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Connectivity properties obey the following hierarchy: convex => star convex => pathwise-connected => connected.

A connected dominating set in a connected graph G is a dominating set in G whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not ...

Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.

An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

The apodization function A(x)=(1-(x^2)/(a^2))^2. Its full width at half maximum is sqrt(4-2sqrt(2))a. Its instrument function is ...

Consecutive numbers (or more properly, consecutive integers) are integers n_1 and n_2 such that n_2-n_1=1, i.e., n_2 follows immediately after n_1. Given two consecutive ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

A map f:X-->Y is called constant with constant value y if f(x)=y for all x in X, i.e., if all elements of X are sent to same element y of Y.

Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another ...