Dirichlet's unit theoremIn mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a positive real number that determines how "dense" the units are. The statement is that the group of units is finitely generated and has rank (maximal number of multiplicatively independent elements) equal to where r1 is the number of real embeddings and r2 the number of conjugate pairs of complex embeddings of K.
Algebraic number fieldIn mathematics, an algebraic number field (or simply number field) is an extension field of the field of rational numbers such that the field extension has finite degree (and hence is an algebraic field extension). Thus is a field that contains and has finite dimension when considered as a vector space over . The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
Outcome (probability)In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space. For the experiment where we flip a coin twice, the four possible outcomes that make up our sample space are (H, T), (T, H), (T, T) and (H, H), where "H" represents a "heads", and "T" represents a "tails".
Korean languageKorean (South Korean: , hangugeo; North Korean: , chosŏnmal) is the native language for about 80 million people, mostly of Korean descent. It is the official and national language of both North Korea and South Korea (geographically Korea). The two countries have established standardized norms for Korean, and the differences between them are similar to those between Standard Chinese in mainland China and Taiwan, but political conflicts between the two countries have highlighted the differences between them.
ZebuThe zebu (ˈziːb(j)uː,_ˈzeːbuː; Bos indicus or Bos taurus indicus), sometimes known in the plural as indicine cattle or humped cattle, is a species or subspecies of domestic cattle originating in the Indian sub-continent. Zebu are characterised by a fatty hump on their shoulders, a large dewlap, and sometimes drooping ears. They are well adapted to withstanding high temperatures, and are farmed throughout the tropical countries, both as pure zebu and as hybrids with taurine cattle, the other main type of domestic cattle.
Sample spaceIn probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.
GaurThe gaur (Bos gaurus; ɡaʊər), also known as the Indian bison, is a bovine native to South Asia and Southeast Asia, and has been listed as Vulnerable on the IUCN Red List since 1986. The global population was estimated at a maximum of 21,000 mature individuals in 2016, with the majority of those existing in India. It has declined by more than 70% during the last three generations, and is extirpated from Sri Lanka and most likely Bangladesh. Populations in well-protected areas are stable and increasing.
PolynomialIn mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1. Polynomials appear in many areas of mathematics and science.
DiophantusDiophantus of Alexandria (born AD 200-214; died AD 284-298) was a Greek mathematician, who was the author of a series of books called Arithmetica, many of which are now lost. His texts deal with solving algebraic equations. Diophantine equations, Diophantine geometry, and Diophantine approximations are subareas of Number theory that are named after him. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality.
Topic and commentIn linguistics, the topic, or theme, of a sentence is what is being talked about, and the comment (rheme or focus) is what is being said about the topic. This division into old vs. new content is called information structure. It is generally agreed that clauses are divided into topic vs. comment, but in certain cases the boundary between them depends on which specific grammatical theory is being used to analyze the sentence. The topic of a sentence is distinct from the grammatical subject.
CausalityCausality (also called causation, or cause and effect) is influence by which one event, process, state, or object (a cause) contributes to the production of another event, process, state, or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause. In general, a process has many causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future.
Causal inferenceCausal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed. The science of why things occur is called etiology, and can be described using the language of scientific causal notation. Causal inference is said to provide the evidence of causality theorized by causal reasoning.
