Subject (grammar)The subject in a simple English sentence such as John runs, John is a teacher, or John drives a car, is the person or thing about whom the statement is made, in this case John. Traditionally the subject is the word or phrase which controls the verb in the clause, that is to say with which the verb agrees (John is but John and Mary are). If there is no verb, as in Nicola - what an idiot!, or if the verb has a different subject, as in John - I can't stand him!, then 'John' is not considered to be the grammatical subject, but can be described as the topic of the sentence.
Madhava seriesIn mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are: All three series were later independently discovered in 17th century Europe.
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.
Series (mathematics)In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance.
Null-subject languageIn linguistic typology, a null-subject language is a language whose grammar permits an independent clause to lack an explicit subject; such a clause is then said to have a null subject. In the principles and parameters framework, the null subject is controlled by the pro-drop parameter, which is either on or off for a particular language. Typically, null-subject languages express person, number, and/or gender agreement with the referent on the verb, rendering a subject noun phrase redundant.
Separable extensionIn field theory, a branch of algebra, an algebraic field extension is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). There is also a more general definition that applies when E is not necessarily algebraic over F. An extension that is not separable is said to be inseparable.
Purely inseparable extensionIn algebra, a purely inseparable extension of fields is an extension k ⊆ K of fields of characteristic p > 0 such that every element of K is a root of an equation of the form xq = a, with q a power of p and a in k. Purely inseparable extensions are sometimes called radicial extensions, which should not be confused with the similar-sounding but more general notion of radical extensions. An algebraic extension is a purely inseparable extension if and only if for every , the minimal polynomial of over F is not a separable polynomial.
Digital imagingDigital imaging or digital image acquisition is the creation of a digital representation of the visual characteristics of an object, such as a physical scene or the interior structure of an object. The term is often assumed to imply or include the , , , printing and display of such images. A key advantage of a , versus an analog image such as a film photograph, is the ability to digitally propagate copies of the original subject indefinitely without any loss of image quality.
Group extensionIn mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If and are two groups, then is an extension of by if there is a short exact sequence If is an extension of by , then is a group, is a normal subgroup of and the quotient group is isomorphic to the group . Group extensions arise in the context of the extension problem, where the groups and are known and the properties of are to be determined.
GradualismGradualism, from the Latin gradus ("step"), is a hypothesis, a theory or a tenet assuming that change comes about gradually or that variation is gradual in nature and happens over time as opposed to in large steps. Uniformitarianism, incrementalism, and reformism are similar concepts. In the natural sciences, gradualism is the theory which holds that profound change is the cumulative product of slow but continuous processes, often contrasted with catastrophism.
