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Given any open set U in R^n with compact closure K=U^_, there exist smooth functions which are identically one on U and vanish arbitrarily close to U. One way to express this ...

A real vector bundle pi:E->M has an orientation if there exists a covering by trivializations U_i×R^k such that the transition functions are vector space ...

The rank of a vector bundle is the dimension of its fiber. Equivalently, it is the maximum number of linearly independent local bundle sections in a trivialization. ...

The partial differential equation u_t+uu_x=nuu_(xx) (Benton and Platzman 1972; Zwillinger 1995, p. 417; Zwillinger 1997, p. 130). The so-called nonplanar Burgers equation is ...

The variety which is an invariant of degree four and is given by the equation y_0^4-y_0(y_1^3+y_2^3+y_3^3+y_4^3)+3y_1y_2y_3y_4=0.

Lockwood (1957) terms the ellipse negative pedal curve with pedal point at the focus "Burleigh's oval" in honor of his student M. J. Burleigh, who first drew his attention to ...

The Burridge-Knopoff model is a system of differential equations used to model earthquakes using n points on a straight line, each of mass m, that interact with each other ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

Caesar's method is an encryption scheme involving shifting an alphabet (so a->c, b->d, c->e, d->f, etc., x->z,y->a,z->b). It is one of the most basic encryption methods, and ...

The Cairo tessellation is a tessellation appearing in the streets of Cairo and in many Islamic decorations. Its tiles are obtained by projection of a dodecahedron, and it is ...