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If different species occur in the octanol-water system by dissociation or association, several P-values and one D-value exist for the system. If, on the other hand, the substance is only present in a single species, the P and D values are identical. P is usually expressed as a common logarithm, i.e. Log P (also Log P ow or, less frequently, Log ...
Likewise, it is used to calculate lipophilic efficiency in evaluating the quality of research compounds, where the efficiency for a compound is defined as its potency, via measured values of pIC 50 or pEC 50, minus its value of log P. [27] Drug permeability in brain capillaries (y axis) as a function of partition coefficient (x axis) [28]
This value can then be used to give some scaling relation between the inflexion point and maximum point of the log-normal distribution. [55] This relationship is determined by the base of natural logarithm, e = 2.718 … {\displaystyle e=2.718\ldots } , and exhibits some geometrical similarity to the minimal surface energy principle.
where log denotes a logarithm to base 10 or common logarithm, and K diss is a stepwise acid dissociation constant. For bases, the base association constant , p K b is used. For any given acid or base the two constants are related by p K a + p K b = p K w , so p K a can always be used in calculations.
A positive free energy change of the surrounding solvent indicates hydrophobicity, whereas a negative free energy change implies hydrophilicity. In this way, the hydrophobic effect not only can be localized but also decomposed into enthalpic and entropic contributions.
The region surrounds the maximum-likelihood estimate, and all points (parameter sets) within that region differ at most in log-likelihood by some fixed value. The χ 2 distribution given by Wilks' theorem converts the region's log-likelihood differences into the "confidence" that the population's "true" parameter set lies inside. The art of ...
The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...
A logarithmic unit is a unit that can be used to express a quantity (physical or mathematical) on a logarithmic scale, that is, as being proportional to the value of a logarithm function applied to the ratio of the quantity and a reference quantity of the same type. The choice of unit generally indicates the type of quantity and the base of the ...