Bra-ket notation splits this inner product ( also called a " bracket ") into two pieces, the " bra " and the " ket ":

Eiffel Software, " The Eiffel Compiler " tecomp and Eiffel-library-developer Gobo have committed to implementing the standard ; Eiffel Software's EiffelStudio 6. 1 and " The Eiffel Compiler " tecomp implement some of the major new mechanisms — in particular, inline agents, assigner commands, bracket notation, non-conforming inheritance, and attached types.

This is analogous to the slash notation (/ a /, / b /) used for phonemes, and the square bracket notation used for phonetic transcriptions (, ).

This bracket notation expressing the error is explained in the article on measurement uncertainty.

( See Interval ( mathematics ) for an explanation of the bracket and parenthesis set notation.

* The left-hand portion,, of a bracket in bra-ket notation, a standard notation used in quantum mechanics

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

( The bracket notation conflicts with a common notation for the Gaussian coefficients.

The Iverson bracket allows the equivalent notation,, to be used instead of

Because of this the Jacobi identity is often expressed using Lie bracket notation:

In transcribing to modern notation, where no compound graphs as ligatures exist, editors usually indicate by a hook, a bracket / brace, or ( less often in polyphonic music ) a slur / phrase mark those notes that were combined into a ligature.

It can even be used as a notation to indicate a group ( bracket smaller to parenthesis ):

For simplicity consider a two-level atomic system with ground and excited states and, respectively ( using the Dirac bracket notation ).

* The character can also occur inside a terminating square bracket pattern, so that matches both "" and "".

However, that figure was reduced in later years when it was determined the survey also included people who play NCAA bracket pools, which are not exactly fantasy sports ( where you pick individual players ).

That spring, according to Mullis, he was driving his vehicle late one night with his girlfriend, who was also a chemist at Cetus, when he had the idea to use a pair of primers to bracket the desired DNA sequence and to copy it using DNA polymerase, a technique which would allow a small strand of DNA to be copied almost an infinite number of times.

NBC's Brian Williams, who attended a dinner with Reagan in mid-2008, recalled, " Mrs. Reagan's vision isn't what it always was so she was taking very halting steps as a lot of folks her age do ... t is so important for folks in her age bracket and in her bracket of life to remain upright and captain of their own ship.

Some accounts of Nostradamus's life state that he was afraid of being persecuted for heresy by the Inquisition, but neither prophecy nor astrology fell in this bracket, and he would have been in danger only if he had practiced magic to support them.

In use the pendulum was hung from a bracket on the wall, supported by the edges of the knife blades resting on flat agate plates.

To use, the pendulum was hung from a bracket on a wall, with the knife blade pivots supported on two small horizontal agate plates, in front of a precision pendulum clock to time the period.

The Unimog was designed with equal-sized wheels, a mounting bracket in front, a hitch in the rear, and loading space in the center.

The result is this masterful work suffers from broken bracket feet, which was often attached with a glue block which ran perpendicular to the base pieces.

The first was the tax structure in the UK: capital gains were taxed at 40 %, earned income was taxed in the top bracket at 83 %, and investment income in the top bracket at 98 %.

Ozzie Nelson was a Rutgers alumnus and keen on college education, but eighteen-year-old Ricky was already in the 93-percent income-tax bracket and saw no reason to attend.

* Animal gut was used to make the cord lines in longcase clocks and for fusee movements in bracket clocks, but may be replaced by metal wire.

A similar pair of pinnacles top the main gable, flanking a window of unusual design ; a bracket projects from the lower lobe to support a large statue ( no longer present ), possibly of the Virgin Mary, to whom the priory was dedicated.

This alternate arrangement was created as a way to get the frame clamp of the derailleur closer to the bottom bracket to be able to clear larger suspension components and allow different frame shapes.

This was understood to allude to the iron bracket of a lamppost at the corner of the Place de Grève and the Rue de la Vannerie, often used by rioters as a makeshift gallows for anti-revolutionaries and those accused of profiteering.

The decorative flourish which was often placed by heraldic artists under the feet, hooves or paws of supporters, chiefly in the 19th century, was disparagingly known by some as the " gas bracket ," although this term never had any official currency ; the only case in which something similar was ever actually mentioned in the blazon was the " arabesque " vert on which the whale supporters of Zaanstad, Noord Holland, the Netherlands, balance.

* Certain companies such as Cannondale ( BB30 open standard, introduced in 2000 ) have made their own unique bottom bracket standards requiring changes in the bottom bracket shell of the bicycle frame in order to accommodate the bottom bracket / crank design.

In late 2006, Campagnolo introduced an outboard bearing design called Ultra-Torque < sup > TM </ sub >, which has each crank arm permanently attached to halves of the axle ( called semi-axles ) which then join in the middle of the bottom bracket with a Hirth joint and a bolt.

" The Beatles ' large earnings placed them in the top tax bracket in the United Kingdom, liable to a 95 % supertax introduced by Harold Wilson's Labour government ( hence the lyrics " There's one for you, nineteen for me ").

It was not age-limited to young men under the age of 20 until 1896, when the OHA introduced the ' intermediate '- level play bracket.

He appears to have introduced the small bracket between the front rail of the seat and the top of the chair leg, or at all events to have made such constant use of it that it has come to be regarded as characteristic of his work.

For Japan, the cars were literally narrowed by a few millimetres on arrival in the country in order that they fit into a lower tax bracket determined by exterior dimensions – this was done by bending the wheel arches inwards.

In the ranking of universities from all over the world, “ World University ranking 2009 ”, Ca ' Foscari University of Venice is one of the few Italian universities mentioned, confirming its placement in the 500 bracket.

Many voters do not perceive the effects of bracket creep, and so the government may prefer to adjust tax brackets manually once every few years-in effect restoring the real tax rates to their approximate pre-inflation levels, but in a way that gives the government the appearance that they are cutting taxes.

The diesel versions, however, have little or no competition since few diesel cars exist in the Indica's price bracket.

For tournaments too large to properly accommodate all wrestlers, some host schools will implement a carry-over bracket system in order to finish a tournament within the standard time restrictions of a few days.

* Hoppers ( due to the unique Cyclone-Feed System, very few hoppers stock hopper, Ricochet hopper, TAC-Cap loader, X-7 Marker Hopper, 240 round ammo box version, and a 450 Round Offset Hopper are available ); Q-Loader also manufactures a Q-Loader System for the A-5, although it typically requires the right receiver to be milled, unless a custom-manufactured attachment bracket is used.

In the QS World University ranking 2010, the University of Trento is one of the few Italian universities mentioned, confirming its placement in the 401 – 500 bracket, while charting in the 201 – 300 bracket in the Engineering, Natural Sciences and Social Sciences subject rankings.