Abstractly, an array reference is simply a procedure of two arguments: an array and a subscript vector, which could be expressed as ; but many languages provide special syntax like ; similarly an array element update is abstractly something like, but many languages provide syntax like.

Abstractly, the probability model for a classifier is a conditional model

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Abstractly, this circle is a cyclic group of order twelve, and may be identified with the residue classes modulo twelve.

Abstractly, it can be defined as the integer triples ( a, b, c ), associated to 3 < sup > a </ sup > 5 < sup > b </ sup > 7 < sup > c </ sup >, where the distance measure is not the usual Euclidean distance but rather the Euclidean distance deriving from the vector space norm

Abstractly, in trying to prove a proposition P, one assumes that it is false, and that therefore there is at least one counterexample.

Abstractly we can say that this is a projective line in the space of all conics, on which we take

Abstractly, these are the left adjoint and right adjoint, respectively, to the inclusion functors of in D. In addition, the truncation functors fit into a triangle, and this is in fact the unique triangle satisfying the third axiom above:

Abstractly it is assumed that the economy consists only of capitalist production and that the capitalist economy is equal to capitalist society.

Abstractly, the method is as follows:

Abstractly, a hierarchy can be modelled mathematically as a rooted tree: the root of the tree forms the top level, and the children of a given vertex are at the same level, below their common parent.

Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these.

He mentions the beats only once '', when he refers to their having revived through mere power and abandonment and the unwillingness to, commit death in life some idea of a decent equivalent between verbal expression and actual experience,, but the entire narrative, is written in the tiresome vocabulary `` of '' that lost `` and '' dying cause, `` and in the '' `` sprung syntax that is supposed to supplant, our mother, tongue.

In the event the total of rupees accruing to the Government of the United States of America as a consequence of sales made pursuant to this Agreement is different from the rupee equivalent of $1,276 million, the amounts available for the purposes specified in paragraph 1, Article 2, will be adjusted proportionately.

In these readings, the double bass is either kept discreetly in the background, or it is dressed in clown's attire -- the musical equivalent of a bull in a china shop.

The cross-sectional area of the cylinders is determined and then the volume of the individual cylinders is computed by multiplying the area by the stroke length, which is the equivalent of the length of the cylinders.

It is well to bear in mind that gasoline will cost from $.80 to $.90 for the equivalent of a United States gallon and while you might prefer a familiar Ford, Chevrolet or even a Cadillac, which are available in some countries, it is probably wiser to choose the smaller European makes which average thirty, thirty-five and even forty miles to the gallon.

For example, when the film is only four minutes old, Neitzbohr refers to a small, Victorian piano stool as `` Wilhelmina '', and we are thereupon subjected to a flashback that informs us that this very piano stool was once used by an epileptic governess whose name, of course, was Doris ( the English equivalent, when passed through middle-Gaelic derivations, of Wilhelmina ).

It is convenient to classify a child's onset ages and completion ages as `` advanced '', `` moderate '' ( modal ), or `` delayed '' according to whether the child's age equivalent `` dots '' appeared to the left of, upon, or to the right of the appropriate short transverse line.

when it represents only itself and on which is its complement ( so that go on is semantically equivalent to board ), on has stronger stress than go does.

When I have instructions to leave is equivalent in meaning to I have instructions that I am to leave this place, dominant stress is ordinarily on leave.

When the same sequence is equivalent in meaning to I have instructions which I am to leave, dominant stress is ordinarily on instructions.

In the first of these sentences if by is the complement of come and Tuesday is an adjunct of time equivalent to on Tuesday, there will be strong stress on by in the spoken language ; ;

In the second sentence if drinking water is a gerundial clause and without drinking water is roughly equivalent in meaning to unless I drink water, there will be stronger stress on water than on drinking ; ;

but if drinking is a gerundial noun modifying water and without drinking water is equivalent to without water for drinking, there will be stronger stress on drinking than on water.

In the Steiners have busy lives without visiting relatives only context can indicate whether visiting relatives is equivalent in meaning to paying visits to relatives or to relatives who are visiting them, and in I looked up the number and I looked up the chimney only the meanings of number and chimney make it clear that up is syntactically a second complement in the first sentence and a preposition followed by its object in the second.

Many Esperantists believe this declaration stabilising the language is a major reason why the Esperanto speaker community grew beyond the levels attained by other constructed languages and has developed a flourishing culture.

The island's climate is warm and moderate, categorised as Temperate, Mediterranean ( Csa ), with modest variation due to the stabilising effect of the surrounding sea.

The effect of these added interactions on the stability of the Solar System is very small, but at first it was not known whether they might add up over longer periods to significantly change the orbital parameters and lead to a completely different configuration, or whether some other stabilising effects might maintain the configuration of the orbits of the planets.

This particular adaptation of the mixed market economy is characterised by more generous welfare states ( relative to other developed countries ), which are aimed specifically at enhancing individual autonomy, ensuring the universal provision of basic human rights and stabilising the economy.

The opposite of this is a lifting body which has no wings, though it may have small stabilising and control surfaces.

This direction of movement of the center of pressure on a reflex-cambered airfoil is stabilising, and a horizontal stabiliser is not necessary.

In Europe, Ammophila arenaria has a coastal distribution, and is the dominant species on sand dunes where it is responsible for stabilising and building the foredune by capturing blown sand and binding it together with the warp and weft of its tough, fibrous rhizome system.

The turret is fitted with the 2K23 system which consists of an automatic loader with 22 rounds ( the remaining 18 rounds are stored in the hull ), a ballistic computer 1V539, a cross-wind sensor, a 2E52-2 stabilising system, the 1D16-3 laser range finder, the 1K13-2 gunner's sight / guidance device, the PPB-1 gunner's sight and an OU-5-1 IR search light.

The baton is lifted, struck, or stroked alternately by the two control sticks (' handsticks ' or ' sidesticks '), stabilising the baton through gyroscopic motion.

In Pilates the aim throughout most stabilising exercises is to maintain these natural curves and create a neutral position for each joint that is close to its optimal alignment.

Due to the seas very much ' surrounding ' the land the area sees a significant effect of the North Atlantic drift, which ensures that the land is cooled in the summer and warmed in the winter, producing a stabilising effect on the temperatures.

The wild plant is planted as a nurse or cover crop, or stabilising plant in land reclamation and specialised landscaping schemes.

The Moon is large enough for its gravity to affect the Earth, stabilising its orbit and producing the regular ebb and flow of the tides.

A partially hollow blade ( 1 / 2 or 1 / 4 for example ) cannot sustain the same degree of sharpness for as long, because as the cutting edge erodes it can eventually reach the stabilising ridge faster, but it is more stable because it is less hollow.

The section has therefore initiated or participated a number of such treatment studies of new atypical antipsychotics and potential mood stabilising medication and is also developing computerised and web-based applications for disease self-management.

It is hoped that telepathic groups, bonded in polymorphous sexual relationships, will form a socially stabilising replacement for the " obsolescent family unit ".

Some restoration work has been carried and it is possible to visit the newly restored gravestones of two famous locals: Johannes Thienemann ( 1863-1938 ), the German ornithologist who founded the Rossitten Bird Observatory ; and Franz Epha, the legendary dune inspector who was able to stop the huge sand dunes from moving by stabilising them with plants.

Again, there is the vexed question of how to assess stabilising selection as contributing to advanced status ; empirically we can see very little reason to regard say, a simple-looking living Onychophoran as anything but primitive, when it is hardly distinguishable from a fossil half a billion years old, but that is no coincidence ; its stable anatomy endured for hundreds of millions of years during which any specimen deviating too far from the norm reproduced poorly.