List multicoloring problems involving the k‐fold Hall numbers

We show that the four‐cycle has a k‐fold list coloring if the lists of colors available at the vertices satisfy the necessary Hall's condition, and if each list has length at least ?5k/3?; furthermore, the same is not true with shorter list lengths. In terms of h^(k)(G), the k ‐fold Hall number of a graph G, this result is stated as h^(k)(C₄)=2k??k/3?. For longer cycles it is known that h^(k)(C_n)=2k, for n odd, and 2k??k/(n?1)?≤h^(k)(C_n)≤2k, for n even. Here we show the lower bound for n even, and conjecture that this is the right value (just as for C₄). We prove that if G is the diamond (a four‐cycle with a diagonal), then h^(k)(G)=2k. Combining these results with those published earlier we obtain a characterization of graphs G with h^(k)(G)=k. As a tool in the proofs we obtain and apply an elementary generalization of the classical Hall–Rado–Halmos–Vaughan theorem on pairwise disjoint subset representatives with prescribed cardinalities. © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 16–34, 2010.     

Neutron scattering from liquid helium three at elevated pressure

The inelastic neutron scattering from liquid³He at 0.7 K has been measured at the saturated vapour pressure, 10 bars, and 20 bars pressure, using the IN5 time of flight spectrometer at the Institut Laue-Langevin. Results were obtained for wavevector transfers,Q, in the region, 1.1<Q<2.4 Å^–1, and for energy transfers,, up to 27 K. There was no indication of a well defined zero sound mode even at an applied pressure of 20 bars. At low wavevector transfers, increasing the pressure increases the intensity at low energy transfers (<10 K), while at higher energy transfers, a decrease in intensity is observed with increasing pressure. At higher wavevector transfers, (Q1.9 Å^–1, the position of the roton minimum in superfluid⁴He), the scattering is a broad distribution, whose peak frequency decreases by more than a factor of 2, on increasing the pressure from S.V.P. to 20 bars. This is a considerably larger change in energy than is expected from previous estimates of the pressure dependence of the effective mass of³He.     

A note on shape and stability calculations in heavy and superheavy nuclei

Attention is focused onto the spurious state contributions inherent in existing equilibrium shape and fission half-life assessments of heavy and superheavy nuclei. The results indicate that compensation for such effects is essential if these calculations are to be considered reliable.     

Magnetic dipole response in rare earth nuclei

Experimental observations in certain rare earth nuclei have established the presence of sizeable B(M1) strength of two peak structure lying in the 5–10 MeV region. The character of the states concerned, studied within a self-consistent Random Phase Approximation using Skyrme forces, are identified to be that of proton and neutron giant spin-flip resonances. Received: 14 July 1997 / Revised version: 20 October 1997     

13C‐15N Connectivity networks via unsymmetrical indirect covariance processing of 1H‐13C HSQC and 1H‐15N IMPEACH spectra

Long‐range ¹H‐¹⁵N heteronuclear shift correlation methods at natural abundance to facilitate the elucidation of small molecule structures have assumed a role of growing importance over the past decade. Recently, there has also been a high level of interest in the exploration of indirect covariance NMR methods. From two coherence transfer experiments, A→B and A→C, it is possible to indirectly determine B?C. We have shown that unsymmetrical indirect covariance methods can be employed to indirectly determine several types of hyphenated 2D NMR data from higher sensitivity experiments. Examples include the calculation of hyphenated 2D NMR spectra such as 2D GHSQC‐COSY and GHSQC‐NOESY from the discrete component 2D NMR experiments. We now wish to report the further extension of unsymmetrical indirect covariance NMR methods for the combination of ¹H‐¹³C GHSQC and ¹H‐¹⁵N longrange (GHMBC, IMPEACH‐MBC, CIGAR‐HMBC, etc.) heteronuclear chemical shift correlation spectra to establish ¹³C‐¹⁵N correlation pathways.     

Generalized Viscoelastic 1-DOF Deterministic Nonlinear Oscillators

The theory of deterministic generalized viscoelastic linear and nonlinear 1-D oscillators is formulated and evaluated. Examples of viscoelastic Duffing, Mathieu, Rayleigh, Roberts and van der Pol oscillators and pendulum responses are investigated. Material behavior as well as additional effects of structural damping on oscillator performance are also considered. Computational protocols are developed and their results are discussed to determine the influence of viscoelastic and structural (Coulomb friction) damping on oscillator motion. Illustrative examples show that the inclusion of linear or nonlinear viscoelastic material properties significantly affects oscillator responses as related to amplitudes, phase shifts and energy loses when compared to equivalent elastic ones.     

Estimation of signal coherence threshold and concealed spectral lines applied to detection of turbofan engine combustion noise

Combustion noise from turbofan engines has become important, as the noise from sources like the fan and jet are reduced. An aligned and un-aligned coherence technique has been developed to determine a threshold level for the coherence and thereby help to separate the coherent combustion noise source from other noise sources measured with far-field microphones. This method is compared with a statistics based coherence threshold estimation method. In addition, the un-aligned coherence procedure at the same time also reveals periodicities, spectral lines, and undamped sinusoids hidden by broadband turbofan engine noise. In calculating the coherence threshold using a statistical method, one may use either the number of independent records or a larger number corresponding to the number of overlapped records used to create the average. Using data from a turbofan engine and a simulation this paper shows that applying the Fisher z-transform to the un-aligned coherence can aid in making the proper selection of samples and produce a reasonable statistics based coherence threshold. Examples are presented showing that the underlying tonal and coherent broad band structure which is buried under random broadband noise and jet noise can be determined. The method also shows the possible presence of indirect combustion noise.     

Rapid drug detection in oral samples by porous silicon assisted laser desorption/ionization mass spectrometry

The demand for analysis of oral fluid for illicit drugs has arisen with the increased adoption of roadside testing, particularly in countries where changes in legislation allow random roadside testing of drivers for the presence of a palette of illicit drugs such as methamphetamine (MA), 3,4‐methylenedioxymethamphetamine (MDMA) and Δ⁹‐tetrahydrocannabinol (THC). Oral samples are currently tested for such drugs at the roadside using an immunoassay‐based commercial test kit. Positive roadside tests are sent for confirmatory laboratory analysis, traditionally by means of gas chromatography/mass spectrometry (GC/MS). We present here an alternative rapid analysis technique, porous silicon assisted laser desorption/ionization time‐of‐flight mass spectrometry (pSi LDI‐MS), for the high‐throughput analysis of oral fluids. This technique alleviates the need for sample derivatization, requires only sub‐microliter sample volumes and allows fast analysis (of the order of seconds). In this study, the application of the technique is demonstrated with real samples from actual roadside testing. The analysis of oral samples resulted in detection of MA and MDMA with no extraction and analysis of THC after ethyl acetate extraction. We propose that, subject to miniaturization of a suitable mass spectrometer, this technique is well suited to underpin the deployment of oral fluid testing in the clinic, workplace and on the roadside. Copyright © 2009 John Wiley & Sons, Ltd.