Austroasiatic languagesThe Austroasiatic languages ˌɒstroʊ.eɪʒiˈætɪk,_ˌɔː- , are a large language family in Mainland Southeast Asia, South Asia and East Asia. These languages are scattered throughout parts of Thailand, Laos, India, Myanmar, Malaysia, Bangladesh, Nepal, and southern China. Austroasiatic constitute the majority languages of Vietnam and Cambodia. There are around 117 million speakers of Austroasiatic languages, of which more than two-thirds are Vietnamese speakers. Of these languages, only Vietnamese, Khmer, and Mon have a long-established recorded history.
Cylindrical coordinate systemA cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.
Spherical coordinate systemIn mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.
Gödel's completeness theoremGödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything universally true is provable".
Combinatorial proofIn mathematics, the term combinatorial proof is often used to mean either of two types of mathematical proof: A proof by double counting. A combinatorial identity is proven by counting the number of elements of some carefully chosen set in two different ways to obtain the different expressions in the identity. Since those expressions count the same objects, they must be equal to each other and thus the identity is established. A bijective proof. Two sets are shown to have the same number of members by exhibiting a bijection, i.
Restriction siteRestriction sites, or restriction recognition sites, are located on a DNA molecule containing specific (4-8 base pairs in length) sequences of nucleotides, which are recognized by restriction enzymes. These are generally palindromic sequences (because restriction enzymes usually bind as homodimers), and a particular restriction enzyme may cut the sequence between two nucleotides within its recognition site, or somewhere nearby. For example, the common restriction enzyme EcoRI recognizes the palindromic sequence GAATTC and cuts between the G and the A on both the top and bottom strands.
Combinatorial principlesIn proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements. The pigeonhole principle often ascertains the existence of something or is used to determine the minimum or maximum number of something in a discrete context.
RoleA role (also rôle or social role) is a set of connected behaviors, rights, obligations, beliefs, and norms as conceptualized by people in a social situation. It is an expected or free or continuously changing behavior and may have a given individual social status or social position. It is vital to both functionalist and interactionist understandings of society. Social role theory posits the following about social behavior: The division of labour in society takes the form of the interaction among heterogeneous specialized positions, we call roles.
Bounded setIn mathematical analysis and related areas of mathematics, a set is called bounded if it is, in a certain sense, of finite measure. Conversely, a set which is not bounded is called unbounded. The word "bounded" makes no sense in a general topological space without a corresponding metric. Boundary is a distinct concept: for example, a circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary. A bounded set is not necessarily a closed set and vice versa.
Role-playingRole-playing or roleplaying is the changing of one's behaviour to assume a role, either unconsciously to fill a social role, or consciously to act out an adopted role. While the Oxford English Dictionary offers a definition of role-playing as "the changing of one's behaviour to fulfill a social role", in the field of psychology, the term is used more loosely in four senses: To refer to the playing of roles generally such as in a theatre, or educational setting; To refer to taking a role of a character or person and acting it out with a partner taking someone else's role, often involving different genres of practice; To refer to a wide range of games including role-playing video game (RPG), play-by-mail games and more; To refer specifically to role-playing games.
Restriction enzymeA restriction enzyme, restriction endonuclease, REase, ENase or restrictase is an enzyme that cleaves DNA into fragments at or near specific recognition sites within molecules known as restriction sites. Restriction enzymes are one class of the broader endonuclease group of enzymes. Restriction enzymes are commonly classified into five types, which differ in their structure and whether they cut their DNA substrate at their recognition site, or if the recognition and cleavage sites are separate from one another.
SphereA sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry.
