Asymptotic expansionIn mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function.
Cardinality of the continuumIn set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers , sometimes called the continuum. It is an infinite cardinal number and is denoted by (lowercase Fraktur "c") or . The real numbers are more numerous than the natural numbers . Moreover, has the same number of elements as the power set of Symbolically, if the cardinality of is denoted as , the cardinality of the continuum is This was proven by Georg Cantor in his uncountability proof of 1874, part of his groundbreaking study of different infinities.
Superfluid helium-4Superfluid helium-4 is the superfluid form of helium-4, an isotope of the element helium. A superfluid is a state of matter in which matter behaves like a fluid with zero viscosity. The substance, which looks like a normal liquid, flows without friction past any surface, which allows it to continue to circulate over obstructions and through pores in containers which hold it, subject only to its own inertia. The formation of the superfluid is known to be related to the formation of a Bose–Einstein condensate.
Hybrid regimeA hybrid regime is a type of political system often created as a result of an incomplete democratic transition from an authoritarian regime to a democratic one (or vice versa). Hybrid regimes are categorized as having a combination of autocratic features with democratic ones and can simultaneously hold political repressions and regular elections. Hybrid regimes are commonly found in developing countries with abundant natural resources such as petro-states.
Percolation thresholdThe percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them.
Beth numberIn mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written , where is the second Hebrew letter (beth). The beth numbers are related to the aleph numbers (), but unless the generalized continuum hypothesis is true, there are numbers indexed by that are not indexed by . Beth numbers are defined by transfinite recursion: where is an ordinal and is a limit ordinal.
AuthoritarianismAuthoritarianism is a political system characterized by the rejection of political plurality, the use of strong central power to preserve the political status quo, and reductions in the rule of law, separation of powers, and democratic voting. Political scientists have created many typologies describing variations of authoritarian forms of government. Authoritarian regimes may be either autocratic or oligarchic and may be based upon the rule of a party or the military.
Limit cardinalIn mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. These cardinals are sometimes called simply "limit cardinals" when the context is clear. A cardinal λ is a strong limit cardinal if λ cannot be reached by repeated powerset operations. This means that λ is nonzero and, for all κ < λ, 2κ < λ.
Gamma distributionIn probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter and a scale parameter . With a shape parameter and an inverse scale parameter , called a rate parameter. In each of these forms, both parameters are positive real numbers.
TotalitarianismTotalitarianism is a form of government and a political system that prohibits all opposition parties, outlaws individual and group opposition to the state and its claims, and exercises an extremely high if not complete degree of control and regulation over public and private life. It is regarded as the most extreme and complete form of authoritarianism. In totalitarian states, political power is often held by autocrats, such as dictators (totalitarian dictatorship) and absolute monarchs, who employ all-encompassing campaigns in which propaganda is broadcast by state-controlled mass media in order to control the citizenry.
