In concluding this section, we should like to give an example which illustrates some of the ideas of the primary decomposition theorem.

Agate is one of the most common materials used in the art of hardstone carving, and has been recovered at a number of ancient sites, indicating its widespread use in the ancient world ; for example, archaeological recovery at the Knossos site on Crete illustrates its role in Bronze Age Minoan culture.

: For example, picture 1 above illustrates the concrete relationship " Cat sits on Mat ".

The use of personal names as rhymes continued into the late 20th century, for example " Tony Blairs " meaning " flares ", as in trousers with a wide bottom ( previously this was " Lionel Blairs " and this change illustrates the ongoing mutation of the forms of expression ) and " Britney Spears ", meaning " beers ".

Similarly, some additional assumption is needed besides the Cauchy – Riemann equations ( such as continuity ), as the following example illustrates

The following example game illustrates a player trying to guess the word hangman using a strategy based solely on letter frequency.

This example illustrates a common occurrence in physical science: when values are related through simple fractions, there is a good possibility that the values stem from a common source.

This example is written in GT. M and exploits and illustrates many features of MUMPS.

To take another example, the minimal pair tip and dip illustrates that in English, and belong to separate phonemes, and ; since these two words have different meanings, English speakers must be conscious of the distinction between the two sounds.

This example nicely illustrates the distinction between constants, parameters, and variables.

This example also illustrates the essential difference between real-time computations and other computations: if the tournament chess program does not make a decision about its next move in its allotted time it loses the game — i. e., it fails as a real-time computation — while in the other scenario, meeting the deadline is assumed not to be necessary.

Whilst the following example illustrates how a desired sound might be achieved in practice, only the final three stages are really subtractive synthesis and the early stages could be considered to be a form of additive synthesis.

As this example illustrates, to say that a definition is " vague " is not necessarily a criticism.

He illustrates this with the example of the generalization " All sodium salts burn yellow ", and asks us to consider the observation which occurs when somebody holds a piece of pure ice in a colorless flame which does not turn yellow:

Androgen insensitivity syndrome ( AIS ) is an example of a DSD that also illustrates that female development is the default for humans.

: The blue picture illustrates an example of fitting the exponential distribution to ranked annually maximum one-day rainfalls showing also the 90 % confidence belt based on the binomial distribution.

The following Java ( SE 6 ) program illustrates the ' shape ' example given below and will output:

# A transformer coupling two circuits may be considered a source of emf for one of the circuits, just as if it were caused by an electrical generator ; this example illustrates the origin of the term " transformer emf ".

The following example illustrates the LZW algorithm in action, showing the status of the output and the dictionary at every stage, both in encoding and decoding the data.

As the example illustrates, the subarrays that Shellsort operates on are initially short ; later they are longer but almost ordered.

This example illustrates the C shell's more conventional expression operators and syntax.

The example of ZFC illustrates the importance of distinguishing the metamathematics of a formal system from the statements of the formal system itself.

A simple example of a grid street pattern ( see diagram ) illustrates the progressive reduction in total street length ( the sum of all individual street lengths ) and the corresponding increase in block length.

The example is written in pseudo C. It illustrates all of the I²C features described before ( clock stretching, arbitration, start / stop bit, ack / nack )

It illustrates Messiaen's use of additive rhythms – in this example the addition of unpaired semiquavers ( sixteenth note s ) to an underlying quaver ( eighth note ) pulse and the lengthening of the final quaver by addition of a dotted note | dot.

Rebus example ( Earth, Nurse ) Answer: Athens Metagram example ( Well, Ball, Walk ) Answer: Wall

For example, a similar tale is recorded in Arabian Nights where Harun al-Rashid plays the same trick on a man he finds sleeping in an alley, and in De Rebus Burgundicis by the Dutch historian Pontus de Heuiter, where the trick is performed by Philip the Good, i. e. Philip III, Duke of Burgundy.

In fact, some -- Anzilotti is the principle example -- went so far as to say that all international law could be traced to the single legal norm, Pacta sunt Servanda.

Scots common law differs in that the use of precedents is subject to the courts ' seeking to discover the principle that justifies a law rather than searching for an example as a precedent, and principles of natural justice and fairness have always played a role in Scots Law.

Compensation was based on the principle of substitution which might include material ( for example, cattle, slave ) compensation, exchange of brides or grooms, or payment of the blood debt.

( The system is not limited to alphabets in the strict technical sense ; languages that use a syllabary or abugida, for example Cherokee, can use the same ordering principle provided there is a set ordering for the symbols used.

Siting weapons this way is an example of the application of the defensive principle of mutual support.

This principle can be extended to engineer a grating with a structure such that it will produce any diffraction pattern desired ; the hologram on a credit card is an example.

To understand the application of the organic principle to questions of value, it is perhaps best to consider Moore ’ s primary example, that of a consciousness experiencing a beautiful object.

Greatest common divisors can in principle be computed by determining the prime factorizations of the two numbers and comparing factors, as in the following example: to compute gcd ( 18, 84 ), we find the prime factorizations 18 = 2 · 3 < sup > 2 </ sup > and 84 = 2 < sup > 2 </ sup > · 3 · 7 and notice that the " overlap " of the two expressions is 2 · 3 ; so gcd ( 18, 84 ) = 6.

A simple example of the operation of the principle can be seen when two rooms are connected by an open doorway and a sound is produced in a remote corner of one of them.

A classic example of the ideo-motor principle in action is the so-called " Chevreul pendulum " ( named after Michel Eugène Chevreul ).

And, as with previous example, the same principle applies when more than two resistors are connected, provided that all are in parallel or all are in series.

A blatant example of the failure to adhere to the principle of least privilege is logging into Windows as user Administrator to read Email and surf the Web.

It also relates to scriptures of other religions by abrogation, explanation, affirming or reformation-an example of progressive revelation as a principle of the religion.

Some widely-used methods of conventional statistics, for example many significance tests, are not consistent with the likelihood principle.

For example, there are explanations based directly on Newton ’ s laws of motion and explanations based on Bernoulli ’ s principle.

While data reduction ( compression, be it lossy or lossless ) is a main goal of transform coding, it also allows other goals: one may represent data more accurately for the original amount of space – for example, in principle, if one starts with an analog or high-resolution digital master, an MP3 file of a given size should provide a better representation than a raw uncompressed audio in WAV or AIFF file of the same size.

In principle, the atomic mass situation is analogous to the above example of Roman mass units.

This aspect of electromagnetic induction is the operating principle behind many electric generators: for example, a rotating bar magnet creates a changing magnetic field, which in turn generates an electric field in a nearby wire.

For example, in his 1997 book Numerology: Or What Pythagoras Wrought, mathematician Underwood Dudley uses the term to discuss practitioners of the Elliott wave principle of stock market analysis.

The most important example is benzene, the structure of which was formulated by Kekulé who first proposed the delocalization or resonance principle for explaining its structure.

He then argues that this principle entails radical conclusions — for example, that affluent people are very immoral if they do not give up some luxury goods to donate the money for famine relief.

Joseph Priestley, for example, in referring to the reaction of steam on iron, whilst fully acknowledging that the iron gains weight as it binds with oxygen to form a calx, iron oxide, iron also loses “ the basis of inflammable air ( hydrogen ), and this is the substance or principle, to which we give the name phlogiston .” Following Lavoisier ’ s description of oxygen as the oxidizing principle ( hence the name oxygen: oxus

An example is the neutral helium atom, which has two bound electrons, both of which can occupy the lowest-energy ( 1s ) states by acquiring opposite spin ; as spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli principle.

In April 1940, Popular Science showed an example of a radar unit using the Watson-Watt patent in an article on air defence, but not knowing that the U. S. Army and U. S. Navy were working on radars with the same principle, stated under the illustration, " This is not U. S. Army equipment.