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A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector v^^ having the same direction as a given ...

A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces M ...

A characterization of normal spaces which states that a topological space X is normal iff, for any two nonempty closed disjoint subsets A, and B of X, there is a continuous ...

The validity of a logical argument refers to whether or not the conclusion follows logically from the premises, i.e., whether it is possible to deduce the conclusion from the ...

Delta(x_1,...,x_n) = |1 x_1 x_1^2 ... x_1^(n-1); 1 x_2 x_2^2 ... x_2^(n-1); | | | ... |; 1 x_n x_n^2 ... x_n^(n-1)| (1) = product_(i,j; i>j)(x_i-x_j) (2) (Sharpe 1987). For ...

Let [arg(f(z))] denote the change in the complex argument of a function f(z) around a contour gamma. Also let N denote the number of roots of f(z) in gamma and P denote the ...

For a second-order ordinary differential equation, y^('')+p(x)y^'+q(x)y=g(x). (1) Assume that linearly independent solutions y_1(x) and y_2(x) are known to the homogeneous ...

A variety is a class of algebras that is closed under homomorphisms, subalgebras, and direct products. Examples include the variety of groups, the variety of rings, the ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...