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  • 1
    Electronic Resource
    Electronic Resource
    Crystal and molecular structure of 2,3-dihydro-.alpha.,.beta.,.gamma.,.delta.-tetraphenylporphyrinatopyridinezinc(II)-benzene solvate (1977)
    s.l. : American Chemical Society
    Journal of the American Chemical Society 99 (1977), S. 6918-6923 
    Details
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ja00463a024
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  • 2
    Electronic Resource
    Electronic Resource
    The gamma distribution as a model for temperature dissipation in intermittent turbulence (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 105-110 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Following a recent theory suggesting that the local average rate of energy dissipation εr follows statistics predicted by the gamma distribution rather than the lognormal distribution, the gamma distribution is further examined here as a model for the local temperature dissipation rate χr. Comparisons of measured moments 〈χmr〉 with those predicted by both the gamma and lognormal distributions clearly favor the gamma model for predicting the power-law exponents of r/L. Based on gamma models for both εr and χr, the bivariate gamma distribution is then examined as a possible model for the joint distribution of dissipation rates εr and χr. In particular, the bivariate gamma model and the bivariate lognormal model are both compared with the inertial-range behavior of measured temperature structure functions up to order 12. Some additional comparisons of these models are also made with data involving mixed moments of the velocity and temperature structure functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857685
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  • 3
    Electronic Resource
    Electronic Resource
    A statistical theory for the distribution of energy dissipation in intermittent turbulence (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 999-1006 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A new statistical theory involving the gamma distribution is presented for the local average rate of dissipation εr. The gamma distribution for εr leads to results for the high-order moments of the velocity structure function that lie between those predicted by the lognormal model and β model and closely follow those of the multifractal model. Comparisons of results predicted by the gamma distribution are made with previously published experimental data, showing excellent agreement. Based on the gamma distribution for εr, the one-dimensional K distribution is developed as a plausible model for the distribution of energy dissipation ε. Some laboratory measurements of velocity fluctuations and certain derived quantities from a modified airjet are also discussed. A good agreement is found by making comparisons of the measured cumulative probability distribution of the squared time derivative of the streamwise velocity component with that predicted by this new model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857412
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  • 4
    Electronic Resource
    Electronic Resource
    The squared power method to fit a plane to a set of points (1976)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 32 (1976), S. 504-506 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The 'power method' provides a computationally easy method for the determination of the best plane through a set of points. By repeatedly taking squares, one rapidly obtains the maximum eigenvalue and corresponding eigenvector of the inertia tensor. The result is the least-squares result when the points have independent, isotropic weights.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739476001095
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  • 5
    Electronic Resource
    Electronic Resource
    A matrix formulation for choosing starting sets in direct methods (1979)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 35 (1979), S. 695-696 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method for finding the strongest starting set of reflections for multisolution direct methods is proposed and compared with the Convergence Method of Germain, Main & Woolfson [Acta Cryst. (1970), B26, 274-285].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739479001595
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  • 6
    Electronic Resource
    Electronic Resource
    A perturbation stable cell comparison technique (1980)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 248-252 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A modified method of describing lattices (or, equivalently, unit cells) is described. In the proposed parameterization, there is no discontinuous measure of agreement such as is found in studies of reduced cells. Although the Niggli reduced cell is uniquely defined for every lattice, the angles of the reduced cell may vary wildly with minor lattice distortions. It is proposed that lattices be described by the sets of seven parameters consisting of reduced-cell edge lengths, the lengths of edges of the reduced cell of the reciprocal lattice, and the reduced-cell volume.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739480000496
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  • 7
    Electronic Resource
    Electronic Resource
    Lattices and reduced cells as points in 6-space and selection of Bravais lattice type by projections (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 1009-1018 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A characterization of crystallographic unit cells as vectors in a Euclidean six-dimensional space (E6 in the usual mathematical notation; here termed G6) is introduced, in which the non-triclinic Bravais lattice types form one-, two-, three- and four-dimensional linear subspaces. This formalism makes the determination of the 'best' Bravais lattice (or lattices) for a particular experimentally determined cell a process of determining Euclidean distances in G6 from the cell to its projections into the subspaces of the lattice types. The elements of vectors in the space are drawn from the Niggli matrix with the unsymmetrical elements doubled. A cell is first reduced and all its nearly Buerger-reduced cells are used in the distance determinations. Thus the smallest distance provides information about both the propriety of the lattice type selection and the instability of the cell reduction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767388006427
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  • 8
    Electronic Resource
    Electronic Resource
    Bravais lattice invariants (1995)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 51 (1995), S. 413-416 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Invariants are those properties by which objects (in chemistry, physics, mathematics etc.) are commonly identified. They remove sensitivity to presentation and allow the intrinsic properties of the object to be seen. Invariants used for unit-cell comparison and for Bravais-lattice identification are reviewed, and proposals are made for possible directions of future research. The results of an exhaustive search for polynomial invariants of the components of the metric tensor through degree 12 are that polynomials in the volume squared are the only non-trivial such invariants.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767394009839
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  • 9
    Electronic Resource
    Electronic Resource
    Statistics of derived intensities (1975)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 245-249 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The variance of diffractometer-collected diffraction intensities is discussed in terms of instrumental instability and uncertainties in the parameter used to bring the intensities to a common scale. It is shown that the inconsistent and/or divergent behavior of the reflections used as standards contributes in a major way to the uncertainty in the scaling parameter and can often account for the largest portion of the variance in excess of the Poisson contribution for reflections with large intensities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739475000496
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  • 10
    Electronic Resource
    Electronic Resource
    Structure of dicyclopenta[ef,kl]heptalene (azupyrene) (1990)
    Oxford [u.a.] : International Union of Crystallography (IUCr)
    Acta crystallographica 46 (1990), S. 439-441 
    Details
    ISSN: 1600-5759
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108270189007857
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