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A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

A variable that may assume complex values.

A complex vector bundle is a vector bundle pi:E->M whose fiber bundle pi^(-1)(x) is a complex vector space. It is not necessarily a complex manifold, even if its base ...

A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with ...

The concatenation of two strings a and b is the string ab formed by joining a and b. Thus the concatenation of the strings "book" and "case" is the string "bookcase". The ...

A function f(x) is said to be concave on an interval [a,b] if, for any points x_1 and x_2 in [a,b], the function -f(x) is convex on that interval (Gradshteyn and Ryzhik 2000).

A concave polygon is a polygon that is not convex. A simple polygon is concave iff at least one of its internal angles is greater than 180 degrees. An example of a non-simple ...

Let mu be a positive measure on a sigma-algebra M, and let lambda be an arbitrary (real or complex) measure on M. If there is a set A in M such that lambda(E)=lambda(A ...