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An ideal I of a ring R is called principal if there is an element a of R such that I=aR={ar:r in R}. In other words, the ideal is generated by the element a. For example, the ...

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

The Reeb foliation of the hypersphere S^3 is a foliation constructed as the union of two solid tori with common boundary.

A function is termed regular iff it is analytic and single-valued throughout a region R.

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...

The second Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 1134, 1135, 1136, and 1137.

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...