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  • 1
    Electronic Resource
    Electronic Resource
    Helix Lifetimes within the Conformational Transition Region. A Random Walk Model (1973)
    s.l. : American Chemical Society
    Macromolecules 6 (1973), S. 684-687 
    Details
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ma60035a008
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  • 2
    Electronic Resource
    Electronic Resource
    On controlled diffusion-limited drug release from a leaky matrix (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 5909-5913 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: How fast can drug molecules randomly escape from a polymer matrix? This important question is of both scientific and practical importance, as increasing emphasis is placed on design considerations that can be addressed only if the physics of drug release is better understood. We study this problem using high accuracy Monte Carlo computer simulations. We find that the nature of drug release depends drastically on the dimension of the matrix and is different depending on whether the matrix is a normal Euclidean space or a fractal material such as a polymer, corresponding to the fact that the basic laws of physics are quite different in a fractal environment. We also find the surprising result that drug release is the same for noninteracting particles as it is for particles with hard-core excluded volume interactions, suggesting that the nature of the matrix is more important than the nature of the interactions among the drug particles in determining drug release.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449622
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  • 3
    Electronic Resource
    Electronic Resource
    Exact random-walk models in crystallographic statistics. II. The bicentric distribution for the space group P\overline{1} (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 55-59 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An exact probability density function for the magnitude of the normalized structure factor |E| has been derived for the space group P\bar 1, taking account of the presence of one non-crystallographic center of symmetry. The function is based on the exact solution of the corresponding random-walk model and its expansion into a Fourier series. The above result is compared with simulated semi-cumulative distributions based on hypothetical structures and very good agreement is obtained for the equal-atom case, as well as for a heterogeneous asymmetric subunit containing fourteen carbon atoms and one uranium atom. The new exact bicentric probability density functions of |E|, for the space group P\bar 1, reduce to the well known asymptotic expressions that are valid for equal-atom structures and a large number of atoms in the asymmetric unit of the space group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000095
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  • 4
    Electronic Resource
    Electronic Resource
    Exact joint probability distribution for centrosymmetric structure factors. Derivation and application to the Φ1 relationship in the space group Pgif"〉\overline{1} (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 401-408 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent applications of exact random-walk techniques to crystallographic structure-factor statistics have now been extended to multivariate joint probability density functions of several structure factors. The technique of deriving such multivariate exact density functions is introduced, and is applied to the study of the simplest sign relationship: Σ1, in the space group P\bar 1. An exact expression is obtained for the probability that the sign of the normalized structure factor E(2h 2k 2l) is positive, given the magnitudes of E(2h 2k 2l) and E(h k l), and an extensive numerical examination of this new expression - as compared with the conventional asymptotic formula for this probability - is presented. It is shown that the asymptotic formula usually underestimates the probability that E(2h 2k 2l) is positive, the discrepancies between the exact and asymptotic results being rather serious when the atomic composition of the asymmetric unit is heterogeneous (even moderately so), and when the number of atoms is small; a paucity of atoms leads to significant discrepancies even in the equal-atom case. On the other hand, for large asymmetric units of low heterogeneity and for high E values, the exact and asymptotic expressions agree very well in their predictions. The qualitative behaviour of the new exact expression is consistent with the known features of the Σ1 relationship and its statistical interpretations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000861
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  • 5
    Electronic Resource
    Electronic Resource
    Exact random-walk models in crystallographic statistics. IV. P.d.f.'s of E allowing for atoms in special positions (1988)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 44 (1988), S. 413-417 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The effect of scatterers, located in variable special positions, on the probability density function of the magnitude of the normalized structure factor has been investigated. Exact characteristic functions have been obtained for all the statistically different variable special positions in triclinic, monoclinic and orthorhombic space groups except in Fdd2 and in the space groups based on the point group 222, and the probability density functions have been evaluated from their Fourier or Fourier-Bessel series expansions. It is seen that the effect of heavy scatterers, located in the special positions investigated, is very marked and should be accounted for in cases of space-group ambiguities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387009255
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  • 6
    Electronic Resource
    Electronic Resource
    Exact conditional distribution of a three-phase invariant in the space group P1. III. Construction of an improved Cochran-like approximation (1993)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 260-265 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An exact representation of the accurately computable conditional probability density function (c.p.d.f.) of the three-phase invariant for the space group P1 was developed in paper I of this series [Shmueli, Rabinovich & Weiss (1989). Acta Cryst. A45, 361–367]. The computation of this function is too time consuming for it to be of practical value. It is therefore desirable to find simple approximations based on the exact result that may be more accurate than the familiar Cochran approximation or its extensions. One such approximation, presented here, has the same functional form as the Cochran approximation but with a modified parameter in place of that appearing in Cochran's distribution. Some of the numerical procedures used in the estimation of this modified parameter are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767392005506
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  • 7
    Electronic Resource
    Electronic Resource
    Exact conditional distribution of a three-phase invariant in space group P1. IV. Further improvements of Cochran-like approximations (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 633-636 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new approximate method of computing the conditional probability density function (c.p.d.f.) of a three-phase invariant is investigated, the results being compared to accurate calculations [Shmueli, Rabinovich & Weiss (1989). Acta Cryst. A45, 361–367]. A direct dependence on N, the number of atoms in the unit cell, is incorporated into the new approximation and its performance in the equal-atom case appears to be excellent over a large range of N values. The polynomial approximation of the recently published method [Posner, Shmueli & Weiss (1993). Acta Cryst. A49, 260–265] has been improved in both accuracy and range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767394002382
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  • 8
    Electronic Resource
    Electronic Resource
    Effects of noncrystallographic symmetry on the Σ1 relationship. I. Bicentric arrangements in Pl (1994)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 50 (1994), S. 605-608 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An exact Fourier representation of the probability for the Σ1 relationship is derived, which takes into account the presence of noncrystallographic centrosymmetry in the asymmetic unit of the space group P{\bar 1}. Illustrative examples show that the main effect of noncrystallographic symmetry is to decrease the probability that E2h is positive, as compared to the corresponding probability in the absence of such symmetry. The effect appears to be more pronounced in the equal-atom case than it is for a structure having a heterogeneous atomic composition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767394002400
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  • 9
    Electronic Resource
    Electronic Resource
    Exact random-walk models in crystallographic statistics. I. Space groups P\overline{1} and P1 (1984)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 651-660 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Probability density functions that are exact solutions to classical random-walk problems have been adapted to represent distributions of the magnitude of the normalized structure factor, for the space groups P\bar and P1. The functions are given by readily summable Fourier and Fourier-Bessel series, and account explicitly for the atomic composition of the asymmetric unit. These new probability density functions have been extensively tested by comparison with simulated histograms of |E|, for a wide range of atomic compositions. The most heterogeneous compositions examined are C14U and C29U, for P\bar 1 and P1, respectively. Very good agreement between the simulated and theoretical distributions has been obtained in all these tests, over the entire (useful) range 0 〈 |E| 〈 3. A distribution of |E| values, recalculated from published data on a triclinic platinum complex with chloroorganic ligands, has also been compared with the new probability functions and excellent agreement with the (expected) P\bar 1 theoretical distribution has been obtained. The discrepancy between the recalculated distribution and the P1 theoretical rules out the latter space group both by visual comparison and quantitative discrepancy criteria. It is concluded that probability density functions are definitely preferable to moments in attempting to resolve a space-group ambiguity. Measures of discrepancy to be used in such statistical tests are proposed and discussed in some detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767384001343
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  • 10
    Electronic Resource
    Electronic Resource
    Exact random-walk models in crystallographic statistics. VII. An all-space-group study of the effects of atomic heterogeneity on the P.d.f.'s of E (1991)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 47 (1991), S. 336-340 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Exact expressions have been found for the probability density functions (p.d.f.'s) of the magnitude of the normalized structure factor for all the two-dimensional and most three-dimensional space groups [Part VI: Rabinovich, Shmueli, Stein, Shashua & Weiss (1991). Acta Cryst. A47, 328–335]. The results of that investigation are used in the present article to examine some effects of atomic heterogeneity, in the various space-group symmetries, on the p.d.f.'s. Some typical comparisons are made between p.d.f.'s based on the central limit theorem and p.d.f.'s computed from exact formulae. In addition, the exact results are compared to histograms of simulated values of |E|. It is found that the p.d.f.'s for some space groups are influenced rather strongly by the presence of outstandingly heavy scatterers, but they are quite insensitive to the presence of such scatterers in other space groups. The often made general statement `The presence of outstandingly heavy scatterers may invalidate the indications of Wilson's statistics' is made more precise here, insofar as it depends on the particular space group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767390013319
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