Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Theoretical study of PO and PO−

The diatomic systems, PO and PO^– are studied, using numerical Hartree-Fock (NHF) and coupled-cluster calculations. The latter employs a hybrid NHF and Slater orbital basis set. Highly accurate CCSD methods predict bond lengths accurate to <0.004 Å and frequencies to 60 cm^–1. In addition the electron affinity of PO is computed to be 0.89 eV compared to an experimental value of 1.09±0.01. Comparisons are made with SCF and MBPT(2) results for PO⁺ using conventional basis sets.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayGuggenheim Fellow     

Characterization of low-molecular weight peptides in champagne wine by liquid chromatography/tandem mass spectrometry

This paper reports the use of an on-line LC–ESI–MS/MS method for the identification and quantification of di- and tripeptides in champagne wine without laborious sample pretreatment. The identification of these compounds, in their underivatised form, is based on identical retention times and ESI–MS spectra to those of reference standards. The presence of nine dipeptides (Arg–Ile, Ile–Arg, Ile–Val, Lys–Phe, Lys–Tyr, Phe–Lys, Tyr–Gln, Tyr–Lys, Val–Ile) and the absence of two tripeptides (Phe–Arg–Arg and Lys–Met–Asn) have been evidenced in the matrix. Calibration curves for each analyte were established using Phe–Arg as internal standard. The calibration curves were linear in the concentration range 0.1–10 mg L⁻¹ with a determination coefficient, r², better than 0.992. The accuracy for the calibration standard was estimated at between 92 and 102%. This method allows high recovery and satisfies the necessary requirements with respect to accuracy, repeatability and sensitivity. The first application of this analytical method to the measurement of di- and tri-peptides in different vintages of champagne wine is reported. Compositional changes in the peptides occurred depending on the vintage.     

Inhibition of homogeneous condensation of SF6 by vibrational excitation

Vibrational excitation of SF₆ by a 10.6 μm CO₂ laser is shown to reduce lifetimes for SF₆ dimers in supersonically expended flows. A possible utility of this phenomenon in controlling condensation rates to separate isotopes is discussed, and a kinetic analysis of the expected isotopic composition of SF₆ in a supersonically expanded stream is presented.     

Prediction of the vibrational spectra of interacting water molecules

A system of computer programs has been developed to predict and interpret the infrared spectra of molecules, ions, radicals and of chemically interacting species. The frequency parameters (or force constants) and the intensity parameters (or atomic polar tensors (APTs)) are calculated using the Gaussian-76 program for $\text{ab}$$\text{initio}$ quantum mechanical calculations with a 4–31G basis set. The resultant wavenumbers and intensities have been used to predict the fundamental infrared spectra of water molecules interacting with different molecular species. The corresponding wavenumber shifts and intensity changes from the spectrum of the non-interacting water molecule are dependent upon both the geometrical orientation and the electron-donating properties of the interacting species. The intensity parameters can be further analyzed by using the charge-charge flux-overlap (CCFO) interpretation of the APTs. This interpretation is helpful in pinpointing the exact source of the perturbation that produces the intensity change. The significance is discussed of each of these CCFO terms in predicting the infrared intensities of molecules undergoing intermolecular interaction.     

The charge-charge flux-overlap model for the interpretation of atomic polar tensors and infrared intensities

The interpretation of infrared intensities using the concepts of atomic polar tensors divided according to contributions from charge-charge flux-overlap (CCFO) terms appears in general to be quite useful. Here we shall illustrate this analysis for the F and H atoms in chemically related molecules to show how their properties vary for CF, CH, OF and OH bonds as R varies in RCF, RCH and ROH molecules.     

Infrared spectrum of acetonitrile: Analysis of Coriolis resonance

The Coriolis resonance between ν₄ and ν₇ in CH₃CN and between ν₁ and ν₅, ν₃ and ν₆, and ν₄ and ν₇ in CD₃CN has been analyzed, applying the technique developed by DiLauro and Mills, to obtain the signs of [$\text{ζ}{}_{\mathrm{r,sa}}{}^{\mathrm{y}}\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$] and the ratio of $\text{?μ}\text{?Q}{}_{\mathrm{r}}$ to $\text{?μ}\text{?Q}{}_{\mathrm{s}}$ for the interacting pairs in CD₃CN. For (ν₄, ν₇) in both CH₃CN and CD₃CN, the sign of [$\text{ζ}{}_{\mathrm{r,sa}}{}^{\mathrm{y}}\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$] is found to be negative as it is also for (ν₁, ν₅) in CD₃CN. For (ν₃, ν₆) the sign of this interaction term is found to be positive. For a given definition of normal coordinates the signs of these interaction terms give the relative signs of $\text{?p}\text{?Q}{}_{\mathrm{r}}$ and $\text{?p}\text{?Q}{}_{\mathrm{sa}}$; our study also gives approximate values for the corresponding ratio [$\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)}\text{(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$]     

Analysis of native amino acids by liquid chromatography/electrospray ionization mass spectrometry: comparative study between two sources and interfaces

The analytical performances of two triple-quadrupole instruments, which differ in their atmospheric-pressure sources, were evaluated for native amino acid analysis. The Applied Biosystems/Sciex API 300 instrument was equipped with a turboIon Spray source and a curtain gas interface while the Waters/Micromass Quattro Ultima instrument was characterized by its Z-spray source. Liquid chromatography/mass spectrometry analysis of native amino acids requires volatile ion-pairing mobile phase additives (mainly perfluorinated carboxylic acids). The effects of the structure and concentration of the ion-pairing reagents as well as the organic modifier percentage on the electrospray response of amino acids were studied in detail. The most favourable chromatographic conditions depend strongly on the mass spectrometer used. Several instrumental parameters were also studied, including spray voltage, transmission lens voltages, temperature of desolvation and auxiliary gas flow rates. The results show substantial qualitative differences depending on the instrument geometry. The quantitative performances of the two triple-quadrupole mass spectrometers were evaluated in terms of limits of detection and quantification. The effects of the matrix on the analyte ionization were also examined, and the long-term stability of the electrospray performance was studied over 12 h using a mobile phase containing the perfluorinated ion-pairing reagents. The study provides information on the robustness of the MS instrument and its detection sensitivity towards native amino acid analysis. It appears that each instrument has its good and bad points since one provides higher sensitivity while another is more robust.