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An almost perfect number, also known as a least deficient or slightly defective (Singh 1997) number, is a positive integer n for which the divisor function satisfies ...

A number n is called a barrier of a number-theoretic function f(m) if, for all m<n, m+f(m)<=n. Neither the totient function phi(n) nor the divisor function sigma(n) has a ...

Let G be an open subset of the complex plane C, and let L_a^2(G) denote the collection of all analytic functions f:G->C whose complex modulus is square integrable with ...

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

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 ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

A complex manifold is a manifold M whose coordinate charts are open subsets of C^n and the transition functions between charts are holomorphic functions. Naturally, a complex ...

It is conjectured that any convex body in n-dimensional Euclidean space has an interior point lying on normals through 2n distinct boundary points (Croft et al. 1991). This ...

The expression im kleinen is German and means "on a small scale." A topological space is connected im kleinen at a point x if every neighborhood U of x contains an open ...

A covering map (also called a covering or projection) is a surjective open map f:X->Y that is locally a homeomorphism, meaning that each point in X has a neighborhood that is ...