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The mean tangent diameter of a solid, also known as the mean caliper diameter, is the caliper dimension obtained by averaging over all orientations.

Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define c_k=sum_(j=0)^(n-k)a_ja_(j+k). Then the merit ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

Let a in C and |a|<1, then phi_a(z)=(z-a)/(1-a^_z) is a Möbius transformation, where a^_ is the complex conjugate of a. phi_a is a conformal mapping self-map of the unit disk ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

The Narayan number N(n,k) for n=1, 2, ... and k=1, ..., n gives a solution to several counting problems in combinatorics. For example, N(n,k) gives the number of expressions ...

Let |z| be a vector norm of a vector z such that ||A||=max_(|z|=1)||Az||. Then ||A|| is a matrix norm which is said to be the natural norm induced (or subordinate) to the ...

Let pi_n(x)=product_(k=0)^n(x-x_k), (1) then f(x)=f_0+sum_(k=1)^npi_(k-1)(x)[x_0,x_1,...,x_k]+R_n, (2) where [x_1,...] is a divided difference, and the remainder is ...

A set X is said to be nowhere dense if the interior of the set closure of X is the empty set. For example, the Cantor set is nowhere dense. There exist nowhere dense sets of ...