If T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).

The arithmetic mean of a variable is often denoted by a bar, for example ( read " x bar ") would be the mean of some sample space.

Though the word atom originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles.

For any real number the absolute value or modulus of is denoted by ( a vertical bar on each side of the quantity ) and is defined as

It turns out that a more suitable quantity for updating is the sum of squares of differences from the ( current ) mean,, here denoted:

The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

The automorphism group of an object X in a category C is denoted Aut < sub > C </ sub >( X ), or simply Aut ( X ) if the category is clear from context.

The automorphism group is sometimes denoted Diff ( M ).

The inner automorphisms form a normal subgroup of Aut ( G ), denoted by Inn ( G ); this is called Goursat's lemma.

The quotient group Aut ( G ) / Inn ( G ) is usually denoted by Out ( G ); the non-trivial elements are the cosets that contain the outer automorphisms.

After describing the manifestation of the Gospel in the Ogdoad and Hebdomad, he adds that the Basilidians have a long account of the innumerable creations and powers in the several ' stages ' of the upper world ( diastemata ), in which they speak of 365 heavens and say that " their great archon " is Abrasax, because his name contains the number 365, the number of the days in the year ; i. e. the sum of the numbers denoted by the Greek letters in ΑΒΡΑΣΑΞ according to the rules of isopsephy is 365:

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

Run-time analysis is a theoretical classification that estimates and anticipates the increase in running time ( or run-time ) of an algorithm as its input size ( usually denoted as n ) increases.

An abelian group is a set, A, together with an operation "•" that combines any two elements a and b to form another element denoted.

These two sequences converge to the same number, which is the arithmetic – geometric mean of and ; it is denoted by, or sometimes by.

In baseball statistics, a hit ( denoted by H ), also called a base hit, is credited to a batter when the batter safely reaches first base after hitting the ball into fair territory, without the benefit of an error or a fielder's choice.

In baseball statistics, a player is credited with a plate appearance ( denoted by PA ) each time he completes a turn batting.

The statement ( x, y ) ∈ R is read " x is R-related to y ", and is denoted by xRy or R ( x, y ).

It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.

The place is inhabited by several hundred warlike women who are anachronisms of the Twentieth Century -- stone age amazons who live in an all-female, matriarchal society which is self-sufficient ''.

since Bourbon whiskey, though of Kentucky origin, is at least as much favored by liberals in the North as by conservatives in the South.

In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.

But apart from racial problems, the old unreconstructed South -- to use the moderate words favored by Mr. Thomas Griffith -- finds itself unsympathetic to most of what is different about the civilization of the North.

The two main charges levelled against the Bourbons by liberals is that they are racists and social reactionaries.

It became the sole `` subject '' of `` international law '' ( a term which, it is pertinent to remember, was coined by Bentham ), a body of legal principle which by and large was made up of what Western nations could do in the world arena.

Ratified in the Republican Party victory in 1952, the Positive State is now evidenced by political campaigns being waged not on whether but on how much social legislation there should be.

He was, and is, with the RAND Corporation, a nonprofit pool of thinkers financed by the U.S. Air Force.

They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.

It is softened by the saltbush and the bluebush, has a peaceful quality, the hills roll softly.

On Fridays, the day when many Persians relax with poetry, talk, and a samovar, people do not, it is true, stream into Chehel Sotun -- a pavilion and garden built by Shah Abbas 2, in the seventeenth century -- but they do retire into hundreds of pavilions throughout the city and up the river valley, which are smaller, more humble copies of the former.

Poetry in Persian life is far more than a common ground on which -- in a society deeply fissured by antagonisms -- all may stand.

Nostalgic Yankee readers of Erskine Caldwell are today informed by proud Georgians that Tobacco Road is buried beneath a four-lane super highway, over which travel each day suburbanite businessmen more concerned with the Dow-Jones average than with the cotton crop.

All but the most rabid of Confederate flag wavers admit that the Old Southern tradition is defunct in actuality and sigh that its passing was accompanied by the disappearance of many genteel and aristocratic traditions of the reputedly languid ante-bellum way of life.

Westbrook further bemoans the Southern writers' creation of an unreal image of their homeland, which is too readily assimilated by both foreign readers and visiting Yankees: `` Our northerner is suspicious of all this crass evidence ( of urbanization ) presented to his senses.

As his disciples boast, even though his emphasis is elsewhere, Faulkner does show his awareness of the changing order of the South quite keenly, as can be proven by a quick recalling of his Sartoris and Snopes families.

The unit of form is determined subjectively: `` the Heart, by the way of the Breath, to the Line ''.

The family moved north across the Ohio River to free ( i. e., non-slave ) territory and made a new start in what was then Perry County but is now Spencer County, Indiana.

Altruism is a motivation to provide something of value to a party who must be anyone but oneself, while duty focuses on a moral obligation towards a specific individual ( e. g., a god, a king ), or collective ( e. g., a government ).

* One-way ANOVA is used to test for differences among two or more independent groups ( means ), e. g. different levels of urea application in a crop.

* Repeated measures ANOVA is used when the same subjects are used for each treatment ( e. g., in a longitudinal study ).

The number of carbon atoms is used to define the size of the alkane ( e. g., C < sub > 2 </ sub >- alkane ).

The names were abandoned in Latin, which instead referred to the letters by adding a vowel ( usually e ) before or after the consonant ( the exception is zeta, which was retained from Greek ).

An argument of this form is invalid, i. e., the conclusion can be false even when statements 1 and 2 are true.

A relatively recent role for amateur astronomers is searching for overlooked phenomena ( e. g., Kreutz Sungrazers ) in the vast libraries of digital images and other data captured by Earth and space based observatories, much of which is available over the Internet.

He thought that certain uses of the verb " to be ", called the " is of identity " and the " is of predication ", were faulty in structure, e. g., a statement such as, " Elizabeth is a fool " ( said of a person named " Elizabeth " who has done something that we regard as foolish ).

Phytomelan is not unique to Asparagales ( i. e. it is not a synapomorphy ) but it is common within the order and rare outside it.

The flower is typically somewhat zygomorphic ( i. e. not radially symmetrical ) and has nectaries.

For example, " aloin " is derived from Aloe vera and Aloe ferox and has important medical uses ( e. g. as a laxative and in the treatment of burns ) as well as cosmetic uses ( e. g. in skin and hair products ).

Another theory by Yule and Burnell ( 1886 ) is based on an entry in the Catalogue of Indian Serpents from the Leyden Museum ( Ray, 1693 ) that reads: Anacondaia Zeylonensibus, id est Bubalorum aliorumque jumentorum membra conterens, meaning " the anacondaia of the Ceylonese, i. e. he that crushes the limbs of buffaloes and yoke beasts.

* There exists a model of ZF ¬ C in which there is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i. e., for any sequence

The Aegean Sea (;, Aigaio Pelagos ; or historically ) is an elongated embayment of the Mediterranean Sea located between the southern Balkan and Anatolian peninsulas, i. e., between the mainlands of Greece and Turkey.

According to Tillich, the last of these three types of existential anxiety, i. e. spiritual anxiety, is predominant in modern times while the others were predominant in earlier periods.