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 ...

\(y = x^2 + a\) represents a translation parallel to the \(y\)-axis of the graph of \(y = x^2\). If \(a\) is positive, the graph translates upwards. If \(a\) is negative, the graph translates ...

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, ...

This is a preview. Log in through your library . Abstract Let TX be the full transformation semigroup on the set X and let S be a subsemigroup of TX. We may associate ...

Abstract: Software modeling has become an everyday practice. Modeling extra-large models have enormous constraints: both memory and computational capacity of a single computer might be insufficient ...

Abstract: Autonomic Computing Systems are oriented to prevent the human intervention and to enable distributed systems to manage themselves. One of their challenges is the efficient monitoring at ...