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 is equivalent to stabilising a flag: upper triangular matrices are precisely those that preserve the standard flag, which is given by the standard ordered basis and the resulting flag < math > 0 <

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.

Though he is also concerned with freeing dance from pedestrian modes of activity, Merce Cunningham has selected a very different method for achieving his aim.

The `` approximate '' is important, because even after the order of the work has been established by the chance method, the result is not inviolable.

Let us not confuse the issue by labeling the objective or the method `` psychoanalytic '', for this is a well established term of art for the specific ideas and procedures initiated by Sigmund Freud and his followers for the study and treatment of disordered personalities.

It is the only method left for a man to escape from a woman's world.

The objective should be to provide a method of getting into print a higher percentage than is now possible of the relevant information in the possession of reporters and editors.

This condition will undoubtedly continue until such time as a state uniform system of evaluation is established, or through mutual agreement of the local assessing officials for a method of standard assessment practice to be adopted.

Another recent achievement was the successful development of a method for the complete combustion in a bomb calorimeter of a metal in fluorine when the product is relatively non-volatile.

Using Edgerton's method, the fast-closing action is obtained from the blackening of a window by exploding a series of parallel lead wires.

Since conventional methods are insensitive at the low frequencies of these molecular transitions, the paramagnetic resonance method is being used instead.

The method used in computing the allotments is specifically set forth in the Act.

The method used for computing the respective Federal and State shares in total program costs is specifically set forth in the Act.

Since the same method of shaping and fitting the dogs and notches is used throughout, we will only describe the construction of one locking bar.

Another method of assuring a clean hole is to first drill a small pilot hole all the way through, then drill half way with the dimensional bit, turn the piece over, and finish from the other side.

It is generally an inaccurate method of rating, for the horsepower is that of the compressor motor, and many other components beside it determine how much cooling you'll get.

The longer I work, the more I am sure that for me, at least, a workmanlike method is important.

One simple method of measuring the expansion of the heart is to tie a thin rubber tube, filled with mercury, around the heart and record the change in resistance as the tube is stretched.

One of the advantages of this method is that the `` pill '' can remain in the patient for several days, permitting observation under natural conditions.

The method used to scan the eye ultrasonically is illustrated in Fig. 6.

More unitized lumber is being shipped on flat cars, and NLRDA studies show that flat cars loaded with the new Type 6-B floating-load method can be unloaded for as little as $.054/mbf.

Although the Af calculation is obvious by analogy with that for gravitational field and osmotic pressure, it is interesting to confirm it by a method which can be generalized to include related effects.

The best way to determine the correct figure ( in captives ) is by direct observation of pairs isolated from birth, a method that produced surprising results: maturing of a male Indian python in less than two years, his mate in less than three ; ;

An example of a school that follows this method is the Musselburgh Grammar School in Scotland.

This method can be illustrated using a Venn diagram as follows.

The specialization restricting the meaning of " science " to natural science follows the rise of Baconian science, which contrasted " natural science " to scholasticism, the Aristotelean method of inquiring from first principles.

The Newton-Raphson method in one variable is implemented as follows:

It follows that another element of philosophical method, common in the work of nearly all philosophers, is philosophical criticism.

An alternative method for quickly constructing a sheepshank is as follows:

Thinking that the method tended to overvalue unsupported queens and undervalue supported jacks, Eric Crowhurst and Andrew Kambites refined the scale as follows:

* Few if any non-English speaking nations use the whole word teaching method. They do not have to ; phonics works for their language because it follows the alphabetic principle: the words are almost entirely spelled as they sound.

He disagreed with the method of answering scientific questions by deduction and described it as follows: " Having first determined the question according to his will, man then resorts to experience, and bending her to conformity with his placets, leads her about like a captive in a procession.

The traditional method of resolving the ambiguity is to observe whether or not another character quickly follows the escape character.

" The Raven " follows an unnamed narrator on a night in December who sits reading " forgotten lore " as a method to forget the loss of his love, Lenore.

The method is as follows:

One method for solving such a system is as follows.

The Lenstra elliptic curve factorization method to find a factor of the given number n works as follows:

The Steiner method of teaching is subsidised by the Government and follows the curriculum from the Federation of Steiner Schools in Flanders.

Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution.

One method for accurate determination of values on a logarithmic axis is as follows:

The steps of this method is summarized as follows.

Printing the finished plate is the same for either method, and follows the normal way for an intaglio plate ; the whole surface is inked, the ink is then wiped off the surface to leave ink only in the pits of the still rough areas below the original surface of the plate.

The chambering method follows a system whereby planks of paulownia are selected and the rocker of the board is cut into each.

An alternative method of obtaining a Bachelor's degree is as follows.

This follows the sine function rather than the tangent function and this method diverges from the " rise over run " method as angles start getting larger ( see small-angle formula ).

The present statute specifies both process and method as follows:

The exact interpretations are unknown, but it probably follows a similar method to aleuromancy.