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Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

A Banach algebra A is called contractible if H^1(A,X)=Z^1(A,X)/B^1(A,X)=0 for all Banach A-bimodules X (Helemskii 1989, 1997). A C^*-algebra is contractible if and only if it ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

Consider a convex plane curve K with perimeter L, and the set of points P exterior to K. Further, let t_1 and t_2 be the perpendicular distances from P to K (with ...

A plot of the cumulative frequency against the upper class boundary with the points joined by line segments. Any continuous cumulative frequency curve, including a cumulative ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The polar curve r=1+2cos(2theta) (1) that can be used for angle trisection. It was devised by Ceva in 1699, who termed it the cycloidum anomalarum (Loomis 1968, p. 29). It ...