in a closed cylindrical pipe with harmonic excitation at one pipe end. Earlier experiments made by Lettau have disclosed that such vibrations may be highly non-linear and may even include shock waves travelling back and forth. The analysis is based essentially on the socalled Ritz-Galerkin method. Emphasis is put on the mechanism of the analysis rather than on a strict mathematical justification hereof. The theoretical results are in close agreement with the experimental evidence. Further a criterion for the presence and absence of shocks is derived.The present investigation was undertaken while the author, on leave from the Technical University of Denmark, was working as a Research Associate ar Stanford University in California on a Research Fellowship from International Cooperation Administration, Washington D. C. Thanks are due to all these institutions.In particular the author wishes to express his sincere thanks to Professor K. Klotter, Division of Engineering Mechanics, Stanford University, for his kind encouragement of the work and valuable criticism.     

The analytic properties of the box diagram amplitude: I

A double spectral representation of Mandelstam type is obtained for the invariant amplitude T of the binary collision process AB → CD involving scalar particles, using unitarity to evaluate the contribution to Im T from a two-particle intermediate state (EF) and making one-pole approximations to the amplitudes for the processes AB → EF, CD → EF. For the case where the masses satisfy the inequalities (m_A+m_B) ? (m_E+m_F), m_C+m_D) ? (m_E+m_F) the above approximations are shown to give the same result as that obtained from the Feynman parametrization of the amplitude arising from the box diagram. The proof proceeds by directly evaluating the box diagram amplitude and in this way we obtain a spectral representation of the amplitude for all allowed mass configurations, including cases for which there are anomalous thresholds and cases for which a double spectral representation no longer exists.