LinearizationIn mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
Stochastic simulationA stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values. These steps are repeated until a sufficient amount of data is gathered. In the end, the distribution of the outputs shows the most probable estimates as well as a frame of expectations regarding what ranges of values the variables are more or less likely to fall in.
Disjunctive normal formIn boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if it is a disjunction of one or more conjunctions of one or more literals. A DNF formula is in full disjunctive normal form if each of its variables appears exactly once in every conjunction.
Algebraic normal formIn Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), Zhegalkin normal form, or Reed–Muller expansion is a way of writing propositional logic formulas in one of three subforms: The entire formula is purely true or false: One or more variables are combined into a term by AND (), then one or more terms are combined by XOR () together into ANF. Negations are not permitted: The previous subform with a purely true term: Formulas written in ANF are also known as Zhegalkin polynomials and Positive Polarity (or Parity) Reed–Muller expressions (PPRM).
Resonant trans-Neptunian objectIn astronomy, a resonant trans-Neptunian object is a trans-Neptunian object (TNO) in mean-motion orbital resonance with Neptune. The orbital periods of the resonant objects are in a simple integer relations with the period of Neptune, e.g. 1:2, 2:3, etc. Resonant TNOs can be either part of the main Kuiper belt population, or the more distant scattered disc population. The diagram illustrates the distribution of the known trans-Neptunian objects. Resonant objects are plotted in red.
NeptuneNeptune is the eighth planet from the Sun and the farthest IAU-recognized planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times the mass of Earth, and slightly more massive than its near-twin Uranus. Neptune is denser and physically smaller than Uranus because its greater mass causes more gravitational compression of its atmosphere. Being composed primarily of gases and liquids, it has no well-defined solid surface.
Stephen HawkingStephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author who, at the time of his death, was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at the University of Cambridge, widely viewed as one of the most prestigious academic posts in the world. Hawking was born in Oxford into a family of physicians.
