mga f*ck lang.. este facts XD

In the classical mechanics of a particle one has dynamical variables which are called coordinates (q) and momenta (p). These specify the state of a classical system. The canonical structure (also known as the symplectic structure) of classical mechanics consists of Poisson brackets between these variables. All transformations which keep these brackets unchanged are allowed as canonical transformations in classical mechanics.

In quantum mechanics, these dynamical variables become operators acting on a Hilbert space of quantum states. The Poisson brackets are replaced by commutators, [q,p] = qp-pq = 1. This readily yields up the uncertainty principle in the form ΔpΔq #8805; 1. This algebraic structure corresponds to a generalization of the canonical structure of classical mechanics.

The states of a quantum system can be labelled by the eigenvalues of any operator. For example, one may write x> for a state which is an eigenvector of q with eigenvalue x. Notationally

Alpha Radiation is the emission of an alpha particle from an atom's nucleus. An a particle contains 2 protons and 2 neutrons (and is similar to a He nucleus ). When an atom emits an alpha particle, the atom's atomic mass will decrease by 4 units and the atomic number will decrease by 2 units. Beta Radiation is the transmutation of a neutron into a proton and electron (followed by the emission of the electron from the atom's nucleus ).When an atom emits a beta particle, the atom's mass will not change (since there is no change in the total number of nuclear particles), however the atomic number will increase by 1 (bcoz the neutron transmutated into an additional proton).Gamma Radiation involves the emission of electromagnetic energy (similar to light energy) from an atom's nucleus. No particles are emitted during gamma radiation, and thus gamma radiation does not itself cause the transmutation of atoms, however gamma radiation is often emitted during alpha and beta radioactive decay

Classically, Euclidean geometry was focused on Compass and straightedge constructions. In modern times, geometric concepts have been extended. Geometry now uses methods of calculus and abstract algebra, so that many modern branches of the field are not easily recognizable as the descendants of early geometry.
early geometry.Fellowcrafts receive several admonitions and exhortations regarding the sciences of geometry and astronomy, and many an initiate has wondered just how far his duty should carry him in undertaking anew the study of branches of mathematics which are associated in his mind with much troubled effort in school days.
While some mathematically-minded men may find the same joy in the study of lines, angles, surfaces, spheres and measurements, which the musician obtains from his notes, the painter from his perspective and colors and the poet from his meter and rhymes, comparatively few brethren rejoice in the study of the mathematically abstruse.