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A map u:R^n->R^n from a domain G is called a map of class C^r if each component of u(x)=(u_1(x_1,...,x_n),...,u_m(x_1,...,x_n)) is of class C^r (0<=r<=infty or r=omega) in G, ...

An equivalence class is defined as a subset of the form {x in X:xRa}, where a is an element of X and the notation "xRy" is used to mean that there is an equivalence relation ...

Two patterns T_1 and T_2 belong to the same Wilf class if |S_n(T_1)|=|S_n(T_2)| for all n, where S_n(T) denotes the set of permutations on {1,...,n} that avoid the pattern T. ...

The number of elements of a group in a given conjugacy class.

A class is a generalized set invented to get around Russell's antinomy while retaining the arbitrary criteria for membership which leads to difficulty for sets. The members ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

The local McLaughlin graph is the graph on 162 vertices and 4536 edges obtained from the McLaughlin graph by vertex deletion of a single vertex and its neighbors, making it ...

A gadget defined for complex vector bundles. The Chern classes of a complex manifold are the Chern classes of its tangent bundle. The ith Chern class is an obstruction to the ...