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Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

Let E be a simply connected compact set in the complex plane. By the Riemann mapping theorem, there is a unique analytic function ...

In 1989, P. Yff proved there is a unique configuration of isoscelizers for a given triangle such that all three have the same length and are concurrent (C. Kimberling, pers. ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

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 ...

Define the correlation integral as C(epsilon)=lim_(N->infty)1/(N^2)sum_(i,j=1; i!=j)^inftyH(epsilon-|x_i-x_j|), (1) where H is the Heaviside step function. When the below ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...

Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...