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In mathematics, a sequence a = (a0, a1, ..., an) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if ai2 ≥ ai−1ai+1 holds for 0 < i < n . Remark: some authors (explicitly or not) add two further conditions in the definition of log-concave sequences: a is non-negative.
Logarithmically concave function. In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality. for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ...
The decimal value of the natural logarithm of 2 (sequence A002162 in the OEIS ) is approximately. The logarithm of 2 in other bases is obtained with the formula. The common logarithm in particular is ( OEIS : A007524 ) The inverse of this number is the binary logarithm of 10: ( OEIS : A020862 ). By the Lindemann–Weierstrass theorem, the ...
Login VSI's flagship product, Login Enterprise, is an automated testing platform that predicts performance, ensures business continuity and reduces risk. Login Enterprise tests the desktop and applications as a whole, from pre-production through to production. Login Enterprise includes standard “out-of-the-box” application template workloads.
Windows Security Log. The Security Log, in Microsoft Windows, is a log that contains records of login/logout activity or other security-related events specified by the system's audit policy. Auditing allows administrators to configure Windows to record operating system activity in the Security Log. The Security Log is one of three logs viewable ...
instead. In developing the analogue for the complex logarithm, there is an additional complication: the definition of the complex integral requires a choice of path. . Fortunately, if the integrand is holomorphic, then the value of the integral is unchanged by deforming the path (while holding the endpoints fixed), and in a simply connected region (a region with "no holes"), any path from to ...