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A primary ideal is an ideal I such that if ab in I, then either a in I or b^m in I for some m>0. Prime ideals are always primary. A primary decomposition expresses any ideal ...

A condition which, if true, guarantees that a result is also true. (However, the result may also be true if the condition is not met.) If a condition is both necessary and ...

An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

There are a number of slightly different definitions of the Fresnel integrals. In physics, the Fresnel integrals denoted C(u) and S(u) are most often defined by C(u)+iS(u) = ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

A merit function, also known as a figure-of-merit function, is a function that measures the agreement between data and the fitting model for a particular choice of the ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

A general system of fourth-order curvilinear coordinates based on the cyclide in which Laplace's equation is separable (either simply separable or R-separable). Bôcher (1894) ...