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The Reidemeister move of type III.

Assemble six 1×2×2 blocks and three 1×1×1 blocks into a 3×3×3 cube.

A moving average may generate an irregular oscillation even if none exists in the original data.

The space of immersions of a manifold in another manifold is homotopically equivalent to the space of bundle injections from the tangent space of the first to the tangent ...

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

An algorithm for computing an Egyptian fraction.

A submodule S of a module M such that for any proper submodule T of M, the submodule generated by S union T is not the entire module M. S is also called superfluous submodule.

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

Consecutive Smith numbers. The first few Smith brothers are (728, 729), (2964, 2965), (3864, 3865), (4959, 4960), ... (OEIS A050219 and A050220).

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...