Why define atoms in real space?

The physics of a system is determined by a variation of the action integral, i.e., by a variation of the space–time volume integral of the Lagrange function. If one demands that the properties of an atom in a molecule be derived from physics, the atom must generate its own space–time volume, requiring that its boundaries be defined in real space. The variations in the action are related to the actions of generators of infinitesimal unitary transformations. In the general case, the action integral is altered by generators acting in both the spacelike and timelike surface bounding the space–time volume, whereas for a total isolated system, the physics is totally determined by their action in just the spacelike surfaces at the two time endpoints. It is shown and illustrated for a one-dimensional system that the definition of an atom corresponds to the possibility of choosing a subsystem in such a way that the contributions to the change in action resulting from the evolution in time of its spatial boundaries vanishes identically. The properties of these subsystems and of the total system of which they are a part are, therefore, determined by one and the same action principle. This choice of subsystem corresponds to the possibility of augmenting the Lagrange function by the divergence of the gradient of the electron density a step that, while leaving the equations of motion unchanged, modifies the generating operators in the required manner. © 1994 John Wiley & Sons, Inc.     

The external magnetic field dependence of RF splitting of57Fe hyperfine lines. NMR + Mössbauer double resonance experiment

We present the results of an experimental investigation of a RF splitting of⁵⁷Fe hyperfine lines in the regime of NMR and Mössbauer double resonance. The experiments have been performed as a function of RF field intensity and static magnetic field magnitude. The intensity of the RF components and the separation between them are extremely sensitive to the frequency and amplitude of the RF magnetic field. The RF splitting of hyperfine lines is inversely proportional to the strength of the static magnetic field.     

Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.     

A comparison of steady-state evoked potentials to modulated tones in awake and sleeping humans.

Steady-state evoked potential responses were measured to binaural amplitude-modulated (AM) and combined amplitude- and frequency-modulated (AM/FM) tones. For awake subjects, AM/FM tones produced larger amplitude responses than did AM tones. Awake and sleeping responses to 30-dB HL AM/FM tones were compared. Response amplitudes were lower during sleep and the extent to which they differed from awake amplitudes was dependent on both carrier and modulation frequencies. Background EEG noise at the stimulus modulation frequency was also reduced during sleep and varied with modulation frequency. A detection efficiency function was used to indicate the modulation frequencies likely to be most suitable for electrical estimation of behavioral threshold. In awake subjects, for all carrier frequencies tested, detection efficiency was highest at a modulation frequency of 45 Hz. In sleeping subjects, the modulation frequency regions of highest efficiency varied with carrier frequency. For carrier frequencies of 250 Hz, 500 Hz, and 1 kHz, the highest efficiencies were found in two modulation frequency regions centered on 45 and 90 Hz. For 2 and 4 kHz, the highest efficiencies were at modulation frequencies above 70 Hz. Sleep stage affected both response amplitude and background EEG noise in a manner that depended on modulation frequency. The results of this study suggest that, for sleeping subjects, modulation frequencies above 70 Hz may be best when using steady-state potentials for hearing threshold estimation.     

Diffeomorphism finiteness for manifolds with ricci curvature andL n/2-norm of curvature bounded

Partially supported by NSF Grants.     

Distribution of magnetization in an easy-plane ferromagnet

Physics and Mathematics Division with Computational Center of the Bashkir Branch of the USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 80, No. 3, pp. 470–473, September, 1989.     

Stability testing in an integrated scheme

ISO Guide 35 deals with RM stability issues and scrutinizes the evaluation of stability testing results under the assumption that either there is no trend at all (a rather rare situation), or any observed deterministic change is insignificant and thus can be neglected. However, market demands for reliable reference materials are obviously not limited to stable or at least seemingly stable materials. In many analytical applications, analytes and measurands under consideration are known, or at least suspected, to be unstable on time scales that may vary widely from measurand to measurand. The Federal Institute for Materials Research and Testing (BAM) has developed (and successfully uses) an integrated approach in its certification practice. The approach is based on an initial stability study and subsequent post-certification monitoring. Data evaluation is model-based and takes advantage of all information collected in the stability testing scheme(s). It thus allows one to deal with any kind of instability observed, to assess limiting time intervals at any stress condition in the range tested, to estimate a final expiry date for materials with detected instabilities or the maximum admissible re-testing interval for seemingly stable materials, and to assess maximum admissible stress loads during delivery of the material to the customer. The article describes (and exemplifies) typical study layout, the model selection, and the integrated data assessment.     

Characterization of low molecular weight hydrocarbon oligomers by laser desorption/ionization time-of-flight mass spectrometry using a solvent-free sample preparation method.

A new solvent-free sample preparation method using silver trifluoroacetate (AgTFA) was developed for the analysis of low molecular weight paraffins and microcrystalline waxes by laser desorption/ionization time-of-flight mass spectrometry (LDI-TOFMS). Experiments show that spectral quality can be enhanced by dispersing AgTFA directly in liquid paraffins without the use of additional solvents. This preparation mixture is applied directly to the MALDI probe. Solid waxes could be examined by melting prior to analysis. The method also provides sufficiently reproducible spectra that peak area ratios between mono- and bicyclic alkane peaks indicated variations in the cycloalkane content of paraffin samples. Dehydrogenation of hydrocarbons observed during the desorption/ionization process was studied by analysis of alkane standards.