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For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...

A semigroup S is said to be an inverse semigroup if, for every a in S, there is a unique b (called the inverse of a) such that a=aba and b=bab. This is equivalent to the ...

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...

In simple algebra, multiplication is the process of calculating the result when a number a is taken b times. The result of a multiplication is called the product of a and b, ...

A parallelohedron is a space-filling polyhedron that fills space using an infinite number of similarly situated copies (Tutton 1964, pp. 567 and 723; Coxeter 1973, pp. ...

"Q.E.F.," sometimes written "QEF," is an abbreviation for the Latin phrase "quod erat faciendum" ("that which was to be done"). It is a translation of the Greek words used by ...

A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...