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A subfield which is strictly smaller than the field in which it is contained. The field of rationals Q is a proper subfield of the field of real numbers R which, in turn, is ...

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...

An experiment E(S,F,P) is defined (Papoulis 1984, p. 30) as a mathematical object consisting of the following elements. 1. A set S (the probability space) of elements. 2. A ...

A polynomial p(x)=sumc_ix^i is said to split over a field K if p(x)=aproduct_(i)(x-alpha_i) where a and alpha_i are in K. Then the polynomial is said to split into linear ...

A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with ...

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

Let K be a number field, then each fractional ideal I of K belongs to an equivalence class [I] consisting of all fractional ideals J satisfying I=alphaJ for some nonzero ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of ...