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Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a Hungarian-British mathematician who mainly worked in graph theory. [1] He served as Erasmus Smith's Professor of Mathematics at Trinity College Dublin from 1964 to 1966. [2] In 1952, he gave a sufficient condition for a graph to contain a Hamiltonian circuit.
Itô integral Y t (B) (blue) of a Brownian motion B (red) with respect to itself, i.e., both the integrand and the integrator are Brownian. It turns out Y t (B) = (B 2 − t)/2. Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process).
In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. [1] More generally, the term motion is a synonym for surjective isometry in metric geometry, [2] including elliptic geometry and hyperbolic ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
It separates — hence the name — the phase space into two distinct areas, each with a distinct type of motion. The region inside the separatrix has all those phase space curves which correspond to the pendulum oscillating back and forth, whereas the region outside the separatrix has all the phase space curves which correspond to the pendulum ...
This motion is the most obscure as it is not physical motion, but rather a change in the very nature of the universe. The primary source of verification of this expansion was provided by Edwin Hubble who demonstrated that all galaxies and distant astronomical objects were moving away from Earth, known as Hubble's law , predicted by a universal ...
Lagrange and Laplace were the first to advance the view that the so-called "constants" which describe the motion of a planet around the Sun gradually change: They are "perturbed", as it were, by the motion of other planets and vary as a function of time; hence the name "perturbation theory". [12]
(A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation.