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A curve alpha on a regular surface M is a principal curve iff the velocity alpha^' always points in a principal direction, i.e., S(alpha^')=kappa_ialpha^', where S is the ...

A general quintic equation a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 (1) can be reduced to one of the form y^5+b_2y^2+b_1y+b_0=0, (2) called the principal quintic form. Vieta's ...

A principal nth root omega of unity is a root satisfying the equations omega^n=1 and sum_(i=0)^(n-1)omega^(ij)=0 for j=1, 2, ..., n. Therefore, every primitive root of unity ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

The truth of an infinite sequence of propositions P_i for i=1, ..., infty is established if (1) P_1 is true, and (2) P_k implies P_(k+1) for all k. This principle is ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

Typesetting "errors" in which exponents or multiplication signs are omitted but the resulting expression is equivalent to the original one. Examples include 2^59^2=2592 (1) ...

A polyhedron having two polygons in parallel planes as bases and triangular or trapezoidal lateral faces with one side lying in one base and the opposite polyhedron vertex or ...

Given an event E in a sample space S which is either finite with N elements or countably infinite with N=infty elements, then we can write S=( union _(i=1)^NE_i), and a ...

The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...