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A logarithmically convex function f is a convex function since it is the composite of the increasing convex function and the function , which is by definition convex. However, being logarithmically convex is a strictly stronger property than being convex. For example, the squaring function is convex, but its logarithm is not.
The logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks: where x ( t) is the overshoot (amplitude - final value) at time t and x(t + nT) is the overshoot of the peak n periods away, where n is any integer number of successive, positive peaks. The damping ratio is then found from the ...
In algebraic geometry, a log structure provides an abstract context to study semistable schemes, and in particular the notion of logarithmic differential form and the related Hodge-theoretic concepts. This idea has applications in the theory of moduli spaces, in deformation theory and Fontaine's p-adic Hodge theory, among others.
Log probability. In probability theory and computer science, a log probability is simply a logarithm of a probability. [1] The use of log probabilities means representing probabilities on a logarithmic scale , instead of the standard unit interval . Since the probabilities of independent events multiply, and logarithms convert multiplication to ...
Nurse log. A nurse log is a fallen tree which, as it decays, provides ecological facilitation to seedlings. Broader definitions include providing shade or support to other plants. Some of the advantages a nurse log offers to a seedling are: water, moss thickness, leaf litter, mycorrhizae, disease protection, nutrients, and sunlight.
It is much easier than to convert logs to their natural values, to add them and again to convert them to logs. Moreover, Gaussian logs yield greater accuracy of result than the traditional computing method and help 5-digit log values to be sufficiently accurate for this method. […] The use of "Gaussians" by Bruce is original in the field of ...
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution. [2] [3] Equivalently, if Y has a normal distribution, then the exponential ...