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Particular examples of k-periodic number theoretic functions are the Dirichlet characters = modulo k and the greatest common divisor function () = (,). It is known that every k-periodic arithmetic function has a representation as a finite discrete Fourier series of the form
MDCalc was founded by two emergency physicians, Graham Walker, MD, and Joseph Habboushe, MD, MBA, [5] and provides over 500 medical calculators and other clinical decision-support tools. [6] The MDCalc.com website was launched in 2005. [5] In 2016, MDCalc launched an iOS app, [7] followed by an Android app in 2017. [8]
dc (desk calculator) is a cross-platform reverse-Polish calculator which supports arbitrary-precision arithmetic. [1] It was written by Lorinda Cherry and Robert Morris at Bell Labs. [2] It is one of the oldest Unix utilities, preceding even the invention of the C programming language. Like other utilities of that vintage, it has a powerful set ...
The multiplicative identity is the unit function ε defined by ε(n) = 1 if n = 1 and ε(n) = 0 if n > 1. The units (invertible elements) of this ring are the arithmetic functions f with f(1) ≠ 0. Specifically, [1] Dirichlet convolution is associative, = (), distributive over addition
If A is a K-algebra, for K a ring, and D: A → A is a K-derivation, then If A has a unit 1, then D(1) = D(1 2) = 2D(1), so that D(1) = 0. Thus by K-linearity, D(k) = 0 for all k ∈ K. If A is commutative, D(x 2) = xD(x) + D(x)x = 2xD(x), and D(x n) = nx n−1 D(x), by the Leibniz rule. More generally, for any x 1, x 2, …, x n ∈ A, it ...
Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (English: The Pendulum Clock: or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks) is a book published by Dutch mathematician and physicist Christiaan Huygens in 1673 and his major work on pendula and horology.
Parametric continuity (C k) is a concept applied to parametric curves, which describes the smoothness of the parameter's value with distance along the curve. A ...
Some care is then required: firstly any function coefficients in the operator D 2 must be differentiable as many times as the application of D 1 requires. To get a ring of such operators we must assume derivatives of all orders of the coefficients used. Secondly, this ring will not be commutative: an operator gD isn't the same in general as Dg.