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Page "Principal ideal domain" ¶ 18
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example and principal
The promenade, for example, continues to take place on the Chahar Bagh, a mile-long garden of plane and poplar trees that now serves as the city's principal street.
Those who revolted unsuccessfully during the war saw the example made of the Mytilenians, the principal people on Lesbos.
For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">
For example, it is thought that ammonites were the principal food of mosasaurs, a group of giant marine reptiles that became extinct at the boundary .< ref name =" Kauffman ">
and this is its Cauchy principal value, which is zero, but we could also take ( 1 ) to mean, for example,
The principal types of graphemes are logograms, which represent words or morphemes ( for example, Chinese characters, or the ampersand & representing the English word and ; also Arabic numerals ); syllabic characters, representing syllables ( as in Japanese kana ); and alphabetic letters, corresponding roughly to phonemes ( see next section ).
Josiah Wedgwood, for example, is described by some commentators as being one of five " principal members " of the society, while others consider that he " cannot be recognized as full member " at all.
* Latin Rite, the principal rite within the Roman Catholic Church as distinguished, for example, from Orthodox Christianity
The word foo is the principal example.
Some ensembles, such as the Orpheus Chamber Orchestra, based in New York City, have had more success, although decisions are likely to be deferred to some sense of leadership within the ensemble ( for example, the principal wind and string players ).
For example, by means of certificates, we can create what is called a " compound principal "-one such principal could be " Alice and Bob have Revoke Authority ".
* Z: the ring of all polynomials with integer coefficients --- it is not principal because the ideal generated by 2 and X is an example of an ideal that cannot be generated by a single polynomial.
For example, the principal square root of 9 is 3, denoted, because and 3 is non-negative.
For example, Buddhism encourages the impartial investigation of nature ( an activity referred to as Dhamma-Vicaya in the Pali Canon )— the principal object of study being oneself.
An example of receiver-type value is ' market value ', or ' willingness to pay ', the principal method of accounting used in neo-classical economics.
This is similar ( but more categorical ) to concepts in group theory or module theory, where a given decomposition of an object into a direct sum is " not natural ", or rather " not unique ", as automorphisms exist that do not preserve the direct sum decomposition – see Structure theorem for finitely generated modules over a principal ideal domain # Uniqueness for example.
For example, the school principal in the film Sixteen Candles ( 1984 ) is an interpretation of the Pantalone character, for his goal is to keep the two main characters from being together and to maintain some type of control of his school.
** Some books, films, video games, and TV shows have one or more eponymous principal characters: Robinson Crusoe, Moll Flanders, Emma, the Harry Potter series, The Legend of Zelda series, I Love Lucy, for example.
The firmness of straw for example, is due to the presence in it of silica, the principal constituent of sand and flints.
The principal mountain passes lie 1800 to above the sea, for example Muztagh pass at, Mongol pass at, Tenghyz pass at and Obo-sarym pass at.
He followed the example of Leo XIII by promoting Thomas Aquinas and Thomism as the principal philosophical method to be taught in Catholic institutions.
A principal example is amber, which is a form of fossilized resin.
For example, Section 302 requires that the company's " principal officers " ( typically the Chief Executive Officer and Chief Financial Officer ) certify and approve the integrity of their company financial reports quarterly.

example and ideal
For example, they might interpret a tomato as a vegetable — according to the English definition of tomato — even though the ideal Blissymbol of vegetable was restricted by Bliss to just vegetables growing underground.
For example, the same techniques used to model ideal gases can be applied to model the behavior of a hard sphere colloidal suspension.
For example, to synthesize iso-octane ( the 8-carbon ideal gasoline ) from the unfunctionalized alkane isobutane ( a 4-carbon gas ), isobutane is first dehydrogenated into isobutene.
* ( for ideal mixtures ) is the concentration in dimensions of of substance ) length < sup >− 3 </ sup >, example
Plato's theory of forms or " ideas " describes ideal forms ( for example the platonic solids in geometry or abstracts like Goodness and Justice ), as universals existing independently of any particular instance.
Parabolic reflectors resolve this, allowing incoming parallel rays ( for example, light from a distant star ) to be focused to a small spot ; almost an ideal point.
For example, the direct sum of the R < sub > i </ sub > form an ideal not contained in any such A, but the axiom of choice gives that it is contained in some maximal ideal which is a fortiori prime.
Silver's catalytic properties make it ideal for use as a catalyst in oxidation reactions, for example, the production of formaldehyde from methanol and air by means of silver screens or crystallites containing a minimum 99. 95 weight-percent silver.
For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall.
For example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum.
For example, one mol of an ideal gas occupies 22. 414 L at 0 ° C and 1 atmosphere whereas carbon dioxide has a molar volume of 22. 259 L under those same conditions.
Instead, the ruler needs only to make himself respectful, and the people will be induced and enlightened by his superior virtues to follow his example – an ideal known as wuwei.
For example, the sampling process in any standard image sensor ( CCD or CMOS camera ) is relatively far from the ideal sampling which would measure the image intensity at a single point.
For example, verisimilitude defined that characters were to based upon the ideal of a type, versus what might be considered realistic.
For example, if 50 % of a system's user base will be accessing the system via a 56K modem connection and the other half over a T1, then the load injectors ( computers that simulate real users ) should either inject load over the same mix of connections ( ideal ) or simulate the network latency of such connections, following the same user profile.
In contrast, the ideal sanity test exercises the smallest subset of application functions needed to determine whether the application logic is generally functional and correct ( for example, an interest rate calculation for a financial application ).
Resistive Ballooning Mode, similar to ideal ballooning, but with finite resistivity taken into consideration, provides another example of a resistive instability.
The true period of an ideal simple gravity pendulum can be written in several different forms ( see Pendulum ( mathematics ) ), one example being the infinite series:
For example, conducting multiple instrument approaches in the actual aircraft may require significant time spent repositioning the aircraft, while in a simulation, as soon as one approach has been completed, the instructor can immediately preposition the simulated aircraft to an ideal ( or less than ideal ) location from which to begin the next approach.
For example, given an ideal gas mixture of nitrogen ( N < sub > 2 </ sub >), hydrogen ( H < sub > 2 </ sub >) and ammonia ( NH < sub > 3 </ sub >):

0.894 seconds.