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The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...

Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...

Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...

The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...