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  • self-similarity  (1)
  • suspensions  (1)
  • 1
    ISSN: 1573-904X
    Keywords: absorption ; dose ; particle size ; permeability ; solubility ; suspensions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A microscopic mass balance approach has been developed to predict the fraction dose absorbed of suspensions of poorly soluble compounds. The mathematical model includes four fundamental di-mensionless parameters to estimate the fraction dose absorbed: initial saturation (Is), absorption number (An), dose number (Do), and dissolution number (Dn). The fraction dose absorbed (F) increases with increasing Is, An, and Dn and with decreasing Do. At higher Dn and lower Do, the fraction dose absorbed reaches the maximal F, which depends only on An. The dissolution number limit on F can appear at both lower Do and lower Dn. Likewise, at higher Do and Dn, the fraction dose absorbed reaches a Do limit. Initial saturation makes a significant difference in F at lower Do and Dn. It is shown that the extent of drug absorption is expected to be highly variable when Dn and Do are approximately one. Furthermore, by calculating these dimensionless groups for a given compound, a formulation scientist can estimate not only the extent of drug absorption but also the effect, if any, of particle size reduction on the extent of drug absorption.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 18 (1986), S. 765-783 
    ISSN: 1573-8868
    Keywords: caves ; fractals ; self-similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Lengths of all caves in a region have been observed previously to be distributed hyperbolically, like self-similar geomorphic phenomena identified by Mandelbrot as exhibiting fractal geometry. Proper cave lengths exhibit a fractal dimension of about 1.4. These concepts are extended to other self-similar geometric properties of caves with the following consequences. Lengths of a cave is defined as the sum of sizes of passage-filling, linked modular elements larger than the cave-defining modulus. If total length of all caves in a region is a self-similar fractal, it has a fractal dimension between 2 and 3; and the total number of linked modular elements in a region is a self-similar fractal of the same dimension. Cave volume in any modular element size range may be calculated from the distribution. The expected conditional distribution of modular element sizes in a cave, given length and modulus, also is distributed hyperbolically. Data from Little Brush Creek Cave (Utah) agree and yield a fractal dimension of about 2.8 (like the Menger Sponge). The expected number of modular elements in a cave equals approximately the 0.9 power of length of the cave divided by modulus. This result yields an intriguing “parlor trick.” An algorithm for estimating modular element sizes from survey data provides a means for further analysis of cave surveys.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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