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For a general second-order linear recurrence equation f_(n+1)=xf_n+yf_(n-1), (1) define a multiplication rule on ordered pairs by (A,B)(C,D)=(AD+BC+xAC,BD+yAC). (2) The ...

By choosing appropriate rules, it is possible to achieve many forms of synchronization within cellular automata. One version, known as the firing squad synchronization ...

The parallelogram law gives the rule for vector addition of vectors A and B. The sum A+B of the vectors is obtained by placing them head to tail and drawing the vector from ...

A siteswap is a sequence encountered in juggling in which each term is a positive integer, encoded in binary. The transition rule from one term to the next consists of ...

A species of structures is a rule F which 1. Produces, for each finite set U, a finite set F[U], 2. Produces, for each bijection sigma:U->V, a function F[sigma]:F[U]->F[V]. ...

Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more ...

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value a together with the ...

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...