Search Results for ""

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...

The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by mu=<x>, (1) where <f> is the expectation value. For a continuous ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

A statement letter or a negation of a statement letter (Mendelson 1997, p. 30).

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...