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Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then an atomic statement ...

A list is a data structure consisting of an ordered set of elements, each of which may be a number, another list, etc. A list is usually denoted (a_1, a_2, ..., a_n) or ...

Informally, a symplectic map is a map which preserves the sum of areas projected onto the set of (p_i,q_i) planes. It is the generalization of an area-preserving map. ...

Every module over a ring R contains a so-called "zero element" which fulfils the properties suggested by its name with respect to addition, 0+0=0, and with respect to ...

A clique covering of a graph G is set of cliques such that every vertex of G is a member of at least one clique. A minimum clique covering is a clique covering of minimum ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

Eliminate each knot crossing by connecting each of the strands coming into the crossing to the adjacent strand leaving the crossing. The resulting strands no longer cross but ...

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...

Given a subset S subset R^n and a point x in S, the contingent cone K_S(x) at x with respect to S is defined to be the set K_S(x)={h:d_S^-(x;h)=0} where d_S^- is the upper ...

The axioms formulated by Hausdorff (1919) for his concept of a topological space. These axioms describe the properties satisfied by subsets of elements x in a neighborhood ...