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Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial ...

A symmetry of a differential equation is a transformation that keeps its family of solutions invariant. Symmetry analysis can be used to solve some ordinary and partial ...

A local sink is a node of a directed graph with no exiting edges, also called a terminal (Borowski and Borwein 1991, p. 401; left figure). A global sink (often simply called ...

An unlabeled transitive digraph with n nodes is called a "topology." The numbers of distinct topologies on n=1, 2, ... nodes are 1, 3, 9, 33, 139, 718, 4535, ... (OEIS ...

The group D_5 is one of the two groups of order 10. Unlike the cyclic group C_(10), D_5 is non-Abelian. The molecule ruthenocene (C_5H_5)_2Ru belongs to the group D_(5h), ...

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

The direct limit, also called a colimit, of a family of R-modules is the dual notion of an inverse limit and is characterized by the following mapping property. For a ...