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The surface given by the parametric equations x = e^(bv)cosv+e^(av)cosucosv (1) y = e^(bv)sinv+e^(av)cosusinv (2) z = e^(av)sinu. (3) For a=b=1, the coefficients of the first ...

The first corona of a tile is the set of all tiles that have a common boundary point with that tile (including the original tile itself). The second corona is the set of ...

A measure nu of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension D and information ...

Given a curved regression, the correlation index is defined by r_c=(s_(yy^^))/(s_ys_(y^^)), (1) where s_y and s_(y^^) are the standard deviations of the data points y and the ...

Let there be N_i observations of the ith phenomenon, where i=1, ..., p and N = sumN_i (1) y^__i = 1/(N_i)sum_(alpha)y_(ialpha) (2) y^_ = 1/Nsum_(i)sum_(alpha)y_(ialpha). (3) ...

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

The cotree T^* of a spanning tree T in a connected graph G is the spacing subgraph of G containing exactly those edges of G which are not in T (Harary 1994, p. 39).

A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...