Definition, Betydelse, Synonymer & Anagram | Engelska ordet LOGARITHM

Definition av LOGARITHM

1. (matematik) logaritm

Exempel på hur man kan använda LOGARITHM i en mening

• Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition.
• The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to.
• In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material.
• The net gain in dB is calculated by taking 10 times the common logarithm of the ratio of the output power to the input power.
• The Meissel–Mertens constant is analogous to the Euler–Mascheroni constant, but the harmonic series sum in its definition is only over the primes rather than over all integers and the logarithm is taken twice, not just once.
• Shor proposed multiple similar algorithms for solving the factoring problem, the discrete logarithm problem, and the period-finding problem.
• The Digital Signature Algorithm (DSA) is a public-key cryptosystem and Federal Information Processing Standard for digital signatures, based on the mathematical concept of modular exponentiation and the discrete logarithm problem.
• In particular, this explains use of integration by parts to integrate logarithm and inverse trigonometric functions.
• In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to instead use the binary logarithm, giving the equivalent form.
• Several important algorithms in public-key cryptography, such as ElGamal, base their security on the hardness assumption that the discrete logarithm problem (DLP) over carefully chosen groups has no efficient solution.
• The design process saw the early adoption of the logarithm (invented in 1615) to generate the curves used to produce the shape of a hull, especially when scaling up these curves accurately in the mould loft.
• A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift.
• The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.
• Geometric Brownian motion, continuous stochastic process where the logarithm of a variable follows a Brownian movement, that is a Wiener process.
• After any sequence of insertions and deletions of keys, the shape of the tree is a random variable with the same probability distribution as a random binary tree; in particular, with high probability its height is proportional to the logarithm of the number of keys, so that each search, insertion, or deletion operation takes logarithmic time to perform.
• Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ.
• Ernst Heinrich Weber states that "the minimum increase of stimulus which will produce a perceptible increase of sensation is proportional to the pre-existent stimulus," while Gustav Fechner's law is an inference from Weber's law (with additional assumptions) which states that the intensity of our sensation increases as the logarithm of an increase in energy rather than as rapidly as the increase.
• The intuition for the Risch algorithm comes from the behavior of the exponential and logarithm functions under differentiation.
• By introducing these transcendental functions and noting the bijection property that implies an inverse function, some facility was provided for algebraic manipulations of the natural logarithm even if it is not an algebraic function.
• In elliptic curve cryptography, the Weil descent attack uses the Weil restriction to transform a discrete logarithm problem on an elliptic curve over a finite extension field L/K, into a discrete log problem on the Jacobian variety of a hyperelliptic curve over the base field K, that is potentially easier to solve because of K's smaller size.

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