Search Results for ""

For a second-order ordinary differential equation, y^('')+p(x)y^'+q(x)y=g(x). (1) Assume that linearly independent solutions y_1(x) and y_2(x) are known to the homogeneous ...

Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

A sequence of uncorrelated numbers alpha_n developed by Wiener (1926-1927). The numbers are constructed by beginning with {1,-1}, (1) then forming the outer product with ...

"The" Y-graph is another term used to refer to a claw graph. The term "Y-graph" is also used to refer to a graph expansion with the Y graph as its base (e.g., Horton and ...

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...

An inconic with parameters x:y:z=a(b-c):b(c-a):c(a-b), (1) giving equation (2) (Kimberling 1998, pp. 238-239). Its focus is Kimberling center X_(101) and its conic section ...

Young's geometry is a finite geometry which satisfies the following five axioms: 1. There exists at least one line. 2. Every line of the geometry has exactly three points on ...

Let f be a real-valued, continuous, and strictly increasing function on [0,c] with c>0. If f(0)=0, a in [0,c], and b in [0,f(c)], then int_0^af(x)dx+int_0^bf^(-1)(x)dx>=ab, ...