Hatred it "brings a process to completion". <poem>I study hatred with great diligence, For that's a passion in my own control, A sort of besom that can clear the soul Of everything that is not mind or sense."</poem> Hatred Hatred or hate is a human emotion. Hatred could invoke feelings of animosity, anger or resentment, which can be directed against certain individuals, groups, entities, objects, behaviors, concepts, or ideas. Hatred is often associated with feelings of anger, disgust and a disposition towards the source of hostility. As an emotion, hatred can be short-lived or long-lasting. It can be of low intensity
Irrational rotation ergodic transformation, but it is not mixing. The Poincaré map for the dynamical system associated with the Kronecker foliation on a torus with angle is the irrational rotation by . C*-algebras associated with irrational rotations, known as irrational rotation algebras, have been extensively studied. Irrational rotation In the mathematical theory of dynamical systems, an irrational rotation is a map where "θ" is an irrational number. Under the identification of a circle with R/Z, or with the interval [0, 1] with the boundary points glued together, this map becomes a rotation of a circle by a proportion "θ" of a full