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Let G be an open subset of the complex plane C, and let L_a^2(G) denote the collection of all analytic functions f:G->C whose complex modulus is square integrable with ...

If f(x) is piecewise continuous and has a generalized Fourier series sum_(i)a_iphi_i(x) (1) with weighting function w(x), it must be true that ...

A bicolorable graph G is a graph with chromatic number chi(G)<=2. A graph is bicolorable iff it has no odd graph cycles (König 1950, p. 170; Skiena 1990, p. 213; Harary 1994, ...

A Bill picture is a sequence of nested regular polygons in which subsequent polygons are each rotated so that they begin one vertex further. The term was coined by Trott ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

The algebraic identity (sum_(i=1)^na_ic_i)(sum_(i=1)^nb_id_i)-(sum_(i=1)^na_id_i)(sum_(i=1)^nb_ic_i) =sum_(1<=i<j<=n)(a_ib_j-a_jb_i)(c_id_j-c_jd_i). (1) Letting c_i=a_i and ...

Bisection is the division of a given curve, figure, or interval into two equal parts (halves). A simple bisection procedure for iteratively converging on a solution which is ...

An extremal graph in which the forced triangles are all the same color. Call R the number of red monochromatic forced triangles and B the number of blue monochromatic forced ...

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...

For a general quadrilateral with sides of length a, b, c, and d, the area K is given by (1) where s=1/2(a+b+c+d) (2) is the semiperimeter, A is the angle between a and d, and ...