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A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...

According to many authors (e.g., Kelley 1955, p. 112; Joshi 1983, p. 162; Willard 1970, p. 99) a normal space is a topological space in which for any two disjoint closed sets ...

Let A be a normed (Banach) algebra. An algebraic left A-module X is said to be a normed (Banach) left A-module if X is a normed (Banach) space and the outer multiplication is ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

Let T be a linear operator on a separable Hilbert space. The spectrum sigma(T) of T is the set of lambda such that (T-lambdaI) is not invertible on all of the Hilbert space, ...

An expanded paper bag, cushion, or pillow has a distinctive shape. Given the dimensions of a flat rectangular bag with dimensions a, b, bounds for the maximum volume of ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

The integral kernel in the Poisson integral, given by K(psi)=1/(2pi)(1-|z_0|^2)/(|z_0-e^(ipsi)|^2) (1) for the open unit disk D(0,1). Writing z_0=re^(itheta) and taking ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...