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The Löwenheim-Skolem theorem is a fundamental result in model theory which states that if a countable theory has a model, then it has a countable model. Furthermore, it has a ...

Consider the Euler product zeta(s)=product_(k=1)^infty1/(1-1/(p_k^s)), (1) where zeta(s) is the Riemann zeta function and p_k is the kth prime. zeta(1)=infty, but taking the ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

The successive overrelaxation method (SOR) is a method of solving a linear system of equations Ax=b derived by extrapolating the Gauss-Seidel method. This extrapolation takes ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...