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Solutions to holomorphic differential equations are themselves holomorphic functions of time, initial conditions, and parameters.

A knot equivalent to a polygon in R^3, also called a tame knot. For a polygonal knot K, there exists a plane such that the orthogonal projection pi on it satisfies the ...

The algebra A is called a pre-C^*-algebra if it satisfies all conditions to be a C^*-algebra except that its norm need not be complete.

Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that the interval [0,n] is contained in D, one can show ...

Let D be a subset of the nonnegative integers Z^* with the properties that (1) the integer 0 is in D and (2) any time that n is in D, one can show that n+1 is also in D. ...

A proof or demonstration is said to be rigorous if the validity of each step and the connections between the steps is explicitly made clear in such a way that the result ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...

A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...