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In identical experiments, an Allais paradox occurs when the addition of an independent event influences choice behavior. Consider the choices in the following table (Kahneman ...

A moment mu_n of a univariate probability density function P(x) taken about the mean mu=mu_1^', mu_n = <(x-<x>)^n> (1) = int(x-mu)^nP(x)dx, (2) where <X> denotes the ...

The Copeland-Erdős constant is the constant with decimal expansion 0.23571113171923... (OEIS A033308) obtained by concatenating consecutive primes: 2, 23, 235, 2357, 235711, ...

The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel. Let ...

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

Consider the general system of two first-order ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y). (2) Let x_0 and y_0 denote fixed points with x^.=y^.=0, so ...

In elliptic n-space, the flat pole of an (n-1)-flat is a point located an arc length of pi/2 radians distant from each point of the (n-1)-flat. For an n-dimensional spherical ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...

The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...