Search Results for ""

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

The Hanoi graph H_n corresponding to the allowed moves in the tower of Hanoi problem. The above figure shows the Hanoi graphs for small n. The Hanoi graph H_n can be ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...