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An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...

An ordinal number is called an initial ordinal if every smaller ordinal has a smaller cardinal number (Moore 1982, p. 248; Rubin 1967, p. 271). The omega_alphas ordinal ...

Let A^' be the outermost vertex of the regular pentagon erected inwards on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The inner Soddy circle is the circle tangent to each of the three mutually tangent circles centered at the vertices of a reference triangle. It has circle function ...

Let Q(x)=Q(x_1,x_2,...,x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be ...

The inverse Gaussian distribution, also known as the Wald distribution, is the distribution over [0,infty) with probability density function and distribution function given ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...