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The radius of curvature is given by R=1/(|kappa|), (1) where kappa is the curvature. At a given point on a curve, R is the radius of the osculating circle. The symbol rho is ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

An analytic function f(z) whose Laurent series is given by f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n, (1) can be integrated term by term using a closed contour gamma encircling ...

Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v ...

If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

Shephard's conjecture states that every convex polyhedron admits a self-unoverlapping unfolding (Shephard 1975). This question is still unsettled (Malkevitch), though most ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...