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The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

If {a_j} subset= D(0,1) (with possible repetitions) satisfies sum_(j=1)^infty(1-|a_j|)<=infty, where D(0,1) is the unit open disk, and no a_j=0, then there is a bounded ...

After a half rotation of the coin on the left around the central coin (of the same radius), the coin undergoes a complete rotation. In other words, a coin makes two complete ...

A cross section of a solid is a plane figure obtained by the intersection of that solid with a plane. The cross section of an object therefore represents an infinitesimal ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

The function f_theta(z)=z/((1+e^(itheta)z)^2) (1) defined on the unit disk |z|<1. For theta in [0,2pi), the Köbe function is a schlicht function f(z)=z+sum_(j=2)^inftya_jz^j ...

Mergelyan's theorem can be stated as follows (Krantz 1999). Let K subset= C be compact and suppose C^*\K has only finitely many connected components. If f in C(K) is ...

Consider a power series in a complex variable z g(z)=sum_(n=0)^inftya_nz^n (1) that is convergent within the open disk D:|z|<R. Convergence is limited to within D by the ...

A conjecture due to M. S. Robertson in 1936 which treats a univalent power series containing only odd powers within the unit disk. This conjecture implies the Bieberbach ...