A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(y = f(x)\) where \(f(x) = x^2\) is the same as the ...

This is a preview. Log in through your library . Abstract We consider a parametric family of integral equations of the first kind, which can be treated as index transformations and generalize ...

Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory, ...

Journal of Music Theory, Vol. 42, No. 2, Neo-Riemannian Theory (Autumn, 1998), pp. 241-263 (23 pages) Connections between parsimonious structures and "modes of limited transposition" from three set ...