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, ...

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 ...

When you create a graph in Excel, the software automatically sizes the X and Y axis lines, so the data you want to display is shown. You can override the settings and set the vertical and horizontal ...

Save guides, add subjects and pick up where you left off with your BBC account. A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the ...

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 ...

The field of model checking has evolved into a fundamental technique for verifying the correctness of software and hardware systems. At its core, model checking systematically explores the state space ...