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### A Dictionary of the Internet (4 ed.)

Reference type:
Subject Reference
Current Version:
2019

... 2.0 A term used to describe the transformation of scientific research that has come about through the extensive use of computers both for the analysis and for the capture of... ## Prussian horse-kicks

A set of data introduced by Bortkiewicz. It illustrates the fact that the frequencies of occurrence of unlikely events follow a Poisson distribution even when there may be variations in the ... ## birthday problem

A well-known, but intriguing probability problem. There are n people in a room. Assume that none is born on 29 February and that the remaining 365 days are all equally likely as birthdays. What is ... ## four squares theorem

Any positive integer can be expressed as the sum of not more that four positive integers. Alternatively it can be expressed as the sum of squares of exactly four non-negative integers, see Lagrange ... ## Lagrange theorem

(sum of four squares)Every natural number can be written as the sum of four squares of integers. This expression is not necessarily unique. For example,1=12+02+02+02,10=32+12+02+02 or 22+22+12+12. ## Gregory–Newton forward difference formula

Let x 0, x 1, x 2,…, x n be equally spaced values, so that x i=x 0+ih, for i=1, 2,…, n. Suppose that the values f 0, f 1, f 2,…, f n are known, where f i=f(x i), for some function f. The ... ## vector norm

For an n-dimensional vector x a vector norm is a non-negative function which satisfies:|x|>0 when x ≠ 0 and |x|=0 when x=0,|k x|=k×|x| for any scalar k,|x+y|≤|x|+|y|. ## Langevin distribution

A distribution used to model spherical data. The probability density function f in the direction (θ, ϕ) (See spherical data) is given byf(θ, ϕ)=c exp[κ{cosθ0 cosθ+sinθ0 sinθ cos(ϕ-ϕ0)}], 0≤θ≤π, -π≤ϕ ... ## degenerate conic

A conic that consists of a pair of (possibly coincident) straight lines. The equation ax 2+2hxy+by 2+2gx+2fy+c=0 represents a degenerate conic if Δ=0, where ## Watson's test

A test of a specified circular distribution, adapted from the Crame´r–von Mises test, and introduced by Geoffrey Watson in 1961. Denote the n observations by θ1, θ2,…, θn and write where F(θ) is the ... ## continuation

1 A concept in programming language semantics, allowing the meaning of program constructs to be defined in terms of the effect they have on the computation remaining to be done, rather than on the ... ## ridit

Ridits provide a method for replacing the categories of an ordinal variable by scores between 0 and 1. Suppose that a variable has five ordered categories: ‘very low’, ‘low’, ‘medium’, ‘high’, and ... ## direction cosines

In a Cartesian coordinate system in 3-dimensional space, a certain direction can be specified as follows. Take a point P such that has the given direction and |OP|=1. Let α, β and γ be the three ... ## zero element

An element z is a zero element for a binary operation ￮ on a set S if, for all a in S, a ￮ z=z ￮ a=z. Thus the real number 0 is a zero element for multiplication since, for all a, a0=0a=0. The term ... ## unconditional inequality

Always true, irrespective of the values taken by the variables so x 2+2x+3>0 is unconditional since it can be expressed as (x+1)2+2>0 which is always>0, but x 2+2x−3>0 is a conditional inequality ... ## partial differential equations

Differential equations that involve two or more independent variables, which in practice are often space and time variables. Because more than one independent variable is present, the “derivatives” ... ## isolated point

A singular point which does not lie on the main curve of an equation but whose co-ordinates do satisfy the equation. For example, y 2=x 4−x 2=x 2 (x 2−1) is not defined for −1 < x < 0, 0 < x < 1, and ... ## statistical equilibrium

A state in which the probability distribution of states remains constant over time. This is an important idea in statistical physics, and in Markov chains, where the existence of an equilibrium ... ## linear piecewise regression model

A model that describes the situation where the graph relating the expectation of the random variable Y and the variable x is linear for x≤x0 and is also linear for x≥x0 but with a different slope. ... ## zero

The real number 0, which is the additive identity, i.e. x+0=0+x=x for any real number x. The element in any ring with the property that x. 0=0. x=0.  View: