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To multiply the size of a d-D object by a factor a, c=a^d copies are required, and the quantity d=(lnc)/(lna) is called the similarity dimension.

An algebra with no nontrivial ideals.

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

The type of homology which results when the spaces being studied are restricted to simplicial complexes and subcomplexes.

If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).

The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...

A long division in which most or all of the digits are replaced by a symbol (usually asterisks) to form a cryptarithmetic.

"The" Smarandache constant is the smallest solution to the generalized Andrica's conjecture, x approx 0.567148 (OEIS A038458). The first Smarandache constant is defined as ...

J_m(x)=(2x^(m-n))/(2^(m-n)Gamma(m-n))int_0^1J_n(xt)t^(n+1)(1-t^2)^(m-n-1)dt, where J_m(x) is a Bessel function of the first kind and Gamma(x) is the gamma function.

The continuous image of a Polish space, also called an analytic set.