In the third category the function is double-valued in this interval.

For example, the parent function y = 1 / x has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant.

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

In this sense, the function and are single-valued and continuous, with continuous derivatives with respect to space and time to whatever order is required, usually to the second or third.

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

Hexameters also have a primary caesura — a break in sense, much like the function of a comma in prose — at one of several normal positions: After the first syllable in the third foot ( the " masculine " caesura ); after the second syllable in the third foot if the third foot is a dactyl ( the " feminine " caesura ); after the first syllable of the fourth foot ; or after the first syllable of the second foot ( the latter two often occur together in a line, breaking it into three separate units ).

“ This doctrine is rooted in Aristotle's conception of the soul, and has antecedents in Hobbes's conception of the mind as a ‘ calculating machine ’, but it has become fully articulated ( and popularly endorsed ) only in the last third of the 20th century .” In so far as it mediates stimulus and response, a mental function is analogous to a program that processes input / output in automata theory.

An example of a projection is the function π < sub > xy </ sub > defined by, which projects an arbitrary point in 3D space to a point on the x – y-plane, where the third coordinate ( z ) is equal to 0.

In Haskell syntax, "" prepends an element to a list, returns a list without its first element, and uses a specified function ( in this case addition ) to combine corresponding elements of two lists to produce a third.

When the third protection level key scheme is used it affects the distribution of a message through the container ( see figure The Third Protection Level Scheme, where F ( P, L ) – distribution function of a message within a container ; P – minimum number of container samples that are needed to embed one message sample ; L – step of a message distribution within a container ).

The introduction of a third electrode, a grid between the filament and the plate, also yields another function.

We can use the three-dimensional theory to solve this problem if we regard u as a function in three dimensions that is independent of the third dimension.

The primary reason for this reluctance to upgrade is that many XMMS plugins ( written by third parties ) are dependent on the older version of GTK + to properly function ( e. g. about boxes and configuration dialogs ).

Given this relationship of public capital and productivity, public capital becomes a third input in the standard, neoclassical production function:

Others argue that NGOs are often imperialist in nature, that they sometimes operate in a racialized manner in third world countries, and that they fulfill a similar function to that of the clergy during the high colonial era.

The regulatory function of LINX is mainly to represent the member ISPs ( as a group ) to these third parties, respond to consultations, and report to and consult with the LINX members regarding any developments that may affect their business or operations.

The third fire had the function of protecting the offerers from attacks of evil spirits and was placed to the South, considered a dangerous direction.

Asymmetric information creates incentives for the party with more information to cheat the party with less information ; as a result, a number of market structures have developed, including warranties and third party authentication, which enable markets with asymmetric information to function.

If a risk averse consumer has a utility function over consumption x, and if is differentiable, then the consumer is not prudent unless the third derivative of utility is positive, that is,.

Included in a number of the structural features that can be recognized in all protein tyrosine kinases are an ATP binding site, three residues that are thought to be associated with the function of the third phosphate group ( often called the gamma-phosphate group ) of an ATP molecule bound to the enzyme, and a possible catalytic site of the enzyme that is an amino acid.

The third important theory of hippocampal function relates the hippocampus to space.

Carl Friedrich Gauss introduced the square bracket notation for the floor function in his third proof of quadratic reciprocity ( 1808 ).

A third, one of at least equal and perhaps even greater importance, is now being traversed: American immersion and involvement in world affairs.

Inevitably, the surviving evidence is not complete enough to determine whether one should interpret, with older scholars, that he wisely curtailed the activities of the Roman Empire to a careful minimum, or perhaps that he was uninterested in events away from Rome and Italy and his inaction contributed to the pressing troubles that faced not only Marcus Aurelius but also the emperors of the third century.

In baseball's earlier decades, a runner on second base could " steal " first base, perhaps with the intention of drawing a throw that might allow a runner on third to score ( a tactic famously employed by Germany Schaefer ).

There is a third view that sees merit in both arguments above and attempts to bridge them, and so cannot be articulated as starkly as they can ; it sees more than one Christianity and more than one attitude towards paganism at work in the poem, separated from each other by hundreds of years ; it sees the poem as originally the product of a literate Christian author with one foot in the pagan world and one in the Christian, himself a convert perhaps or one whose forbears had been pagan, a poet who was conversant in both oral and literary milieus and was capable of a masterful " repurposing " of poetry from the oral tradition ; this early Christian poet saw virtue manifest in a willingness to sacrifice oneself in a devotion to justice and in an attempt to aid and protect those in need of help and greater safety ; good pagan men had trodden that noble path and so this poet presents pagan culture with equanimity and respect ; yet overlaid upon this early Christian poet's composition are verses from a much later reformist " fire-and-brimstone " Christian poet who vilifies pagan practice as dark and sinful and who adds satanic aspects to its monsters.

The first line represents the subject, the second the author ( and perhaps title ), the third and fourth dates of editions, indications of translations, and critical works on particular books or authors.

At least a third of the Red terror and perhaps most of the White terror was centrally led.

Following a proposal put forward by The Welwyn Garden Heritage Trust, town-planner Andrés Duany has suggested that designated " Garden Villages " could be built within Hertfordshire to relieve some of the pressure for new homes, with perhaps a third Garden City to follow.

Following the Industrial Revolution, perhaps a third of the world's economic output is derived from manufacturing industries — more than agriculture's share.

The driver may have a defense to those allegations, perhaps if the accident occurred at low speed, and was unavoidable ( maybe due to some third party intervention ).

The injured person may, however, argue that the driver was still responsible ( perhaps the driver should have used the horn of the vehicle to alert the third party ), or there may be other allegations.

In the miniatures of this style, the emphasis seems to be more on the posture of the player than the detail of their faces ; this crossed, lounging style is only found in the folios of the Libro de tablas, the third section of the Libro de juegos which explicates the game of backgammon, again perhaps indicative of the work of a particular artist.

The third section is perhaps the most complex, and attempts to convey the concepts and language necessary to describe behavior and conversation between individuals.

Even on the CoCo, a quite minimalist hardware platform, it was possible under OS-9 / 6809 Level One to have more than one interactive user running concurrently ( for example, one on the console keyboard, another in the background, and perhaps a third interactively via a serial connection ) as well as several other non-interactive processes.

The third, and perhaps best, alternative starting positions have been designed to make the formation of stalemate wedges less likely.

From the late third millennium BC until the 8th century BC it was inhabited by peoples called Opici and Osci ( perhaps Askenazi ) and also by Oenotrians, Phoenicians, Mycenaeans, Ausones, Sicilians, Morgeti and Itali.

The key idea behind AFH is to use only the “ good ” frequencies, by avoiding the " bad " frequency channels — perhaps those " bad " frequency channels are experiencing frequency selective fading, or perhaps some third party is trying to communicate on those bands, or perhaps those bands are being actively jammed.

Ælfthryth was the widow of Æthelwald, Ealdorman of East Anglia and perhaps Edgar's third wife.

* A third possibility advanced by Ernst Wilhelm Hengstenberg is that Iscariot means " the liar " or " the false one ," perhaps from the Hebrew File: HebrewIscariot-1. jpg.

Co-written with William Rowley and perhaps a third collaborator, who may have been Philip Massinger or Thomas Heywood.

Joan à Beckett Weigall was born in St Kilda East, Victoria, Australia, the third daughter of They're à Beckett Weigall, a prominent judge who was related to the Boyd family, perhaps Australia's most famous and prolific artistic dynasty.

Graves tells that Turner would outline a scene, sit doing nothing for two or three days, then suddenly, " perhaps on the third day, he would exclaim ' there it is ', and seizing his colours work rapidly till he had noted down the peculiar effect he wished to fix in his memory.

Broadwater County is perhaps best known as the home of Canyon Ferry Lake, the third largest body of water in Montana.

* The quinze-et-le-va ( fifteen and the go ): attending the player's humour, who, perhaps, was resolved to follow his fancy, and still lay his money upon the same card, which was done by crooking the third corner of his card.